U.S. patent number 3,648,035 [Application Number 04/829,283] was granted by the patent office on 1972-03-07 for system and method for optimizing processor or equipment profit.
This patent grant is currently assigned to Industrial Nucleonics Corporation. Invention is credited to Dwight L. Hart, Henry T. Jaggers, Charles S. Walker.
United States Patent |
3,648,035 |
Hart , et al. |
March 7, 1972 |
SYSTEM AND METHOD FOR OPTIMIZING PROCESSOR OR EQUIPMENT PROFIT
Abstract
In the embodiment specifically described and illustrated, there
is disclosed a system and method for maximizing the profit of a
tobacco manufacturing process by computing a measure of the process
spread, which can be calculated either in response to standard
deviation or fraction defective. In response to the calculation of
process spread, the average weight of cigarettes manufactured is
controlled to maximize profit so that average weight is minimized
and variable percentage of the cigarettes weigh less than a limit
value. Those cigarettes weighing less than the limit value are
identified and the tobacco therein is reused.
Inventors: |
Hart; Dwight L. (Worthington,
OH), Jaggers; Henry T. (Columbus, OH), Walker; Charles
S. (Columbus, OH) |
Assignee: |
Industrial Nucleonics
Corporation (N/A)
|
Family
ID: |
25254071 |
Appl.
No.: |
04/829,283 |
Filed: |
June 2, 1969 |
Current U.S.
Class: |
700/34; 177/50;
131/905; 250/358.1; 700/36; 700/122; 702/173 |
Current CPC
Class: |
G05B
13/042 (20130101); G05B 15/02 (20130101); G07C
3/14 (20130101); A24C 5/3412 (20130101); Y10S
131/905 (20130101) |
Current International
Class: |
A24C
5/34 (20060101); A24C 5/32 (20060101); G05B
13/04 (20060101); G05B 15/02 (20060101); G07C
3/00 (20060101); G07C 3/14 (20060101); G06g
007/66 (); G05b 013/02 () |
Field of
Search: |
;235/150,150.1,151,151.1,151.13,151.33 ;250/83.3D ;131/21B |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Botz; Eugene G.
Assistant Examiner: Gruber; Felix D.
Claims
We claim:
1. A system for controlling the average value of a processor or
equipment output to achieve maximum economic profit, said output
having a variable spread of values, comprising gauge means for
deriving a response indicative of the value of a property of the
processor or equipment output, means responsive to the gauge means
response for deriving a first signal indicative of the spread of
values of the property, means responsive to the first signal for
deriving a second signal indicative of the average value of the
property which maximizes profit of the processor or equipment for
the particular spread of values determined by said first signal
deriving means, said second signal deriving means selecting said
average value represented by said second signal in accordance with
said spread so that a significant percentage of the processor or
equipment output will have a value which renders said percentage
undesirable for its intended use, said percentage increasing for
larger spreads, said second signal deriving means continuing to
increase said percentage so long as the economic profit is thereby
increased, and decreasing said percentage when the economic profit
decreases due to the increasing counteracting economic loss caused
by the increase in said undesirable percentage, and means
responsive to the second signal for activating the processor or
equipment so that the average value of the property approaches the
average value determined by said second signal deriving means.
2. The system of claim 1 wherein the first signal deriving means
includes means for computing standard deviation as a measure of the
spread of values.
3. The system of claim 1 wherein the first signal deriving means
includes means for computing the spread of values as a ratio of the
property values outside a limit value to the total property values
for a fixed interval.
4. The system of claim 1 wherein the first signal deriving means
includes means for computing the spread of values as a ratio of the
property values outside a limit value to the total property values
for a fixed interval which is a function of time.
5. The system of claim 1 wherein the first signal deriving means
includes means for computing the spread of values as a ratio of the
property values outside a limit value to the total property values
for a fixed interval which is a function of output quantity.
6. The system of claim 3 wherein said computing means includes
means for deriving a binary signal in response to the gauge means
response having a value outside the limit value.
7. The system of claim 6 wherein said binary signal deriving means
includes an integrator responsive to a constant voltage indicative
of the limit value linearly combined with the gauge means
response.
8. The system of claim 1 wherein the first signal deriving means
includes means for computing the spread of values as a ratio of the
property values outside a limit value to the total property values
for a fixed interval which is a function of time, and wherein said
computing means includes means responsive to the number of binary
signals derived in a fixed time interval, said binary signals
derived in response to the gauge means response having a value
outside the limit value.
9. The system of claim 6 wherein the fixed interval is a function
of the output quantity, and said means for deriving the second
signal is responsive to the number of binary signals derived for a
fixed output quantity.
10. The system of claim 1 wherein the second signal deriving means
includes means for deriving said second signal as an output
indicative of the deviation of said average value from a reference
value for the property.
11. The system of claim 10 wherein the second signal deriving means
further includes means for combining the first signal with a
constant amplitude signal in accordance with:
K.sub.1 .times.S+K.sub.2
where:
K.sub.1 is constant proportionality factor determined by economic
properties of the processor or equipment,
S is the amplitude of the first signal, and
K.sub.2 is the amplitude of the constant amplitude signal,
determined by economic properties of the processor or
equipment,
to derive an indication of average value deviation from the limit
value.
12. The system of claim 10 further including means responsive to
the first signal and the output of the second signal deriving means
for deriving another average value signal in response to a
previously derived average value signal.
13. The system of claim 12 further including means responsive to
the second signal for deriving another signal indicative of a
previously derived spread indicating signal, and means for
determining the deviation between the previously derived spread
indicating signal and the spread indicated by the first signal.
14. The system of claim 1 wherein said activating means comprises
means for activating said processor or equipment so that the
average value of the property substantially equals the average
value determined by said second signal deriving means.
15. A system for controlling the average weight of cigarettes
during manufacture by a cigarette making equipment comprising gauge
means for deriving a response indicative of the weight of a
predetermined length of cigarette rod, means responsive to said
gauge means for deriving a first signal indicative of the spread of
weights in said lengths, means responsive to the first signal for
deriving a second signal indicative of the average weight for said
predetermined lengths which maximizes profit of the equipment for
the particular spread of weights determined by said first signal
deriving means, said second signal deriving means selecting said
average weight represented by said second signal in accordance with
said spread so that a significant percentage of the cigarette rod
predetermined lengths has a weight less than a limit weight, said
percentage increasing for larger spreads, said second signal
deriving means continuing to increase said percentage so long as
the economic profit is thereby increased, and decreasing said
percentage when the economic profit decreases due to the increasing
counteracting economic loss caused by the increase in said
percentage having a weight less than said limit weight, and means
responsive to the second signal for activating the equipment so
that the average weight for the predetermined lengths approaches
the average weight determined by said second signal deriving
means.
16. The system of claim 15 including means for combining the spread
indicating signal with a constant signal to derive a third signal
indicative of deviation of said average weight from the lower
limit, memory means responsive to said third signal, means
responsive to said memory means for deriving a feedback signal
indicative of a previously determined value of said third signal,
and means for comparing the third signal derived by said combining
means with the previously determined value of said third signal to
modify the average value.
17. The system of claim 15 including memory means for deriving a
third signal indicative of a previous value of the second signal,
means responsive to said third signal for comparing the previous
value of the second signal with the second signal derived by said
second signal deriving means to modify the average value.
18. The system of claim 15 including memory means for deriving a
third signal indicative of a previous value of the second signal,
means responsive to said third signal for comparing the previous
value of the second signal with the second signal derived by said
second signal deriving means to modify the average value.
19. The system of claim 18 wherein the memory means derives the
second signal that indicates average weight.
20. A system for controlling the average value of a property of
discrete articles produced by a processor or equipment to achieve
maximum profit, said property having an established limit value and
an initial average value, comprising means responsive to said
property of the articles for deriving a first signal indicative of
the fraction thereof that is defective, means responsive to the
first signal for deriving a second signal indicative of a new
average value of the property which maximizes profit of the
processor or equipment, said new average value being selected by
said second signal deriving means so that a significant percentage
of the processor or equipment output is defective, said percentage
increasing for larger indications of fraction defective, said
second signal deriving means continuing to increase said percentage
so long as the economic profit is thereby increased, and decreasing
said percentage when the economic profit decreases due to the
increasing counteracting economic loss caused by the increase in
said fraction defective, and means responsive to the second signal
for activating the processor or equipment so that the average value
of the property substantially equals the new average value
determined by said second signal deriving means.
21. A system for controlling the average weight of cigarettes
during manufacture by cigarette-making equipment, said weight
having a predetermined limit value and an initial average value,
comprising means responsive to the cigarettes for deriving a first
signal indicative of the percentage thereof that is defective,
means responsive to the first signal for deriving a second signal
indicate of a new average weight for the cigarettes which maximizes
profit of the equipment, said new average weight being selected by
said second signal deriving means so that a significant percentage
of the cigarettes has a weight less than said limit value, said
significant percentage increasing for larger defective percentages,
said second signal deriving means continuing to increase said
percentage so long as the economic profit is thereby increased, and
decreasing said percentage when the economic profit decreases due
to the increasing counteracting economic loss caused by the
increase in said defective percentage, and means responsive to the
second signal for activating the equipment so that the average
weight of the cigarettes approaches the average weight determined
by said second signal deriving means.
22. The system of claim 21 wherein said second signal deriving
means includes means for adding a constant amplitude signal to
another signal directly proportional to said first signal.
23. A system for controlling the average weight of cigarettes
during manufacture by cigarette-making equipment, said weight
having a predetermined limit value and an initial average value,
said equipment including means for separating defective cigarettes
from acceptable cigarettes, means for reclaiming the defective
cigarettes and means for feeding the reclaimed cigarettes back to
an input of the equipment, said system comprising means for
detecting defective cigarettes being produced by said equipment,
means responsive to said detecting means for activating said
separating means in synchronism with the passage of defective
cigarettes into a zone defining said separating means, means
responsive to said detecting means for deriving a first signal
indicative of the percentage of cigarettes that is defective, means
responsive to the first signal for deriving a second signal
indicative of a new average weight for the cigarettes which
maximizes profit of the equipment, said new average weight being
selected by said second signal deriving means so that a significant
percentage of the cigarettes has a weight less than said limit
value, said percentage increasing for larger defective percentages,
said second signal deriving means continuing to increase said
percentage so long as the economic profit is thereby increased, and
decreasing said percentage when the economic profit decreases due
to the increasing counteracting economic loss caused by the
increase in said defective percentage, and means responsive to the
second signal for activating the equipment so that the average
weight of the cigarettes substantially equals the average weight
determined by said second signal deriving means.
