E. HARVEY BARNETT Monsanto Chemical
Co., Organic Division, St. Louis 77, Mo.
Introduction to Evolutionary Operation This is the w a y to improve quality, increase throughput, or reduce cost during routine operation of a chemical plant
E
vornTmNARY OPERATION, usually called EVOP, is a technique for improving the operation of a process. It is ordinarily applied to chemical processes. First proposed by Dr. G. E. P. Box ( 7 ) , it is now in use in many locations and is pointing the way to significant savings. An illustration of the way EVOP works is due to Box. Suppose a biologist captures lobsters off the coast of Maine. He measures two characteristics of these lobsters, length of claw and pressure exerted between the claws. The lobsters are tagged, and later samples tell which lobsters live long enough to reproduce. A two-dimensional plot of data is shown in Figure 1. Contours have been drawn which join those points having equal probability of survival. The contours are of logical shape, for lobsters which have claws too short or too weak cannot defend themselves against their enemies, nor can they gather food effectively. I t is also known that long claws would make a lobster clumsy and the excessive leverage of long claws and high pressure might cause the lobster to break his own claw: the best configuration is represented by the inner closed contour. I t is expected that offspring would tend to have the characteristics of the parents with minor variations. But the offspring with more favorable characteristics beget offspring with even more favorable characteristics. A group which is initially on the side of the hill will move up the hill in the course of several hundreds or thousands of generations and will eventually occupy the hilltop. If the environment changes, location of the hilltop changes and the species must, and will, resume its climb to the top. The contours of Figure 1 might also represent the yield of a chemical reaction as a function of pressure and reactor length at constant flow. I n this case, a different location of the contours would be caused by a different flow rate. Two things are necessary for this evolutionary process to occur in nature: mutation, or change, and selection of the most favorable offspring. These criteria suffice for improving the yield of the analogous chemical process. However, typical policy in chemical production has been to forbid
500
change of a controlled variable in the plant without special permission. Several special licenses may have been granted in a year, but only rarely for change of more than one variable at a time. Further, the method of determining which condition was more favorable was often inadequate. This is not to say that processes were never improved. A foreman may have noticed that when the solvent was wet the yield was low. An operator may have observed that the centrifugal time cycle was shorter in the winter when the cooling water was colder. By these means most processes were improved gradually over a period of time and most were eventually operating at nearly optimum conditions. I t has been tacitly assumed that a new process is never a t optimum conditionsin fact, it is possible that a new process will not operate at all. But assume for the moment that all the combinations of possible conditions have been thoroughly explored on the bench and the process has had a careful pilot-plant investigation. In spite of all the data and correlations which have been accumulated, most organic reactions act differently in the large-scale plant. This is especially true when uncertain quantities as heat transfer, agitation, distillation column efficiency, others, are important. It is, therefore, necessary to optimize in the plant. Evolutionary Operation provides a system for optimizing a plant; for exploring the relationships among independent and dependent variables. EVOP consists of the systematic introduction of very small changes in selected independent variables
Experimental Designs
Various experimental designs can be used and a statistician would select an appropriate design to fit the particular case. He would weigh such factors as interaction, linearity, and the use of previous knowledge.
CATALYST C ONCE N TRATION
PRESSURE EXERTED
-
BY CLAW
LENGTH OF CLAW
Figure 1. Per cent of lobsters which live to reproduce
INDUSTRIAL AND ENGINEERING CHEMISTRY
which affect a process, and the statistical selection of the best set of conditions. This system is one which can be used by operating personnel without special assignment of research chemists and technical service engineers. In fact, the principal difficulty is the quantitative determination of response which is often yield or concentration of wanted compounds. But given a process in which the important process variables are controlled, and given a measurement of the critical response quantities, EVOP can be run and will usually result in improvements in cost or quality. To illustrate, let us show the course of a typical EVOP. Suppose the important independent (controlled) variables are catalyst concentration and temperature, and the dependent variable which will be observed is yield. The real response contours are shown in Figure 2. If the initial process is at A , phase I may be run, then 11, and finally 111. “Which way is up” is the only information necessary to follow this path. Chemical processes have been operated for many years to produce materials useful to other industries and to consumers. Today these processes can also be operated to produce information useful in their own improvement.
