I
by W. J. Youden National Bureau of Standards
STATISTICAL A
W O R K B O O K
DESIGN
F E A T U R E
Evolutionary Operation
E C
trations of reagents? The best catalyst recycle sequence? The best arrangement of purification facilities? A method of operating a process which As they begin to answer these quesalso tells how to improve the process tions in successive phases of evolutionary operation, their results sugI HE Princeton University Conferlem is evolutionary operation. This gest new areas for study. ences bring together academic and technique was devised by George The second point to make is that nonacademic people to discuss a E. P. Box in his capacity as statisto avoid any pronounced drops in broad range of topics. In December tician at Imperial Chemical Indusperformance that would involve 1958 the conference topic was Process tries, Ltd. He is currently director substantial costs, only minor changes Development by Statistical Methods. of the Statistical Techniques Research in the levels of the operating variAbout 100 industrialists, together Group at Princeton University. ables arc permitted. The consewith 30 from universities and Box published an account of this quence of making only small delibergovernment, were invited to listen to work in the English journal Applied ate changes in the operating condiexpositions on new statistical methStatistics [6, 81 (1957)]. This paper tions is that the effect on the process ods. An impressive feature of this was reprinted, with two other papers performance is of the same order of conference was the first-hand reports on the same topic, in the Proceedmagnitude as the normal fluctuations of actual experiences in applying ings of the Second Stevens Symthat take place anyway. The probthese methods to regular production posium on Statistical Methods in the lem, therefore, is to detect changes in processes. A good share of the Chemical Industry. This sympoperformance that are the result of the time was devoted to the evolutionarysium on January 25, 1958, was sponslight alterations in the operating operation of industrial processes. sored by the American Society for conditions. This is achieved by Quality Control and the Stevens deciding upon some simple cycle of Limitations of Institute of Technology. T h e changes in operating conditions and Laboratory Experimentation supply of the proceedings is exrepeating the cycle a sufficient numhausted. More readily accessible is ber of times so that chance fluctuaTransferring a process from the a paper "Condensed Calculations for tions average out and the real effects laboratory to full scale plant producEvolutionary Operation Programs" appear. tion involves the same sort of probin the first issue (March 1959) of the lems that inventors encounter in the There is wide latitude as to the new statistical journal Technometrics. dimensional effects that arise beparticular sequence of changes in The last column gave a brief account tween demonstration models and operating conditions that may be of this new journal. full scale pieces of equipment. T h e introduced in the process. Experipilot plant scale for studying a procence shows that schemes in which Evolutionary Operation ess bears witness to the difficulties three variables are tested out in each in attaining the same yields and This column draws on the original phase can often be conveniently efficiencies in plant production that article in Applied Statistics and the handled without interfering with the appeared to be possible on the badiscussions at the Princeton Conusual production routine. With two sis of laboratory experiments. I n ference. The discussions brought and three variable schemes, the runs general the preliminary estimates out convincing evidence for the can be made in short sequences of for the optimum levels of the operatworkability of this approach to five sets of operating conditions. ing variables prove to be only improving process performance. The advantage of a short sequence approximations. Approximations lies not only in simplicity but in The first point to emphasize is that obtained from pilot plant scale favoring the maintenance of conevolutionary operation does not undoubtedly will be better, but may stancy of environmental and other mean a team of experimenters understill require adjustment when full conditions for the duration of the taking complicated experiments in scale production is undertaken. sequence. If all factors, apart from the plant. Rather, evolutionary those deliberately changed, arc kept operation is really a method of The plant process itself is hardly constant, the comparisons within the operating the plant and can, and suited to the type of experimental sequence will be greatly improved. approach that is feasible in the usually does, go on indefinitely. For example, changes in raw malaboratory. Wastage by reason of Invariably there is an almost terials are likely to be less prolow yields or unacceptable quality limitless number of questions to nounced in a short sequence than in is prohibitively expensive on a plant which the plant operators do not a lengthy one. scale. Nevertheless, the answer know the answers. Are they using the sought is one that holds good in the best temperature-time cycles? The In a typical two-variable scheme, plant. One approach to this probmost effective and economic concenthe current standard set of operating I/EC
W
ORKBOOK FEATURES
79 A
STATISTICAL DESIGN
I/EC
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conditions constitutes one of the five sets of operating conditions. Each of the two variables is tried slightly above and slightly below the standard value for this variable. The variations are tried in the four possible combinations: both high, both low, one high and the other low, and the reverse combination. The Stevens Symposium proceedings have a numerical example in a paper by J. S. Hunter. This example concerns a batch process and the particular step studied is a cleaving operation. The standard operating conditions were 300° C. for 3 hours. These conditions were varied as shown below. 305° C. 300° C. 295° C.