24. A system for controlling the average value of a processor
output to achieve maximum economic profit, said output having a
variable spread of values, said processor including means for
separating defective output from an acceptable output and means for
reclaiming the defective output for reuse comprising gauge means
for deriving a response indicative of the value of a property of
the processor or equipment, means responsive to the gauge means
response for deriving a first signal indicative of the spread of
the values of the property, means responsive to the first signal
for deriving a second signal indicative of the average value of the
property which maximizes profit of the processor or equipment for
the particular spread of values determined by said first signal
deriving means, said average value and spread being such that a
significant percentage of the processor or equipment output has a
value outside of a limit value, said percentage increasing for
larger spreads, means responsive to the second signal for
activating the processor or equipment so that the average value of
the property substantially equals the average value determined by
said second signal deriving means, means responsive to said gauge
means for deriving an indication of which portion of the output is
defective, and means responsive to said defective indication means
for activating said separating means in synchronism with defective
output being in a zone defined by said separating means.
25. A system for determining the amount by which a target value
should be displaced from a reference target to achieve maximum
profit for a processor deriving an output having a spread of values
about an average value, said processor output being measured by
gauge means deriving a response having a predetermined value in
response to the output having a value equal to the reference target
and deviating from the predetermined value as the output value
deviates from the reference target, comprising means responsive to
the gauge response for deriving a signal indicative of the spread
of values, and means responsive to said signal for deriving an
indication of the target deviation from the reference target that
maximizes the economic profit of the processor, said target
deviation being displaced by larger amounts from the reference
target for small spreads relative to large spreads, said target
deviation being less than a deviation between the reference target
and a limit value beyond which the output is considered defective,
the target deviation and spread of values being related such that
for increasing spreads a greater percentage of the output has a
value beyond the limit value, said indication deriving means
including means for deriving said target indication as a percentage
of said reference target.
26. The system of claim 25, wherein said indication deriving means
includes means for deriving another signal indicative of the
displacement between the lower limit and the target deviation from
the reference target as a percentage of the reference target.
27. The system of claim 26 wherein said another deriving means
includes means for combining the spread indicating signal with a
second signal.
28. A control system for a processing apparatus using a costly
input quantity for forming a product with a variable property
dependent on said input quantity, said apparatus including means
for adjusting the value of said variable property and producing
concomitant changes in the amount of said input quantity used in
forming said product, said control system comprising
gauging means for producing a succession of signals indicative of
measured values of said property in successive portions of said
product,
means for producing a signal indicative of a limiting value for
said measured values, said limiting value being so selected that
portions of said product having measured property values outside of
the limiting value are deemed undesirable for their intended use,
other portions of said product being deemed desirable for said
use,
means providing a signal indicative of a temporary target value for
said measured values,
means responsive to said measured value and said target value
signals for controlling said adjusting means for said processing
apparatus to regulate the average value of said measured values,
said average value determining the cost of forming the product
including both the desirable and undesirable portions thereof,
means responsive to said measured value signals for deriving a
statistical quantity signal indicative of the spread of said
measured values of said property,
means responsive to one of said target and statistical quantity
signals for deriving a signal functionally related to an optimum
value for the other of said target and statistical quantity signals
in accordance with a statistically derived function dependent on
said limiting value and relating the cost of using said input
quantity as represented by said target value to the cost of
producing an amount of undesirable material which is functionally
related to said statistical quantity signal so as to minimize the
cost of producing the desirable portion of said product, and
means responsive to said optimum value related signal and the
existing value of said other of said target and statistical
quantity signals for producing a change in said temporary target
value signal whereby said controlling means regulates said
processing means to produce said product with a changed average
value for said measured values, said change causing said other of
said target and statistical quantity values to approach said
optimum value whereby the cost of producing said acceptable portion
of said product is minimized.
29. A control system as in claim 28 wherein said statistical
quantity signal deriving means comprises means responsive to said
measured value signals and said limiting value signal for deriving
a reject portion signal, said reject portion signal being
indicative of the spread of said measured values as a function of
said limiting value and said target.
30. A control system as in claim 28 wherein said statistical
quantity signal deriving means comprises means for computing the
variance of said measured values, and
wherein said optimum value signal deriving means comprises means
responsive to said variance for deriving an optimum value for said
target value.
31. A control system for a processing apparatus using a costly
input quantity for forming a product with a variable property
dependent on said input quantity, said apparatus including means
for adjusting the value of said variable property and producing
concomitant changes in the amount of said input quantity used in
forming said product, said control system comprising
gauging means for producing a succession of signals indicative of
measured values of said property in successive portions of said
product,
means for producing a signal indicative of a limiting value for
said measured values, said limiting value being so selected that
portions of said product having measured property values outside of
the limiting value are deemed undesirable for their intended use,
other portions of said product being deemed desirable for said
use,
means responsive to said measured value signals and said limiting
value signal for deriving a reject portion signal indicative of the
portion of said product which is undesirable, said reject portion
signal being further indicative of the cost of producing the
undesirable portion of the product,
means providing a signal indicative of a temporary target value for
said measured values,
means responsive to said measured value signals and said target
value signal for controlling said adjusting means for said
processing apparatus to regulate the average value of said measured
values, said average value determining the cost of forming the
product including both the desirable and undesirable portions
thereof,
means responsive to one of said target value and reject portion
signals for deriving a signal functionally related to an optimum
value for the other of said target and reject portion values in
accordance with a statistically function dependent on said limiting
value and relating the cost of using said amount of said input
quantity as represented by said target value to the cost of
producing said undesirable portion of the product as represented by
said reject portion signal so as to minimize the cost of producing
the desirable portion of the product, and
means responsive to said optimum value related signal and the
existing value of said other of said target and reject portion
signals for producing a change in said temporary target value
whereby said controlling means regulates said processing means to
produce said product with a changed average value for said measured
values, said change causing said other of said target and reject
portion values to approach said optimum value whereby the cost of
producing said desirable portion of said product is minimized.
32. A control system for a processing apparatus using a costly
input quantity for forming a product with a variable property
dependent on said input quantity, said apparatus including means
for adjusting the value of said variable property and producing
concomitant changes in the amount of said input quantity used in
forming said product, said control system being adapted to regulate
said processing apparatus so as to produce a major portion of said
product deemed desirable for its intended use and a minor portion
deemed undesirable for said use, said control system comprising
gauging means for producing a signal indicative of the measured
value of said property,
means providing a signal indicative of a temporary target value for
said measured value,
means responsive to said measured value and said target value
signals for controlling said adjusting means for said processing
apparatus to regulate the average value of said measured values,
said average value determining the cost of forming the product
including both the desirable and undesirable portions thereof,
means responsive to said measured value signal for deriving a
statistical quantity signal indicative of the spread of said
measured values of said property,
means responsive to one of said target and statistical quantity
signals for deriving a signal functionally related to an optimum
value for the other of said target and statistical quantity signals
in accordance with a statistically derived function relating the
cost of using said input quantity as represented by said target
value to the cost of producing an amount of undesirable material
which is functionally related to said statistical quantity signal
so as to minimize the cost of producing said product,
means responsive to said optimum value related signal and the
existing value of said other of said target and statistical
quantity signals for producing a change in said temporary target
value signal whereby said controlling means regulates said
processing means to produce said product with a changed average
value for said measured values, said change causing said other of
said target and statistical quantity values to approach said
optimum value whereby the cost of producing said product is
minimized.
33. A control system as in claim 32 wherein said statistical
quantity signal deriving means comprises means for computing the
variance of said measured value signal, and
wherein said optimum value signal deriving means comprises means
responsive to said variance for deriving an optimum value for said
target value.
34. A system for controlling the average weight of cigarettes
during manufacture by a cigarette making equipment comprising gauge
means for deriving a response indicative of the weight of a
predetermined length of cigarette rod, means responsive to said
gauge means for deriving a first signal indicative of the spread of
weights of said lengths, means responsive to the first signal for
deriving a second signal indicative of the average weight for said
predetermined lengths which maximizes profit of the equipment for
the particular spread of weights determined by said first signal
deriving means, said second signal deriving means selecting said
average weight represented by said second signal in accordance with
said spread so that some of the cigarette rod predetermined lengths
have a weight to cause customer dissatisfaction, the amount of rod
predetermined lengths causing dissatisfaction increasing for larger
spreads, and means responsive to the second signal for activating
the equipment so that the average weight of the predetermined
lengths substantially equals the average weight determined by said
second signal deriving means.
35. The system of claim 34 further including means responsive to
said gauge means for rejecting those portions of the rod lengths
having weights to cause customer dissatisfaction.
36. The system of claim 34 wherein the second signal deriving means
includes a function generator for determining the effect on profit
of the rod lengths causing customer dissatisfaction reaching the
customer as a function of the spread of cigarette weight.
37. A method of controlling the average value of a processor or
equipment output parameter to achieve maximum economic profit
comprising producing a signal indicative of the spread values of
the output parameter, and controlling the average value of the
parameter in response to said signal so that for large spreads the
percentage of output parameter having a value outside a limit for
desirable values is greater than for small spreads, said
controlling operation including adjusting the average value toward
said limit to produce a larger percentage of output parameter
having a value outside said limit so long as the economic profit is
thereby increased, but adjusting the average value away from the
limit when the economic profit decreases due to the increasing
counteracting economic loss caused by the magnitude of said
percentage.
38. The method of claim 37 further including the step of reclaiming
that portion of the output having a value outside of the limit for
desired values.
39. A method for controlling the average value of a processor or
equipment output parameter having a predetermined limit for
desirable values and an initial average value to achieve maximum
economic profit comprising producing signals indicative of said
limit value, said initial average value and the defective
percentage of the output which is outside said desirable limit
value, and controlling the average value of the parameter in
response to said signals so that for large defective percentages
the percentage of output parameter having a value outside a limit
for desirable values is greater than for small defective
percentages, said controlling operation including adjusting the
average value toward said limit to produce a larger percentage of
output parameter having a value outside said limit so long as the
economic profit is thereby increased, but adjusting the average
value away from the limit when the economic profit decreases due to
the increasing counteracting economic loss caused by the magnitude
of said percentage outside said limit.