TEMPERATURE
Figure 2. This is the course of a typical evolutionary operation to improve yield
1(-*
I*/
i *
Figure 3. These are examples of twoand three-variable EVOP designs
Figure 4. These comparisons are from the two variable EVOP designs
The recommended design for general use is based on the time-tested two-level factorial in which each independent factor will be held at a low and a high level. All possible combinations of lows and highs are run. The graphs in Figure 3 show that the two-variable design is a square; the three-variable, a cube. I n each case the basic factorial is augmented by adding a center point. These EVOP designs can be extended to any number of dimensions. A set of experimental runs which includes each of the designed combinations once is called a cycle. After several cycles (replications) have been made, the general location of this pattern may be moved or variables may be dropped from the experiment or added to begin another phase. It must be understood that the meaning of “low” and “high” is relative. The
changes made within a cycle of an EVOP are of small magnitude; so small that the effect on the observed variable is expected to be detectable only after several cycles have been run. Another facet of design concerns interactions. These are all too common in chemical processes-for example, less catalyst is required at a higher temperature. Second-order relationships may also be present within the experimental factors as well as among them. However, the simpler first-order designs recommended here will lead generally upward.
block of runs with another. For the twovariable case shown in Figure 4, five experiments yield a total of five statistics : Effect of A Effect of B Interaction effect AB Change-in-mean effect (CIM) Grand mean
1. 2. 3. 4. 5.
Data are rarely error-free. Hence effect A-for example, which was obtained as the difference between the average response at the higher level of A and the average at the lower level of A-contains error. A number representing the amount of error is necessary for comparison with the effect. If the effect is small compared with the error, then the effect may not be real at all, but merely the result of errors. If the effect is large compared with the error, it is concluded that the effect is really present and that it operates in the indicated direction,
Analysis of Data These designs result in the usual comparisons of a factorial ( 2 ) : all main effects and first-order interactions can be independently estimated. I n addition, a warning of curvature is obtained and the grand mean is useful for comparing one
C A L C U L A T I O N OF AVERAGES
ZALCULATION OF STANDARD DEVIATION P R E V I O U S SUM
5
JJ-02
-= r . 1 9 = 0 . 3 5 = 0 . 4 1 6 NEW
5 =RANGE
K
x
=u
NEW SUM 5
-
-
_ -
NEW A V E R A G E
-
,*
.
P f i - 6 4 1 7 3 591 30.531 7 5 81
NEW A V E R A G E S IN. S./N)
AIR
I
A EFFECT
* A
81
7 8~
CI,
El
9 fi
AB
10.18
D F
7.86 9.G-6.
B
n
E
17.52x U
G
1-7G
21
2
U
I
10.18
m-.&%-
18.78
G
t
2
J
u
L
5
-
”REVIOUS A V E R A G E 5
~
8.60
D
yg Ei
L 2-
DESIGN
u
I0.53
I
d
r w0
+2!
8.44
=m
O F 95% E R R O R L I M I T S
133
L
X S A
8.76
-
4A
0.80~1 ’- 0 6
FOR NEW E F F E C T S A , B . AB
1.33
X S A
0.Ro
FOR T O T A L CHANGE -IN-MEAN
M
X S A
K
N
+:
=*
I 06
EFFECT
0.80
=*
0.95
FACTORS
- -
L -
M -
0.30
1.96
0.35
1.33
1.19
1.09
0.98
5
0.37 0.38
0.95
0.85
6
0.39
0.85
0.76
7
0.40
0.70
0.70
8
0.40
0.72
0.65
1.76
EVOLUTIONARY OPERATION TWO V A R I A B L E WORK S H E E T
PRODUCT RESPONSE
Figure 5.