©5
·3 · 1
©2 170
180 Minutes
©4 190
The cycle consists of five batches run in the sequence shown by the numbers. The order can be varied in subsequent cycles and this will provide protection against any unknown influence that might have a time cycle of the duration of the sequence. Usually there are a number of items of interest that can be recorded for each batch. The yield, per cent impurity, or physical state of the product, for example, may all be of interest and often require some compromise that ensures an acceptable product at as low a cost as possible. Because the program is simple, the data may be recorded on a score board to make possible continuous visual evaluation as the cycles progress. The yields, as given by Hunter, for the first four cycles were : Cycle I II III IV Range
1 63.7 62.1 59.6 63.5 4.1
Batch Yiel 2 62.8 65.8 62.1 62.8 3.7
It is helpful to display the averages in a form which connects the results with the operating condition as shown at the end of the fourth cycle. Temp., ° C. ' 305 300 295
Average % Yield Time, Minutes Trô Î8Ô Î9Ô 61.9 64.6 62.2 63.4 65.7
Examination of the averages indicates that a lower temperature and 80 A
A Workbook
Feature
longer t i m e h a v e a favorable effect on the yield. T h e best average is 3.5% above the average for the s t a n d a r d operating conditions. O n the other h a n d , the individual b a t c h yields in the four repetitions show considerable variation. T h e average r a n g e shown by four yields is a b o u t 4 . 5 % . T h e cycles m u s t be continued until either visual or statistical scrutiny of the d a t a gives a firm indication of the best c o m b i n a tion of these two operating variables. T h i s best c o m b i n a t i o n naturally e n o u g h becomes the n e w s t a n d a r d operating conditions a n d in t u r n the center of a n o t h e r cycle t h a t permits further exploration of other levels of these operating variables. T h e r e are clear gains to be h a d byclosing in on o p t i m u m operating conditions as soon as possible. T h e r e fore the decision to shift to other levels of the variables a n d to c h a n g e the variables u n d e r study should not be unnecessarily delayed. T o this end an a p p r o p r i a t e system for evaluating the d a t a , cycle by cycle, is an integral p a r t of the p r o g r a m . Statistical Evaluation Appraisal of the d a t a by visual inspection does not as a rule m a k e the best use of the information in the records. T h e ranges, it is true, give a n idea of the variation between repeat runs u n d e r the same set of operating conditions. But these ranges m a y be inflated by differences between the cycles. I n d e e d , the cycle averages plotted against time m a y reveal the presence of swings or trends in the process. E a c h cycle average is based on a composite of for Operating Conditions 3 4 63.2 67.2 65.S 67.6 62.0 65.3 67.9 62.6 5.9 5.0
5 60.5 61.3 64.1 61.7 3.6
the five sets of operating conditions. T h e s e averages are shown for each cycle. Cycle Av. yield
I II III IV ALL 63.5 64.5 62.6 63.7 63.6
Certainly it is possible t h a t other conditions d u r i n g cycles I, I I , a n d I V were generally favorable to high yields. But d u r i n g cycle I I I low results are conspicuous. S o m e exp l a n a t i o n m a y exist for the generally
INDUSTRIAL AND ENGINEERING CHEMISTRY
poor showing in this cycle, but this is not the immediate problem. The question at hand concerns a comparison of the five sets of operating conditions. If conditions are generally unfavorable (or favorable) for the duration of a cycle, the yields in that cycle are lowered (or raised) in consequence. The comparisons among the five sets of operating conditions may in fact be very little the worse for changes from cycle to cycle. The ranges shown among the four repeat results from the four cycles of course do reflect changes from cycle to cycle and therefore are hardly an appropriate basis for judging differences in yields between sets of operating conditions. Confronted with this situation experimenters have sometimes "adjusted" the yield figures so as to make all cycles have the same average. This may be accomplished by altering the yields in any cycle by the difference between the cycle average and the grand average of all cycles. The adjusted data do not change in the least the relative ratings of the different operating conditions. They will, however, give smaller ranges, appropriate for estimating the precision of comparisons among the operating conditions. Box and Hunter in their paper in Technometrics have developed a simple calculation procedure for which the error appropriate for judging differences between the averages can be estimated with just the sort of adjustment of the data described above. They reduced the calculations to a simple routine conveniently carried out on standard work sheets. T. L. Koehler, American Cyanamid Co., reported at the Stevens Conference that 20 programs were running. Last October, in Buffalo, F. S. Riordan told the Chemical Division Conference of ASQC that this method of operation was proving highly successful at the Chemstrand nylon plant in Pensacola, Fla.
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