40. A method of controlling the average value of a property of a
processor or equipment output to achieve maximum economic profit,
said output property having a variable spread of values, comprising
the steps of producing a first signal indicative of the spread of
values of said property, in response to said signal producing
another signal indicative of the average value of the output
property which maximizes profit of the processor or equipment for
the particular spread of values indicated by said first signal,
said average value being determined in accordance with said first
signal so that a significant percentage of the processor or
equipment output has a value outside of a limit value, said
percentage increasing for larger spreads so long as the economic
profit is thereby increased but so that said percentage is
decreased when the economic profit decreases due to the economic
loss due to the increasing percentage of the output having a
property value outside the limit value, and activating the
processor or equipment in response to said another signal so that
the average value of the output approaches the average value
indicated by said another signal for maximizing profit.
41. A method of controlling the average value of a property of
articles produced by a processor or equipment to achieve maximum
profit comprising the steps of deriving a signal indicative of the
spread of values of the property of the articles produced, from
said spread indicative signal producing a computed signal
indicative of an optimum average value for the property based on
the cost of materials utilized in the article manufactured and
affecting said property as well as on the adverse effects of
customer dissatisfaction due to some of the articles having
property values less than a desirable value, said optimum average
indicated by said computed signal minimizing the amount of material
utilized to maximize profit taking into account the increasing cost
of customer dissatisfaction as the number of articles having
property values less than said desirable value is increased, and
controlling the processor or equipment in response to said computed
signal so that the average value of the articles is substantially
the optimum average indicated thereby.
Description
The present invention relates generally to process control systems
and methods and, more particularly, to a system and method for
maximizing the profit of a process in response to a measure of the
spread of values of the processor output.
No equipment or processor can produce an output always having the
same value, no matter how precisely controlled. Instead, the output
of any equipment or processor always covers a range or spread of
values. The spread of values is determined by the degree to which
the processor or equipment can be controlled and its internal
tolerance characteristics, as well as characteristics of inputs.
The spread amongst the output values of a processor or equipment
can often be determined or closely approximated by a function known
as a normal or standard distribution, which defines the well known
bell-shaped curve when plotted on an x-y coordinate basis as
quantity of output values versus output values per se. The normal
distribution bell curve for the output of a processor or equipment
is a bell curve having a maximum value for the quantity of output
values at the average output value.
Processors and equipment that are rigidly controlled, having tight
tolerances and responsive to closely controlled inputs, produce an
output having a narrow spread of values, defined by a distribution
curve having a relatively sharp peak. In contrast, processors and
equipment which are not rigidly controlled, having sloppy
tolerances and inputs subject to wide variations, product outputs
which generally have a wide range or spread of values. A measure of
the spread of values produced by a processor or equipment is a
function known as the standard deviation, which is defined as the
root-means-square value of the deviations of the output from the
average value of the output. If a perfect processor or equipment
existed, all of the output thereof would be equal to the mean and
the standard deviation of the processor or equipment would equal
zero so that the distribution curve would appear as a spike at the
average value. Of course, no such perfect processor or equipment
exists and the output of any actual system or processor exhibits a
spread of values defined by a distribution curve whose
characteristics can be determined for the particular process
involved by ordinary statistical methods.
It is well known that the standard deviation, .sigma., or variance,
V, of the output of a real time processor is defined as:
where:
T = the time interval during which the processor is operating,
F(T) IS THE VARIATION OF THE PROCESSOR OUTPUT EVER THE INTERVAL
T,
f(t) = the average value of f(t) during the interval T, and
t = time.
For processors or equipment producing discrete output elements,
Equation (1) can be rewritten as:
where:
N = the number of discrete elements produced by the processor or
equipment,
i successively equals every integer between 1 and N,
X.sub.i = the value of the ith output element of the processor,
and
X = the average value of the N elements produced by the
processor.
For processors producing an output that conforms with a known
distribution function another measure of the spread or range of
values of the processor output can be found by determining the
ratio or percentage of the quantity of output values on either side
of a particular value of output sufficiently removed from the
average output value. The average value of the processor output
generally cannot be utilized as the particular value because if the
distribution function is not skewed, for example, the fraction of
values relative thereto is always one-half. By selecting the
particular value at a point where a product is considered
defective, a convenient measure of process spread can be attained
by determining the percentage or fraction of the processor or
equipment output that is defective. In other words, a measure of
the standard deviation or spread of values derived by a processor
or equipment can be ascertained by finding the percentage of output
having values less than or greater than a limiting value at which
the processor or equipment output is considered as being
defective.
Mathematically, the fraction defective (F.D.) or 0.01 times reject
percentage of the output of a processor or equipment producing N
discrete elements can be expressed as:
where:
X.sub.i = the value of the ith output element of the processor,
X.sub.L = a lower limit value, below which values of X.sub.i are
considered defective,
i successively assumes every value between 1 and N,
f(X.sub.i -X.sub.L)=0 for X.sub.i .gtoreq.X.sub.L, and
f(X.sub.i -X.sub.L)=1 for X.sub.i <X.sub. L.
If X.sub.L is an upper limit value, above which values of X.sub.i
are considered defective, f(X.sub.i -X.sub.L)=0, for X.sub.i
.ltoreq.X.sub.L and f(X.sub.i -X.sub.L)=1, for X.sub.i
>X.sub.L.
Typically, processors and equipment have been operated in the past
by controlling the processor output to an average value that is
sufficiently removed from a limit value, where a defective product
is not likely to be produced, on the basis of experience of the
processor output spread of values, without reference to the
processor current performance. If an input to a processor or
equipment is generally subject to relatively wide fluctuations but
the processor or equipment can be controlled with a relatively
large degree of stability, the prior art has generally set the
processor or equipment so that is produces an output having an
average value considerably removed from the limit value so that a
minimum number of defective output is produced. If the variation of
the input to such a processor or equipment should decrease over a
relatively long time interval, the average value for the processor
output is usually not changed even though a considerably reduced
portion of defective output will be derived. By maintaining the
processor or equipment output at a constant average value when the
processor input variation range decreases the possible profit which
the processor or equipment can produce is reduced.
For example, in cigarette manufacturing, cigarettes having a
certain minimum weight are considered as acceptable to the
consumer. If the cigarette manufacturer can produce cigarettes
having an average value as close as possible to the lower
acceptable weight limit, he produces a product for which he can
have the greatest profit. In an opposite manner, the paper
manufacturer desires to produce paper having the largest possible
moisture content relative to a limit value at which the paper
becomes discolored. Hence, the paper manufacturer attempts to
produce a product having the greatest moisture without exceeding an
upper limit value. In the prior art, these average values were
generally selected on an a priori basis, based upon previous
experience without particular regard to the spread of values.
While the prior art has generally relied on experience to set a
target value for the average value of a processor or equipment
output, there are some teachings that the average value should be
controlled in response to a measurement of the processor output
spread of values. In particular, systems have been proposed wherein
the average value of a processor output is adjusted so that a
predetermined fraction defective or product output is obtained, or
so that the average value is removed from a limit value according
to a predetermined function of the standard deviation. By
maintaining the processor or equipment output at an average value
to achieve a predetermined fraction defective, the processor or
equipment operates in a more efficient manner to produce a product
having a greater profit margin. The greater profit margin arises
because the average value of the output can be brought closer to a
limit value.
In a theoretically perfect processor or equipment, producing an
output having a standard deviation of zero, the average and limit
values would coincide to provide maximum profit since this would
result in the product having the greatest quantity of acceptable
output for the least amount of input. While the limit and average
values derived from a theoretical processor should coincide to
maximize profits, in a real processor maximum profits are not
actually achieved by translating the average value to the limit
value. If the limit and average values of a real processor
coincide, one-half of the processor or equipment output would be
defective, assuming that the processor output follows a normal
distribution function. Because of the input material cost necessary
to produce the processor or equipment output and the operating cost
of the processor or equipment, it is apparent that an output which
is one-half defective is intolerable. While in many processors, the
output product can be reused, the cost of processor operation and
reclaiming defective product preclude coincidence between the
processor average value and a limit value for maximum economic
profit.
We have found that the average output value of processors or
equipment can be controlled relative to a limit value in response
to the spread of output values to achieve maximum economic profit.
Stated differently, if a processor or equipment produces an output
having a first standard deviation, .sigma..sub.1, to achieve a
maximum profit the processor or equipment should be controlled to
produce an output having an average value which is removed from the
limit value by a certain increment .DELTA.X.sub.1. If, however, the
processor or equipment produces an output having a second value of
standard deviation, .sigma..sub.2, maximum economic profit is
attained by controlling the processor or equipment so that the
average value of its output is removed from the limit value by a
second increment, .DELTA.X.sub.2. We have found that a mathematical
relationship exists between process spread and deviation of average
value from limit value to achieve maximum profit. The mathematical
function is different for each processor or equipment, and in fact
differs between types of different processors or equipment within a
group.
After the average value of the processor or equipment output which
maximizes profit as a function of spread has been determined, the
processor output average value is varied or controlled by adjusting
a target value for the processor output as a deviation from a
nominal target or standard average value, determined on an a priori
basis. In response to the computed deviation a set point or target
for the processor or equipment output is established. Thereby, a
target reset relative to the nominal or standard average value for
the processor or equipment output is provided. The nominal target
and the deviation from target establish a set point or actual
target for a negative feedback type controller for the processor or
equipment output. Once a stabilized condition has been reached, the
negative feedback controller actuates the processor or equipment to
produce an output having an average value coinciding with the set
point.
More specifically according to the present invention the usage of a
costly input quantity such as a raw material input or energy input
is to be reduced to such an extent that a significant percentage of
the processor output will be found defective on a subsequent
inspection. If the average value of the output is controlled to a
value closer to the limit value, an economic gain is realized
because of the reduction in the amount of the costly input quantity
used for a given amount of the product produced. On the other hand,
however, if the average output value is so controlled to a value
closer to the limit value, for a given process spread a greater
percentage of the output will be found to be defective, and an
economic loss results.