=fL0fx
A
F O R NEW AVERAGES
L
10.4
x 4
U
u
m/3 - 1
=
” ” X X u 1.19 +u-a
8.88
u x
5
NEW SUM S / l N - l l
t
A
m
786
B
UL.46
lfwix
CHANGNN-MEAN EFFECT
F
7.86
‘a cu
2-
-
t n . 6 3
c
=
EFFECT ~
c
-
78.97
‘ALCULATIONS
I
B EFFECT
R
D)
-
-
YEW SUMS IN. 5 . )
S A
F Xa m D I e Y
These two-variable example calculations are for cycles 1 and 2 VOL. 52, NO. 6
JUNE 1960
501
STATISTICS IN C H E M I C A L PROCESSES Figure 5 shows a calculation form for obtaining the four comparisons and the error limits for the two-variable case. The error limits are obtained by replication-that is, by noting how well the response checks on repeated application of the same set of experimental conditions. This calculation is based on an estimation of the standard deviation from the range. Instructions which accompany the form make it self explanatory. Note that no standard deviation is obtained on the first cycle. The forms in this article have been altered slightly from the original work of Box and Hunter (4). The 95% confidence limits used here will result in a wrong conclusion one time in twenty. Students' t has been used in setting these limits to allow not only for the uncertainty in the value of an effect, but also to allow for the uncertainty in the standard deviation. Box and Hunter (5) set t = 2 and use a previous estimate of error on the early cycles. An effect is termed significant when its estimated value plus or minus its error limits does not include zero. No effect is significant on cycle 2 of this example, as all the confidence ranges include zero. The possibility has not yet been eliminated that the effects are really negligible. Cycle 3 of the same EVOP is shown in Figure 6. The B effect, temperature, has
Directions for Two-Variable Calculation Form Differences
Subtract new observations from old averages. sign of the difference Add the new observations to the old sums
New sums New averages Calculation of effects
Divide the new sums by n, the number of the cycle (For example, the A effect) Write the new average for operating condition 3 and 4 opposite C and D. Add these two to get the number in space F. Carry out corresponding operations to get the number for space G The next operation is subtraction. If F is larger than G, recopy G under F and subtract G from F. If G is larger than F , recopy F under G and subtract F from G. In either case divide by 2 and the sign of the quotient is shown on the form
Change in Mean effect
Copy F and G as shown and add these two. A is multiplied by 4. The next operation is subtraction as above. Divide by 5
Calculation of standard deviation
Range-This is the algebraic difference between the largest difference and the smallest difference. The range is always positive Examples:
Therangeof1.2,1.3,0.2,--1.5, - 0 . I i s 2 . 8 The range of 1.7, 0.3, 0.7, 0.9, 1.2 is 1.4 The range of -2, -7, - 5 , - 8 , -3 is 6
Read K,L,and
Constants
M factors from the table
been found significant with 95y0 confidence since 1.69 =t1.06 = 0.63 + +2.75. Zero is not a likely value for the effect of temperature. Run data for this example were obtained by adding random errors with a standard deviation of 1.OO to the true re-
+
+
CALCULATION O F AVERAGES
1
O P E R A T I N G CONDITIONS
Note the algebraic
2
3
sponse (Figure 6). This true response was obtained from a real process by multiple regression methods. The signal received is approximately correct and estimate of standard deviation is very good. A minimum would be located by proceeding in the opposite direction. CALCULATION O F STANDARD DEVIATION
4
5
5
P R E V I O U S SUM NEW
5 =RANGE
x
K
=3.95.0.30=1.185 NEW S U M
5
NEW A V E R A G E
5A
I
NEW S U M S / l N - l l NEW SUMS
IN. S.)
A EFFECT
9.94
c
E753
D - . & . J 3 L
E
4
7
F O R NEW E F F E C T S A , E , AB
3
F-A-
1.96
L
LZ.23-
2 l L . 3 3
2
M
i
1-76
+u -
8.65,
A
4
5
xLa2L3AL&Q 5
u
6
x 5
7 8
I
t o . 2 5 REMARKS:
3-4A TIME, hrs.
RESPONSE PHASE
Figure 6. These two-variable example calculations are for cycle 3 INDUSTRIAL AND ENGINEERING CHEMISTRY
EFFECT
1 . 1 8 5 = * 3.09 L -
M
_ .
-90
1.96
1.76
0.35
1.33
1.19
0.37
1.09
0.98
0.38
0.95
0.85
0.39
0.85
0.76
0.40
0.78
0.70
0.40
0.72
0.65
-
EVOLUTIONARY OPERATION TWO V A R I A B L E WORK SHEET
PRODUCT
502
I.185=' 3.33
FACTORS
K
+F~10.58
X S A
-
N
CHANGE-IN-MEAN E F F E C T
u
X S A
F O R T O T A L CHANGE - I N - M E A N
BY
Ex a m p I e
A.