The economic loss may occur because the manufacturer will not
permit the defective portion of the product to be placed on the
market, and in this case he incurs the expense of either scrapping
the defective product portion or reclaiming the material used
therein. In another case the manufacturer may segregate the
defective product portion and sell it at a reduced price which is
much less than he could obtain for the regularly acceptable
product. In still another case the manufacturer may allow the
defective product portion to be marketed along with the acceptable
produce, realizing that this will result in a predictable amount of
customer dissatisfaction which will correspondingly reduce his
share of the total consumer market for his product.
The present invention provides methods and means whereby the
economic gain achieved by operating closer to the limit and the
economic loss occasioned by the defective product portion are
mathematically related as a function of process spread so that the
maximum economic profit is realized.
While the present invention has general utility, it has particular
utility in conjunction with processes and equipment which produce a
defective output that can be identified and reused. The
applicability of the invention to processes and equipment wherein
reclaimable material comprises an output occurs because the output
average value can be translated closer to the limit value in these
instances. In addition, problems of customer dissatisfaction with
defective products in attempting to maximize profit do not occur if
outputs having values beyond a limit are separated and reclaimed,
rather than being put into the stream of commerce.
In accordance with one specific embodiment of the invention, the
profit of a cigarette facility is maximized in response to the
spread in the weight of the cigarettes produced thereby.
Applicability of the cigarette making facility to the invention as
a preferred embodiment results from the ability to readily identify
and reclaim cigarettes having a weight less than a predetermined
limit value. In addition, it has been found that the relationship
between the spread of cigarette weight and the deviation of the
average value from the limit value to obtain maximum profit is very
nearly a straight line function in the practical operating range
for presently existing facilities. Because of this linear
relationship, it is a relatively easy procedure or requires little
apparatus to relate desired average or target weight to defective
cigarettes produced.
It is, accordingly, an object of the present invention to provide a
new and improved controller for a processor or equipment whereby
maximum profit is achieved for a variable spread of output values
and a particular set of quality and manufacturing cost
parameters.
Another object of the invention is to provide in a processor for
manufacturing a product having defective segments which are readily
identifiable and reclaimable, a system and method for deriving an
optimum portion of defective product while driving the product
average value towards a limit value to maximize processor
profit.
A further object of the invention is to provide a new and improved
system for and method of setting a target value of a processor or
equipment to achieve maximum economic profit and for resetting the
target value as changes in output value spreads occur.
Still another object of the invention is to provide a new and
improved system and method for maximizing profit of a machine
producing a product while maintaining a high degree of customer
satisfaction.
A further object of the invention is to provide a new and improved
system for and method of controlling a cigarette making machine to
maximize profit.
The above and still further objects, features and advantages of the
present invention will become apparent upon consideration of the
following detailed description of several specific embodiments
thereof, especially when taken in conjunction with the accompanying
drawings, wherein:
FIG. 1 is a partly schematic and partly block diagram of a
cigarette making machine controlled in accordance with one
embodiment of the present invention;
FIG. 2 illustrates standard distribution of cigarette weights to
describe a typical operation of the system of FIG. 1;
FIG. 3 is a plot of percent low rejects versus average weight
necessary to achieve maximum profit with the system of FIG. 1;
FIGS. 4-6 are block diagrams of alternate embodiments of that
portion of the system of FIG. 1 wherein target value for maximum
profit is computed;
FIG. 7 is a plot useful in describing still another embodiment of
the present invention; and
FIG. 8 is a block diagram which can be employed to implement
another embodiment of the invention relying upon the plots of FIG.
7.
The specifically disclosed and illustrated embodiment about to be
described is concerned with a cigarette making machine which
produces cigarettes having a nominal or standard weight of 1,000
milligrams and a low weight limit of 900 milligrams, below which a
particular cigarette is considered to be defective. It is to be
understood, however, that the principles of the invention are
applicable to other processors or equipment, as well as to the
manufacture of cigarettes having different nominal and limit
values. In such instances, of course, the profit characteristics
are different from those described and illustrated infra.
Reference is now made specifically to FIG. 1 wherein tobacco from
an external source 12 is delivered to feeder apparatus 13. From
feeder 13, tobacco is conveyed on belt 14 in controlled quantities
to rod former 15. The amount of tobacco conveyed between feeder 13
and rod former 15 is controlled in response to an output opening in
the feeder and the vertical position of rotary knife 16 above belt
14. The vertical position of rotating knife 16 is varied by
automatic controller 17 having a tachometer feedback, preferably of
the type disclosed in United States Pat. No. 3,130,733 to Martin.
The controlled amount of tobacco conveyed on belt 14 downstream of
knife 16 is combined in rod former 15 with a paper supply from
source 18 to produce cigarette rod 19 in a well known manner. Rod
19 is translated by well known means, not shown, to cutter 20,
which produces individual, predetermined length cigarettes which
are later sorted and packaged. The velocity of the cigarette rod
emerging from former 15 is monitored by tachometer generator 21
which produces one output pulse for each length of rod commensurate
with a cigarette of the type being manufactured.
The density properties of rod 19, as it emerges from former 15, are
monitored with nucleonic gauge comprising penetrating radiation
source 22 and ionization detector 23, positioned on opposite sides
of the rod. Ionization detector 23 derives a DC output signal
voltage inversely proportional in amplitude to the density of rod
19. The output signal of detector 23 is fed to gauge network 24 of
a well-known type, as described in U.S. Pat. Re. 25,476 to Radley
et al. As described in the Radley et al. patent, gauge network 24
includes sensitivity setting 25 and standard weight setting 26. For
a particular value of the standard weight of the cigarettes being
manufactured, settings 25 and 26 are adjusted so that gauge network
24 derives a DC output voltage having a linear relationship to the
density of rod 19 as the rod passes between source 22 and detector
23. If the density of rod 19 as it passes by the gauging station
including source 22 is such that a cigarette has a weight equal to
that of standard weight setting 26, the output of gauge network 24
is zero. For increasing and decreasing densities of rod 19, the
output voltage of network 24 goes positive and negative,
respectively, in a manner linearly related to the weight of the
cigarettes which are being produced. The output of gauge network 24
is thereby an analog signal linearly related to the weight of a
unit length of cigarette rod equal to one cigarette minus a target
value established by the nominal standard weight for a cigarette
determined by setting 26.
The output of network 24 is fed in parallel to reject classifying
network 28 and linear combining or summing node 29. The other input
to summing node 29 is derived from toggle switch 31, selectively
connected to contacts 32 and 33. With switch 31 set on contact 32,
as illustrated, a positive voltage indicative of a manually set
deviation from standard weight signal is fed into summing node 29.
With switch 31 engaging contact 33 a DC signal derived from an
automatic control network 35, described infra, is fed to one of the
inputs of summing network 29. Standard weight deviation source 34
and network 35 are set or automatically derive a signal,
respectively, to change the nominal target value of standard weight
setting 26 so that the economic profit which can be derived from
the cigarette making apparatus can be maximized. The signal
supplied to summing node 29 by switch 31 can be thought of as a
target reset for the nominal target of standard weight setting 26.
Summing node 29 can thereby be thought of as a deviation of
cigarette weight from a target determined by standard weight
setting 26 and the signal on contact 31.
In operation, with standard weight setting 26 being set, for
example, to a value commensurate with a cigarette weight of 1,000
milligrams and standard weight deviation setting 34 being set to a
value commensurate with -50 milligrams, the cigarette making
apparatus produces cigarettes having an average weight of 950
milligrams. If the weight of a cigarette length in the rod should
be, for example, 960 milligrams, gauge network 24 derives an output
signal having a negative value and an amplitude commensurate with
-40 milligrams, the deviation between the 960 milligram cigarette
detected by the gauging station and the 1,000 milligram setting of
input 26 to network 24. The -40 milligram signal derived by gauging
network 24 is combined with a +50 milligram signal fed into source
34, whereby summing network 29 derives an output signal indicating
that the cigarette rod has a weight of 10 milligrams in excess of
the desired setting established by sources 26 and 34. The signal
derived by summer 29 is fed to automatic controller 17 which drives
knife 16 downwardly by an appropriate amount until the output of
summing network 29 is zero and the desired average value for a
cigarette length of the rod has been reached.
To determine if a particular cigarette length is defective, as
determined by the weight thereof being less than a predetermined
value or lower limit, the output of gauge network 24 is fed to
reject identification network 28. Network 28 includes a source of
DC voltage 36 having an amplitude commensurate with the rod density
which produces cigarettes having a weight equal to the lower limit.
For a typical standard weight setting 26, the potential of source
36 is commensurate with a density which produces cigarettes having
a weight 100 milligrams removed from the standard weight. Hence, a
lower limit of 900 milligrams is established for standard weights
of 1,000 milligrams, while a lower limit of 1,000 milligrams would
be set if the standard weight were 1,100 milligrams. Since the
output of gauge network 24 is a bipolarity signal having a zero
value in response to coincidence between the weight of cigarettes
in rod 19 being coincident with the standard weight, rather than in
absolute terms of weight, there is no need to change the amplitude
of source 36 if the standard weight of a cigarette should be
changed.
The variable amplitude density signal derived from gauge 24 is
compared with density signals for lower limit as derived from
source 36 in integrator 37 for a time period equal to the time
required for one cigarette length of rod 19 to pass through the
gauging station comprising source 22. If the weight of the rod over
a one cigarette length should exceed the lower limit of 900
milligrams, the output of integrator 37 is negative, while a
positive voltage is derived if the cigarette weight is less than
the lower limit. To derive these bipolarity signals, integrator 37
includes a high-gain, polarity-reversing operational amplifier 38.
Bridging the input and output terminals of amplifier 38 is
capacitor 39, discharged instantaneously once during each cigarette
processing time in response to switch 41 being closed by each
output pulse of tachometer 21. The input terminal of amplifier 38
is responsive to the output of gauge network 24, as well as the DC
potential derived by source 36, as coupled through summing
resistors 42. Thereby, if the average density of a particular
cigarette passing the gauge station including source 22 is less
than or greater than the lower limit density established by DC
source 36, positive and negative voltages are respectively derived
from amplifier 38 immediately prior to closure of switch 41.
The output voltage polarity of amplifier 38 immediately prior to
each closing of switch 41 is sensed by trigger network 43, which is
of a well-known type. To this end, trigger network 43 is responsive
to output pulses derived by tachometer generator 21 so that the
output of amplifier 38 is fed thereto only immediately prior to
each closure of switch 41. In response to positive and negative
voltages being coupled to trigger circuit 43, binary one and zero
signals are respectively derived thereby. Thereby, for each
defective cigarette, having a weight less than the lower limit
offset established by source 36, circuit 43 derives a binary one
output.
The binary one and zero signals derived by trigger circuit 43 are
fed to synchronous delay 44, preferably of the shift register type.
Binary one signals loaded into the initial stage of the shift
register comprising synchronous delay 44 are propagated to higher
order stages of the shift register in synchronism with the movement
of the cigarette rod in response to pulses supplied to the delay
element by tachometer generator 21. The number of stages included
in the shift register comprising delay 44 is such that a particular
segment of rod 19 as it passes within the gauging station 22 is
positioned at reject kicker 45, downstream of cutter 20, at the
same time that an output is derived by the delay element. Thereby,
if a defective cigarette passes through the gauge station including
source 22, a binary one output value derived by said element 44 as
that region of rod 19 passes above reject kicker 45. The output of
synchronous delay 44 is coupled to solenoid 46 which is energized
only by binary one outputs of the delay to energize kicker 45.
thereof,
Those defective cigarettes which are separated and identified from
cigarettes weighing more than the reject limit are fed to a
reclamation processor 47. Reclamation processor 47 removes the
tobacco from the paper of the rejected cigarette and supplies this
tobacco back to feeder 13 so that it can be reused in the
process.
The apparatus and process specifically described to this point are
well known to those skilled in the art and generally form no part
of the present invention.
Because of the inability of the cigarette processing machinery
described to produce cigarettes all having the same weight, there
is a spread of weights amongst the cigarettes produced by the
processor of FIG. 1. The spread of weights follows generally the
normal distribution curve, of the type illustrated by curves 51-53
in FIG. 2, where the number of cigarettes having a particular
weight is plotted against weight. Curves 51 and 52 represent equal
relatively wide distributions of cigarette weights, i.e., curves 51
and 52 have the same relatively large standard deviation, while
curve 53 represents a relatively narrow spread of cigarette
weights. The wide spreads of curves 51 and 52 generally result from
tobacco in source 12 having a relatively inhomogeneous density and
may be attributed to loose tolerances in the mechanism comprising
the tobacco manufacturing apparatus. A narrow spread, as
illustrated by curve 53, occurs if the tobacco in source 12 has a
consistent density and each of the mechanical elements in the
tobacco manufacturing apparatus is tightly adjusted to close
tolerances.
Curve 51 illustrates the distribution of cigarette quantity for the
cigarette manufacturing apparatus producing cigarettes to a target
equal to that of the standard weight setting 26 as occurs in
response to a zero offset being coupled to summing node 29 via
switch 31. Even for the wide spread of values indicated by curve
51, having an average value coincident with the cigarette standard
weight (indicated by vertical line 54), virtually none of the
cigarettes weighs less than the lower limit, indicated by vertical
line 55. Thereby, with the distribution of curve 51, a processor
target equal to the standard weight setting results in cigarettes
having an average weight considerably greater than the lower limit
value which a consumer is willing to accept and virtually no
cigarettes having a weight less than a lower limit, indicated by
vertical line 55. The tobacco manufacturer is able to attain a
greater profit if he changes the average cigarette weight so that
is is closer to lower limit line 55 even though a greater portion
of the cigarettes are defective because they have weights less than
the lower limit value. Hence, to attain a greater profit margin
with a spread indicated by curve 51, the average value of the
cigarettes produced is translated to a lower value. The lower
average value merely causes a translation of curve 51 to the left,
without changing the shape thereof, so that the greatest number of
cigarettes have a weight indicated by vertical line 56, which
coincides with the average value of curve 52. Shifting curve 51
from an average value commensurate with the standard weight line 54
to line 56 results in a greater percentage and amount of the
cigarettes having a weight less than lower limit weight 55. The
amount of defective weight cigarettes is the area to the left of
line 55 and under curve 52, indicated by crosshatched area 57.
If the tobacco manufacturing equipment and process produce
cigarettes having a very narrow spread of values, as indicated by
curve 53, even greater savings and higher profits can be achieved.
In particular, with the narrow spread illustrated by curve 53, for
maximum profit the average value of the cigarettes produced is
translated extremely close to lower limit weight 55, to the weight
indicated by vertical line 58. The amount of defective cigarettes
for the narrow distribution curve 53, the cross-hatched area 59
under curve 53 and to the left of line 55, in terms of percentages
is less than for the wide spread of curve 52. For narrow cigarette
distribution spreads, maximum profit is attained for a lower
fraction defective than for wide cigarette distribution spreads. In
other words, in cigarette manufacturing, the greater or wider the
distribution of values the more defective cigarettes should be made
and reclaimed to maximize profit. The realization that a lower
fraction defective for a narrow spread than for a wide spread
produces maximum profit is a deviation from past thinking and
certain prior art systems wherein it was attempted to maintain
fraction defective constant, or by the same token to maintain the
average value removed from a limit value by a multiple of standard
deviation, .sigma..
The relationship we have found to exist between fraction defective
and the deviation between the average value or control target from
the lower limit to attain maximum profit in a tobacco processor of
the type illustrated in FIG. 1 is shown by curve 61 of FIG. 3. To
derive curve 61, there are first plotted the series of curves
labeled .sigma..sub.M =1 %, .sigma..sub.M =2 %, etc. These curves
show the percent of the total production (percent low rejects)
falling below a lower limit LL as a function of the separation
CT-LL of the process mean (average) and the lower limit for the
assumed .sigma. values of 1 percent, 2 percent etc. Since the
typical cigarette making process has been found to follow a normal
distribution, the standard deviation .sigma. is normalized to the
process mean and the percentage of low rejects are then obtained
directly from statistical tables found in many available
handbooks.
It is understood that when the automatic controller 17 is set to
operate with a given control target CT, the controller will
automatically regulate the process so that the process mean will
correspond to the control target CT. Referring to FIG. 2, the
selection of a control target CT which is less than the standard
weight results in a nominal saving in tobacco cost, for a
predetermined number of cigarettes produced, which saving can
readily be computed for a number of arbitrarily selected values for
CT. For each selected CT value, there is a corresponding value for
CT-LL, and a further corresponding value of percent low rejects
which can be read from the appropriate one of the curves labeled
.sigma..sub.M =1 percent, .sigma..sub.M =2 percent, etc. The cost
of producing this percentage of low rejects is then computed for
each value of CT, and the reject cost is subtracted from the
nominal saving to determine the net saving.
It is found that as CT is reduced from the standard weight, thus
decreasing CT-LL, the net saving increases up to a certain point.
Beyond this point, however, as the percent rejects increase
rapidly, it is found that the net saving begins to decrease as CT
is further reduced. The value of CT-LL which produces the maximum
saving can thus be determined and used to locate a point P on the
appropriate one of the curves .sigma..sub.M =1 percent,
.sigma..sub.M =2 percent, etc. The procedure is repeated for each
of the other assumed values of .sigma., to locate all of the points
P.sub.1 to P.sub.6 shown in FIG. 3. Curve 61 is a smooth curve
drawn through these points, and is the locus for the most economic
operation of the machine to maximize profit.
It is understood that other processes to which the invention can be
applied may not follow a normal distribution, and unfamiliar
processes must be statistically analyzed before the foregoing
procedure is adopted in toto. If the process does not follow a
normal distribution, the use of a handbook tables based thereon may
not be appropriate, and the percent low reject figures must be
computed from the actual distribution functions determined
experimentally according to well known statistical procedures.
From FIG. 3, it is to be noted that in the region of practicality,
where standard deviation, in terms of percentage of standard
weight, is between 2 and 5 percent, curve 61 can be closely
approximated as a straight line function 61a defined by:
(CT-LL)=3.1%+0.658 (% rejects) (4)
where:
(CT-LL) = the deviation of the desired target from the lower limit
in percent of standard weight,
3.1 % = a constant, and
(percent rejects) is commensurate with fraction defective as
defined by Equation (3) supra.
To determine the fraction of or percent defective input for
Equation (4) and derive a target offset signal indicative of the
amount by which the average value of the cigarettes should be
changed to optimize or maximize profit, network 35 of FIG. 1 is
provided. property, of by a decreases
To determine percent or fraction defective, which is commensurate
with the ratio of the area of crosshatched region 57 to the total
area under the curve 52, for example, the number of defective
cigarettes in a predetermined number of manufactured cigarettes is
found. To derive a signal indicating when the cigarette maker has
processed a predetermined number of cigarettes, predetermined
counter 71 is provided and connected to be responsive to the output
of tachometer generator 21. Counter 71 is set to any suitable
number, such as 1,000, so that a binary one output signal is
generated thereby in response to 1,000 cigarettes being processed
by the cigarette making apparatus. The binary one output signal
derived by counter 71 is supplied to timing generator 72 which
generates three out of phase but of like frequency pulses, designed
by M1, M2 and M3. Pulses M1, M2 and M3, occurring in mutually
exclusive time periods in the order named, are derived by generator
72 so that the leading edge of the first and the trailing edge of
the latter coincide substantially with the leading and trailing
edges of each one thousandth pulse derived by tachometer generator
21.
The M1 output pulse is fed to counter 73, having a count advance
input responsive to the binary one defect indicating signals of
trigger network 43. The M1 pulses are also fed to digital-to-analog
converter 74, having a signal input responsive to the count stored
in counter 73 during a readout operation. In response to the M1
pulses, the counting action of counter 73 is terminated and the
output of digital-to-analog converter 74 is cleared to zero.
Thereby, after 1,000 pulses have been generated by tachometer
generator 21, counter 73 stores a count indicative of the number of
defective cigarettes manufactured during the previous 1,000
cigarettes produced and any previous signal stored in
digital-to-analog converter is removed.
In response to the M2 output pulse of timing generator 72, counter
73 is activated so that the count stored therein is read out and
coupled to digital-to-analog converter 74. Converter 74 responds to
the output of counter 73 and generates a DC analog voltage level
commensurate therewith. The analog voltage level generated by
converter 74 is maintained until the next M1 pulse is derived by
timing generator 72, i.e., while the next 1,000 cigarettes are
being processed.