FH R
CYCLE ( DATE
N
I
5-11-
L
59
Interpretation of Signals
Information is obtained from an Evolutionary Operation as to whether the experiment included variables which had a significant influence on the response. If it did, these effects are found to exceed the 95% confidence interval for effects. If an effect is positive, and the response is to be maximized, the variable should be changed in a positive direction. If more than one variable is significant, these variables should be changed simultaneously by the amounts proportional to the effects ( 3 ) . This rule applies as long as the change-in-mean (CIM) effect is small. Caution should be used in making changes when the C I M effect is not small and especially when it is significant. The possible relationships of the experimental location to the response surface are shown in Figure 7 . The C I M effect is the difference between the y value a t the center point and the average of the two y values for the extreme points. When EVOP begins, assume that the value of the independent variable A is not optimum (Figure 7 , A ) . The A effect is found to be significant since the slope is steep, but C I M effect is not significant. As later phases proceed closer to the peak, Figure 7,B applies. Enough cycles are run to show A significant, but the C I M effect may or may not be significant depending on the spread of the experiment with respect to the actual response, the curvature of the response curve, and size of experimental error. But, the C I M effect is not expected to be small. When the response maximum is finally included within the experimental space, it is possible that the independent variable will still have a significant effect (Figure 7C). The C I M effect should be significant. The usual picture is Figure 7 0 where the slope of the independent variable (the effect) is near zero and the C I M effect is significant. Note that the C I M effect is negative for a convex surface. Figure 7 E is also possible when the true maximum is a point on a relatively large plateau or when the size of the experimental pattern is too small in relation to the curvature. Stated simply, the interaction effect measures nonlinearity or nonplanarity. This is not always true, however, since the design which straddles a peak symmetrically has zero interaction. In general, the existence of an interaction means that A has a different effect on the response at the low level of B than it does at the higher level of B. Multiple Responses
Any number of response variables can be observed for each run. These are calculated separately. I t will ordinarily be desired to maximize some of them, minimize some, and hold some within limits.
interpretation of the change-in-mean effect
;;;p;~; ____-_-------_I
\
INDEPENDENT
I t is likely that conflicts will arise: T o maximize the yield the temperature must be increased, but this will cause the formation of too much tar, for example. T o resolve complex conflicts, it is advisable to determine the response surface and plot them all on the same diagram or model with lines which represent the known limits. This technique (6) is of great value when combined with a priori knowledge and wisdom of the production man and the chemist to select the conditions for future operations. Organization for EVOP
An EVOP can actually be designed, run, and calculated by a production foreman or supervisor, or this can be done by the chemical statistician. Such factors as time available, background, and existing line-staff relationships should be considered before assigning responsibility in any particular case. On two things, general agreement is:
1. Design and interpretation should utilize all the theoretical and practical knowledge which is available. 2. The generation of ideas is of critical importance (8). EVOP points the way up only for the variable being studied. If other variables are likely to be important, they must be studied.
To these ends there should be an EVOP committee or an informal group which will meet occasionally to review data, interpret signals, and select likely variables for investigation. This group may be composed of production supervisor, staff technical production advisor, technical servicesrepresentative, research chemist, and chemical statistician. Early discussions should include the analytical methods development chemist, since it is often found that one or more analyses are required for which no standard method exists. I n fact, EVOP is expected to require a significant number of new methods and special analyses. I n some cases, the prospect of significant improvements will justify the pur-
VARIABLE
A
chase of a new analytical instrument or plant stream analyzer. Training for EVOP
Persons who will come into contact with EVOP should understand a t least what it is and what it does. This includes production foremen, analytical chemists, the research group, technical services engineers, and management to the level of vice president or higher. For some it is enough to read a journal article or a n intra-company report. Others need, or want, first-hand knowledge. For these a course should be organized which covers the topics of this article and their statistical background. The most effective training involves doing, and EVOP can be done in the classroom through the use of an electrical analog (7,9) of a process. literature Cited
(1) Box, G. E. P., A#@. Statistics 6, No. 2, 3-23 (1957). (2) Box, G. E. P., Connor, L. R., Cousins, W. R., Himsworth, F. R., Sillitto, G. P., in “The Design and Analysis of Industrial Experiments,” (0.L. Davies, ed.) pp. 247-67, Oliver and Boyd, London, ~
1954.
. ,Popper,
F., Trans. Inst. Chem. Engrs. 34,280-93 (1956). (7) Heigl, J. J., Wilson, J. A., “Description of an Electrical Analog of a Research Problem,” Esso Research and Engineering Co., Products Research Div., Linden, N. J. (Oct. 13, 1955). (8) Koehler, T. L., Tafipi 42, 261-4 (1959). (9) Moder, J. J., Jr., Indust. Qual. Control 13, No. 4, 16-21 (October 1956).
RECEIVED for review September 22, 1959 ACCEPTED April 12, 1960 Division of Industrial and Engineering Chemistry, 136th Meeting, ACS, Atlantic City, N. J., September 1959. VOL. 52, NO. 6
JUNE 1960
503