In response to the M3 output pulse of timing generator 72, the
count stored in counter 73 is cleared and a zero state is
maintained therein. In response to succeeding binary one defective
indicating output signals of trigger network 43, the count of
counter 73 is advanced and the process continues. In the manner
described, it is believed obvious as to how digital-to-analog
converter 74 derives an analog output indicative of the fraction or
percent defective of cigarettes having a weight less than the lower
limit.
The fraction defective output signal of digital-to-analog converter
is applied in parallel to safety limit comparator 76 and network 75
which automatically performs the initial computations necessary to
produce a change in the average cigarette weight to achieve maximum
profits, i.e., optimum target and percent rejects, for the
particular spread under the specified conditions. Safety limit
comparator 76 derives a binary zero output signal as long as the
voltage generated by converter 74 is commensurate with a fraction
defective within prescribed low and high boundaries, typically
selected as 1.5 and 7 percent fraction defective, respectively. If
the output voltage of converter 74, except during the resetting
operation thereof, is outside of the high or low limits, comparator
76 derives a binary one signal level that actuates alarm 77, which
may be of the aural or visual type, and overrides the position of
contact 31 to drive the contact into engagement with terminal 322.
Thereby, if the weight distribution exceeds predetermined high or
low limits an operator is appraised of that factor and can manually
control the cigarette processor target. High and low limits for
process fraction defective are included to provide for
malfunctioning of both the tobacco system equipment and the gauging
and calculating apparatus, events which can be detected in response
to the defective percentage being outside of limits defined by 1.5
and 7.5 percent.
To compute the deviation of desired target from lower limit as a
percentage of standard weight (CT-LL) percent that results in
maximum profit for a particular spread of output values, as
measured by percent reject, in accordance with Equation (4), the
output of digital-to-analog converter 74 is applied across the
input terminals of potentiometer 78, having a slider 79 adjusted to
a scale factor of 0.658. The variable DC product voltage at slider
79 is combined with a constant voltage at slider 81 of
potentiometer 82, having a value commensurate with the constant 3.1
percent, dictated by Equation (4). The voltages derived from taps
79-81 are linearly combined in summing network 83, the output
voltage of which is a function of the deviation of desired target
from lower limit, in percent of standard weight.
The target deviation from lower limit calculated for the 1,000
cigarettes processed during the sampling period between the two
immediately preceding timing pulses t.sub.1 and t.sub.2 derived by
generator 72, is compared with the deviation determined during the
previous sampling period, defined by timing pulses t.sub.2 and
t.sub.3, to indicate the amount by which the target should be
adjusted. To these ends, network 86 is provided.
Network 86, in addition to being responsive to the current target
deviation indicating output signal of summing network 83 during the
period between t.sub.1 and t.sub.2, includes a feedback network
responsive to the previously computed optimum target during the
period between t.sub.2 and t.sub.3 and an input indicative of lower
weight limit, in terms of percentage deviation from standard
weight. The output signal of network 86, derived from sample and
hold analog memory 87, is fed through analog delay 88 to summing
network 89 and the minuend input of subtracting network 91. The
subtrahend input 91a of subtraction network 91 is responsive to a
DC voltage input having a value commensurate with the lower weight
limit, in terms of percent deviation from standard weight. The
output of subtraction network 91 is a DC voltage commensurate with
the deviation from the lower limit of the previously calculated
target offset from standard value in percent standard value,
(CT-LL).sub.M necessary to achieve maximum profit. The previous
target deviation signal relative to lower limit output of
subtraction network 91 is compared with the presently computed
signal indicative of deviation from lower limit (CT-LL).sub.T in
subtraction network 92, having minuend and subtrahend inputs
respectively responsive to the output signals of adder 83 and
subtracter 91.
The difference signal derived from subtraction network 92 is
applied across the input terminals of potentiometer 93, having a
slider 94 adjusted so that the target value cannot be translated to
the full degree indicated by the output signal of subtracter 92.
Typically, the setting of slider inserts a 0.25 gain factor on the
output of subtracter 92. Thereby, stability of the processor is
maintained despite changes in the process spread and target
overshoot and oscillation is prevented. The signal on tap 94 is
added to the output of analog delay 88 in summing network 89, the
output of which feeds analog memory 87.
Analog memory 87 is of the sample and hold type, including an input
responsive to the M3 pulse derived by timing generator 72. Thereby,
once every 1,000 cigarettes, the signal stored in analog memory 87
is updated and the memory derives a constant output voltage for the
next 1,000 cigarettes being manufactured. The effect of analog
delay element 88 is such as to decouple the transient, step nature
of analog memory 87 from the input to subtracters 89 and 91 while
memory 87 is responsive to the output of the former subtracter.
To convert the percent of standard weight output of memory 87 into
a signal indicative of deviation in absolute terms, multiplier 84
is provided. Multiplier 84 responds to the output of memory 87 and
the DC voltage of source 85, which is set by a ganged potentiometer
arrangement simultaneously with the setting of the standard weight
input 26 of gauge network 24. The output of multiplication network
84 is thereby a DC analog voltage commensurate with the deviation
of desired target from standard weight, in terms of cigarette
weight. To monitor the deviation from standard weight signal
derived by multiplier 84, DC voltmeter 95 is provided.
To provide a better understanding as to the manner by which the
system of the present invention functions to adjust the target
value of the cigarette processor shown, several examples will be
considered. In each of the examples, it will be assumed that the
standard cigarette weight is 1,000 milligrams, the lower limit
equals 900 milligrams, a value 10 percent less than standard
weight, contact 31 engages terminal 33 and the process is governed
by the set of curves shown by FIG. 3.
The system is initially presumed to have been in operation and
stabilized at a standard deviation, .sigma., of 2 percent of
standard weight (i.e., 20 milligrams) which results in a fraction
defective of 1.6 percent and a deviation of desired target from
lower limit of 4.2 percent of standard weight as appears from the
point labeled P.sub.2 in FIG. 3. The 4.2 percent output of summing
circuit 83 of network 75 is translated by network 86 into a
deviation from standard weight of 5.8 percent of standard weight,
the output of analog memory 87 that is fed to multiplier 84 that
drives terminal 33 with a voltage indicative of 58 milligrams.
Let it now be assumed that for the 1,000 cigarettes just processed,
the standard deviation is again 2 percent so that the fraction
defective output of digital-to-analog converter is 1.6 percent. The
1.6 percent fraction defective output of digital-to-analog
converter 74 is translated by network 75 into a voltage
commensurate with 4.2 percent of standard weight. The output of
analog memory 87, indicative of a 5.8 percent deviation from the
standard weight to achieve maximum profit for the preceding 1,000
cigarettes, is subtracted from the 10 percent lower weight limit
input signal to subtraction network 91. The resulting 4.2 percent
output signal of subtracter 91 is compared with the 4.2 percent
output signal of subtracter 83 in subtractor 92, the output of
which is thereby 0 voltage. Since the output voltage of subtracter
92 is 0, the output of analog memory 87 does not deviate before and
after the M3 pulse is generated by timing generator 72 and the
target value for the next 1,000 cigarettes produced is the standard
weight setting input 26 for gauge network 24 minus 58 milligrams,
or 942 milligrams.
For 1,000 cigarettes produced during the period considered, 942,000
milligrams of tobacco are used at the beginning of the process. Of
the 1,000 cigarettes produced, 18 weight less than 900 milligrams
so that the amount of tobacco fed back from reject kicker 45
through reclamation station 47 to tobacco feeder 13 is less than
16,200 milligrams. Thereby, the total amount of tobacco required to
make the 982 cigarettes is 925,800 milligrams.
Let it now be assumed that due to some property of the input
tobacco or the tobacco processing equipment, the standard deviation
of the cigarettes produced suddenly jumps to three percent, whereby
the output of digital-to-analog converter 74 jumps vertically in
FIG. 3 to point P.sub.7 to a potential commensurate with a percent
defective of 8.4. The 8.4 percent output of digital-to-analog
converter 74 is converted into a deviation from lower limit for
average value of 8.6 percent by network 75. The 8.6 percent output
voltage of network 75 is compared in subtraction network 92 with
the previous desired average value deviation from lower limit of
4.2 percent, as derived from subtracter 91. The resulting +4.4
percent output signal of subtracter 92 is multiplied by a constant
factor, generally on the order of 0.25, in potentiometer 93. The
resulting voltage at tap 94 of potentiometer 93, commensurate with
1.1 percent, is added to the -5.8 percent indicating output signal
of analog delay circuit 88 in addition network 89. In response to
the next M3 pulse derived by generator 72, the 4.7 percent output
voltage of network 89 is fed to analog memory 87, converted to a
target deviation weight of 47 milligrams by multiplier 84, the
output of which is coupled to summing node 29 via switch contact
31.
Assuming that the standard deviation remains at a value of 3
percent, the output of analog memory 87 is translated along the
.sigma.=3 percent curve finally to attain a deviation of target
from standard value commensurate with -4.6 percent whereby the
actual target and average weight of cigarettes produced is 954
milligrams. For 1,000 cigarettes made by rod former 15 and sliced
by cutter 20, 954,000 milligrams must be supplied to feeder 13 by
tobacco source 12. In accordance with FIG. 2, of these 1,000
cigarettes, 33 1/2 cigarettes weigh less than 900 milligrams so
that the amount of tobacco fed to feeder 13 by reclaimer 47 is less
than 30,150 milligrams. Thereby, the amount of tobacco required to
make the 966.5 cigarettes which are considered as satisfactory is
923,850 milligrams. By comparing the figures for steady state
operation at standard deviations of .sigma.=2 percent and 3
percent, it is seen that the average value for the lower standard
deviation is closer to the lower limit and that the number of
defective cigarettes is greater for the wider process spread.
Reference is now made to FIG. 4 of the drawings wherein a modified
form of the portion of network 35, FIG. 1, for computing the target
deviation, is illustrated. In the system according to FIG. 4,
circuit elements 101-109 and 111 replace elements 78, 79, 81-83 and
92-94 of FIG. 1. Other elements corresponding to those shown in
FIG. 1 bear the same reference numerals, and in particular those
elements shown in FIG. 4 which receive input signals or provide
output signals are the same elements shown in FIG. 1. In the
embodiment of FIG. 4, the percent reject output signal of
digital-to-analog converter 74 is compared with a previous percent
reject signal, as derived from the input of multiplier 84, to
derive a percent reject deviation signal. The deviation signal is
modified by a parameter related to the economic profit performance
of the cigarette manufacturing equipment to control the reset
target, the slope of the curve of FIG. 3. To determine the percent
rejects and enable a deviation from past values to be determined,
Equation (4) is solved for percent rejects and can thereby be
written as:
(% rejects)=1.52(CT-LL)%-4.72% (5).
In order to solve Equation (5), two cigarette producing machine
parameters are involved, namely 1.52 and 4.72 percent. Since the
slope of the curve of FIG. 3 as well as the constants of Equation
(5) are necessary to determine the optimum average value in the
FIG. 4 system, in contrast to only a pair of parameters for the
system of FIG. 1, the latter embodiment is deemed slightly
preferable to that of the former.
Considering the specific apparatus of FIG. 4, the DC analog output
voltage of converter 74 indicative of percent rejects between
t.sub.1 and t.sub.2 is compared in subtraction network 101 with a
feedback signal indicative of the percent rejects during the 1,000
cigarette processing period between t.sub.2 and t.sub.3. The
feedback signal applied to subtracter 101, derived in a manner
described infra, is applied to the subtrahend input, while the
minuend input of the subtracter is responsive to the output of
digital-to-analog converter 74. The output of subtracter 101,
indicative of the deviation between the past and present percent
reject signals, is applied between the input terminals of
potentiometer 102, having a slider 103.
By reference to FIG. 3, the value of the gain setting for slider
103 which gives a full correction to the proper new value on the
straight line operating locus 61a is found to be 0.18. Then in
order to prevent overshoot and assure stability to the system in
response to changes in the percent rejects between 1,000 cigarette
samples, the slope factor in the setting of slider 103 is modified
appropriately, being typically reduced by a factor of 0.9. For the
particular tobacco making facility having a performance dictated by
FIG. 3, the setting of slider 103 thereby inserts a gain factor of
0.16 in the deviation output voltage of subtraction network 101.
The voltage at the slider 103 of potentiometer 102 is thereby a
measure of the percentage change in the deviation between adjacent
1,000 cigarette processing periods for the desired target relative
to the lower limit, the same factor as is derived from slider 94 of
potentiometer 93 in FIG. 1.
The output voltage at slider 103 is processed in analog adder 89,
analog memory 87 and multiplier 84 in exactly the same manner as
described supra with regard to FIG. 1 to derive an input signal to
summing node 29 indicative of the target offset from the standard
value. In addition, the output of analog memory 87 is fed back
through analog delay element 88 to the input of adder 89 and
subtracter 91 in the same manner as described supra. The output of
subtracter 91 is thereby a signal indicative of the deviation of
the desired target from the lower limit in terms of percentage of
the standard value.
The output of subtracter 91 is applied to an analog computer
network designed to solve Equation (5), supra. In particular, the
desired target deviation from lower limit for the previous 1,000
cigarette processing period, as derived from the output of
subtracter 91, is multiplied by one-half of the 1.52 factor of
Equation (5) in potentiometer 104, having a slider 105 which is
appropriately positioned. The voltage at slider 105 is multiplied
by a factor of 2 in noninverting operational amplifier 106, the
output of which is a DC voltage directly proportional to
1.52(CT-LL) percent. The output of amplifier 106 is added to the DC
voltage developed at slider 107 of potentiometer 108, having a DC
reference voltage applied to its terminal 109. For the specific
situation of Equation (5), slider 107 is set so that the voltage
derived thereby is commensurate with 4.72 percent. The voltages at
the output of amplifier 106 and at slider 107 are respectively
applied to the minuend and subtrahend inputs of subtracter 111,
which derives a DC output voltage directly proportional to the
percent rejects of the previous 1,000 cigarette processing period,
between timing pulses t.sub.2 and t.sub.3.
Reference is now made to FIG. 5 of the drawings wherein there is
illustrated still another embodiment of the system of FIG. 1. In
the FIG. 5 embodiment, the basic philosophy involved in determining
the desired target from the lower limit is the same as that
employed in FIG. 1. In the system of FIG. 5, however, counter 73
and digital-to-analog converter 74 are replaced with pulse rate to
voltage converter 121, whereby the fixed sampling period of the
FIG. 1 embodiment is not employed. Also, the network 86 of FIG. 1
is replaced according to FIG. 5 with circuit elements 122-127.
Those elements shown in FIG. 5 which receive input signals or
provide output signals are the same elements shown in FIG. 1.
Referring now particularly to the embodiment of FIG. 5, the output
of trigger network 43 is applied directly to pulse rate to voltage
converter 12 which linearly converts the rate at which pulses are
derived by the trigger network into a DC analog voltage. The output
of converter 121 is directly proportional to the frequency with
which binary one pulses are applied thereto by trigger circuit 43,
so that as the number of pulses per unit time being fed to the
converter increases and decreases, the output voltage thereof
similarly increases and decreases. The DC voltage derived by
converter 121 is fed to potentiometer 78, the output of which is
combined in summing network 83 with the voltage at slider 81 of
potentiometer 82, in exactly the same manner as described in
conjunction with FIG. 1 for generating an indication of deviation
of desired target from lower limit.
The DC output voltage of adding network 83 is added to a DC voltage
proportional to lower limit, in terms of percent deviation from the
standard value, in summing network 122, having an output which is a
function of desired target, in terms of deviation from standard
weight. The desired target weight functional signal, derived from
summing network 122, is compared with an averaged past value of
desired target in subtraction network 123, the output of which is
thereby a function of the difference between target deviation from
standard value presently being applied to the cigarette system and
an updated value thereof.
The difference output of subtracter 123 is applied to potentiometer
124 having a slider 125 positioned to achieve stability, as
discussed supra with regard to potentiometer 93 and slider 94 of
FIG. 1. The gain adjusted deviation signal at slider 125 is added,
in addition network 126, to a signal indicative of the averaged
past target value, derived from an integrating or signal averaging
network 127. Network 127, which may be of the RC low pass filter
type, has a time constant on the order of 30 to 60 seconds to
provide an effect similar to that attained by the sampling
operation of FIG. 1.
The output of signal averaging network 127 is fed back to the
minuend input of subtracter 123 and to one input of adder 126, to
provide the signals indicative of the target offset presently being
fed into the tobacco making apparatus. The output signal of adder
126 fed to multiplier 84 is converted to a true weight signal from
the percentage signal which had been processed.
While the system of FIG. 5 has been described as a modification of
the FIG. 1 embodiment, it is to be understood that the principles
are equally applicable to the system of FIG. 4. In particular, the
percent reject output signal of converter 121 could be applied
directly to subtracter 101 and each of the other elements connected
therewith.
Reference is now made to FIG. 6 of the drawings wherein there is
disclosed still another embodiment of the invention, wherein target
offset is determined directly in response to standard deviation of
the density variations within rod 19 as it passes the gauging
station comprising source 22. In the system according to FIG. 6,
elements 131, 132 and 134-141 replace classifying network 28 and
elements 71-79 and 81-83 of FIG. 1. The gauge network 24 which
provides the input, and the subtraction network 92 which provides
the output signals, are the same elements shown in FIG. 1. To
determine maximum profit in terms of target offset from a lower
limit, standard deviation can be determined in accordance with well
known techniques and algebraically combined with predetermined
factors. In particular, the mathematical relationship between
desired target relative to lower limit and standard deviation
is:
(CT-LL)%=1.2.sigma.%+1.8% (6)
Referring now more particularly to FIG. 6, the output signal of
gauging network 24 is applied to variance computer 131, which may
be of the type disclosed in U.S. Pat. No. 2,965,300 to Radley et
al. Computer 131 includes a clock source so that it periodically
derives an output signal in accordance with variance, as dictated
by Equation (1) supra. The variance output of computer 131 remains
constant between the activation of the clock source, whereby the
computer output is a series of constant amplitude voltages which
have virtually step function transitions, similar to the output of
digital-to-analog converter 74.
The output of variance computer 131 is applied to conventional
analog computer type square root network 132. The output of square
root circuit 132, a DC voltage directly proportional to the
standard deviation of the output of gauge 24 over a predetermined
time interval, is converted to a percentage of standard weight in
division circuit 134, having a divisor input source 135 that is a
constant voltage set in accordance with the standard weight setting
26 of gauge network 24. The standard deviation percentage output of
division network 134 is applied to an analog computing network
which solves Equation (6).
The analog computer circuit for solving Equation (6) includes
potentiometer 136, having input terminals responsive to the output
voltage of division circuit 134. Tap 137 of potentiometer 136 is
set in accordance with the 1.2 proportionality factor of Equation
(6) and supplies a voltage commensurate with 1.2.sigma. in terms of
standard weight percentage to one of the inputs of summing network
138. The other input to summing network 138 is a DC analog voltage
commensurate with the 1.8 percentage factor of Equation (6), as
derived from slider 139 of potentiometer 140 that is driven with a
constant DC voltage at terminal 141.
The resultant output of summing network 138 is a DC analog voltage
commensurate with the deviation from the lower limit for the
desired target to achieve maximum profit. The output voltage of
summing network 138 is processed identically to the output voltage
of summing network 83, FIG. 1, or in target resetting network
86.
The concept of computing the deviation from a present standard
deviation and an updated standard deviation, as set forth in the
embodiment of FIG. 4, is equally applicable to the embodiment of
FIG. 6. In particular, the output of division circuit 134 can be
compared directly with a signal proportional to present standard
deviation as computed by an analog computer network responsive to
the output of subtraction network 91, FIG. 4, in accordance
with:
.sigma.%=0.833(CT-LL)%-1.5 (7)
According to another aspect of the invention, the profit of a
process controller can be optimized by fabricating a quantity of
defective product that is put into the stream of commerce and
determining what adverse effects the defective produce has on sales
of the product. A penalty factor is provided for each defective
product put into the stream of commerce and utilized in determining
the control target or average value to enable achievement of
optimum results equated to maximize profit.
In the specific alternate embodiment about to be described,
cigarettes having a weight less than a lower limit are not rejected
but are allowed to pass into the stream of commerce with the
understanding that such cigarettes are likely to result in a
dissatisfied customer and adversely affect future sales of the
cigarettes by a predetermined factor, referred to as a penalty
factor. In the present instance, a 2:1 penalty factor is provided
for each defective cigarette passed into the stream of commerce.
The standard deviation, .sigma., of the cigarettes produced is
correlated into dissatisfied customers, to control the cigarette
average weight (CT). As the average weight of each cigarette
produced decreases, for a given value of .sigma., the number of
dissatisfied customers is expected to increase.
As the value of .sigma. increases, for a given value of average
cigarette weight, the number of dissatisfied customers increases.
The number of dissatisfied customers as a function of standard
deviation and average value is cumulative in that a relatively
small number of customers is dissatisfied with a cigarette having a
weight of 1,000 milligrams but a considerably larger number is
dissatisfied with cigarettes having an average weight of 950
milligrams. To determine the total customer dissatisfaction,
therefore, it is necessary to accumulate or integrate the number of
dissatisfied customers for each cigarette average weight from the
lowest standard deviation to the actual highest standard deviation.
This cumulative total of customer dissatisfaction is multiplied by
a penalty factor relating to the likelihood of reduced future sales
as a result of customer dissatisfaction.
A set of curve illustrating production costs, customer
dissatisfaction costs and optimum control target as a function of
control target and standard deviation is illustrated in FIG. 7. In
the curve of FIG. 7, it is assumed that a 2:1 customer
dissatisfaction penalty is provided, i.e., for each defective
cigarette put into the stream of commerce, the manufacturer suffers
a penalty equal to twice the profit he would normally make from
that cigarette. For example, if the profit per cigarette were
normally 0.05 cents, the penalty would be 0.1 cents and the
manufacturer would lose 0.05 cents for each dissatisfied
customer.
Referring now more specifically to FIG. 7, cost is plotted as a
function of average cigarette weight as a percentage of standard
weight, CT percent. A pair of exemplary values of CT percent are
illustrated by dashed straight lines 201 and 202, indicating
cigarette average weights of 85 percent and 100 percent of standard
weight, respectively. Dashed curves 203-208 indicate the cost to
the manufacturer in customer dissatisfaction for these different
standard deviations, based upon the 2:1 penalty ratio for standard
deviations of 1 percent through 6 percent, respectively. It is seen
from curves 203-208 that with a very small standard deviation of 1
percent the cost to the cigarette manufacturer due to defective
products getting into the stream of commerce is very small if the
average weight of the cigarette is maintained greater than 85
percent of standard weight. As the standard deviation increases,
whereby a greater percentage of defective cigarettes is likely to
be produced, the cost to the cigarette manufacturer increases as a
result of customer dissatisfaction, as shown by curves 203-208.
Each of curves 203-208 is asymptotic to a 0 cost line for average
cigarette weight approaching infinity and increases in value for
decreasing values of CT percent. At any particular value of CT
percent the value of each of curves 203-208 is directly related to
the value of .sigma. with which it is associated.
Also plotted on FIG. 7 is straight line 209 which shows the cost of
producing cigarettes, in terms of tobacco, as a function of CT
percent. Curve 209 is a straight line because the cost of producing
the cigarettes increases directly as the average weight of the
cigarettes increases. Costs relating to factors such as paper,
machinery and power, are so minimal as to have virtually no effect
on production cost curve 209.
To determine the cost of producing cigarettes with optimum profit,
taking into account the customer dissatisfaction cost curves
203-208 and the tobacco cost curve 209, cost values at
corresponding average cigarette weights along the two curves are
added together to produce total cost curves 211-216 for the six
values of .sigma.. The minimum value of each of curves 211-216
gives the value of CT for maximum profit for each .sigma. to enable
optimum target curve 217 to be produced. Hence, to derive the point
P.sub.11 on curve 217, which gives the value of CT percent that
produces the most profit for a .sigma.=1 percent, curve 203 is
added to line 209 to derive curve 211, the minimum value on curve
211 is found and correlated with a value of CT percent. Similarly,
the values of P.sub.12 -P.sub.16 are successively derived by
combining the different values of curves 204-208 with the values of
curve 209 at common values of CT to produce curves 212-216 and the
minimum of each of curves 212-216 is correlated with a different CT
percent. Curve 217, in actuality, is slightly nonlinear but can be
approximated closely as a straight line function, similarly to the
manner by which the straight line function of FIG. 3 was
approximated.
To control a process, such as the process illustrated in FIG. 1,
with a curve based on FIG. 7, the value of .sigma. for the process
is computed. From the computed value of .sigma., a value of CT is
calculated which will give optimum profit. The value of CT which
will give optimum profit is compared with a value of CT previously
utilized to control the average cigarette weight and the deviation
between the two values enables a new value for CT to be derived. As
in the previously described embodiments, a weighting factor is
included for the deviation between the desired and previous values
of CT to prevent overshoot. Of course, any embodiment utilizing the
principles of FIG. 7 does not include the reject and reclamation
apparatus of FIG. 1, indicated as including synchronous delay 44,
reject kicker 45, solenoid 46 and reclamation processor 47.
Further, the fraction defective computing apparatus of FIG. 1 would
be replaced with a standard deviation type computer, of the type
described in conjunction with FIG. 6.
Reference is now made specifically to FIG. 8 of the drawings
wherein there is illustrated an embodiment of the invention
relaying upon the optimum target curve 217 of FIG. 7. In the system
according to FIG. 8, elements 131, 132, 134, 135 and 221-226
replace classifying network 28 and elements 81-83 of FIG. 1, and
network 86 is modified as described hereinafter. In the system of
FIG. 8, the process standard deviation (.sigma.) as a percentage of
standard weight is computed by circuit elements comprising variance
computer 131, square root network 132 and division network 134,
driven in response to the output of gauge network 24 and standard
weight circuit 135 in the manner indicated supra with regard to
FIG. 6. The output of division network 134, a DC voltage indicative
of standard deviation as a percentage of standard weight, is
applied across the terminals of potentiometer 221, having a tap 222
set in accordance with the slope of curve 217, FIG. 7. The DC
voltage at tap 222 is added in analog computer addition network 226
to a constant DC voltage derived from slider 223 of potentiometer
224, energized by a constant positive DC voltage at terminal 225.
The voltage derived from tap 223 is commensurate with an offset
cost value of curve 217, whereby the output voltage of adding
network 226 is indicative of the value of CT on curve 217
corresponding with the value of .sigma. derived by division network
134. Thereby, the output signal of addition network 226 is a DC
voltage indicative of the average weight of cigarettes produced
during a just completed time interval which will result in optimum
operation of the cigarette processor of FIG. 1, if no cigarettes
are rejected and a 2:1 penalty factor is assigned for all
cigarettes which result in customer dissatisfaction.
The desired value of cigarette average weight for the just
completed segment of the process operation is compared with the
previous value of desired average weight in network 86, which
functions in a manner similar to network 86 described supra in
conjunction with FIG. 1. In the network 86 of FIG. 8, however, the
desired average weight is compared with the previous desired
average weight directly and no subtraction of lower limit values is
included. Thereby, network 86 of FIG. 8 differs from that of FIG. 1
by being responsive directly to the value of CT, as derived from
adder 226, and does not include a subtracter 91. Instead, the
subtracter 92 in the network of FIG. 8 is driven directly by the
output of analog delay network 88, as is adding network 89. As in
the system of FIG. 1, the system of FIG. 8 includes potentiometer
93, having slider 94, whereby a damping factor is provided for
calculated deviations between previous desired values, as derived
from analog delay network 88, and the most recently computed
cigarette average weight value.
To consider the operation of the system of FIG. 8, initially assume
that stable operation at .sigma.=2 % and CT=87.5 % has been
achieved with a total cost indicated by point P.sub.12, FIG. 7.
Next assume that the tobacco input density spread suddenly changes
so that .sigma. jumps from 2 percent to 3 percent and cost jumps to
the point indicated by P.sub.22, FIG. 7. At point P.sub.22 profit
is no longer optimized because the customer dissatisfaction cost
has increased due to the larger number of low weight, undesirable
cigarettes being sold. To decrease customer dissatisfaction and
again maximize profit, the average cigarette weight must be
increased so that a lower number of undesirable, low weight
cigarettes will be sold. The cost of the low weight undesirable
cigarettes will, however, be greater for .sigma.=3 % than for
.sigma.=2 % because of the added tobacco in each cigarette and the
larger quantity of undesirable cigarettes that will reach the
market. Maximum profit for .sigma.=3 % is achieved by operating
knife 16 of the FIG. 1 system so that the average cigarette weight
is gradually changed from point P.sub.22 to point P.sub.13.
In the FIG. 7 system, under the initial stabilized condition, the
.sigma.=2 % output of divider 134 is translated into a value of CT
of 87.5 percent by the network including adder 226, whereby
cigarettes costing 0.05 cents are produced. In response to the
change of .sigma. from 2 percent to 3 percent, the desired target
value signal derived from adder 226 jumps to approximately 90
percent. The 90 percent signal derived from adder 226 is compared
with the previous desired average weight value signal of 87.5
percent in network 86. Network 86 responds to the difference
between the two desired weight signals to translate gradually the
average weight of each unit length of cigarette rod from 87.5
percent to 90 percent of standard weight to maximize profit and
produce cigarettes costing 0.052 cents.
While there have been described and illustrated several specific
embodiments of the invention, it will be clear that variations in
the details of the embodiments specifically illustrated and
described may be made without departing from the true spirit and
scope of the invention as defined in the appended claims. For
example, the concepts of the present invention can be utilized to
control the standard weight deviation input to summing circuit 29
on a manual basis in response to observations of meter 95.
The analog computer arrangements above described are particularly
adapted for profit maximizing control of a single processing
machine, whereas in many plants, such as some cigarette
manufacturing plants, a number of similar machines are operating
simultaneously. In this case the practice of the invention is
preferably implemented by using a digital computer which is
operated on a time sharing basis to serve a number of machines in a
manner similar to that described in U.S. Pat. No. 3,147,370, issued
Sept. 1, 1964, to W. B. Lowman. The data for the profit maximizing
functions, such as those shown graphically in FIGS. 3 and 7, are
stored in the computer memory, the control targets for the various
machines are computed sequentially in response to the input data,
and the updated target setting signals are routed to the several
machine controllers on a periodic basis. Since the digital computer
preferably uses the conventional table look-up system, the actual
points on the profit maximizing curves, as at 61 and 217, are used
instead of the linear approximations thereto, so that the small
errors due to nonlinearity are avoided.
* * * * *