ABSTRACT

Proven methods are available to search for improved manufacturing conditions without experiencing economic penalties. At an industrial scale it is important that any operating adjustments avoid the production of off-specification product, shun unexpected product variations, and directly relate any operating variable changes to resulting process effects.

Experimental designs and optimization methods provide a structured approach to process improvement. They are efficient in that they maximize the amount of information that can be obtained from experimental measurements and expansive in that they often detect favorable operating conditions not previously considered. Unfortunately, these structured methods, developed to guide small-scale studies, have limitations reducing their appeal for industrial applications: (1) they rely on observing comparatively large process effects so that the influence of random process variations (noise) can be ignored and (2) they simultaneously investigate several variables with the result that the effects of individual variables are often obscured. Although coined to identify a particular process improvement technique, Evolutionary Operation has since become a generic term identifying process improvement methods suitable for use with manufacturing operations. Two appealing Evolutionary Operation adaptations are EVOP and SEVOP. Both take advantage of multiple replications to keep process effects small enough to satisfy manufacturing quality requirements. In addition, both methods are able to adopt favorable process improvements unexpectedly generated by the interaction between operating variables. EVOP (the original evolutionary operation technique) was developed by G.E.P. Box at Imperial Chemical Industries and has been widely applied in industry. It is based on a particular experimental design, the factorial design, in which up to three variables can be simultaneously studied. After completing an EVOP phase, a team of experts reviews the results to select the conditions for the next phase. SEVOP (singular evolutionary operation) is a recent development at Montana State University that is based on two of the simplest structured techniques: the paired observations experimental design and the Hooke-Jeeves optimization method. During a SEVOP phase, all operating variables are separately studied to explore the influence of each. Using the optimization method, the combination of variable settings is continually adjusted to seek the most promising operating condition. Very few heuristics were suggested for EVOP, but these have been expanded to include applicable rules-of-thumb from the more extensive collection developed for SEVOP. To simplify the application of the SEVOP heuristics, they have been organized into a practical decision strategy. Effective worksheets arrange EVOP and SEVOP process measurements and calculations so that interpretation of results is apparent. Experience has proven that an excellent means for assimilating EVOP and SEVOP concepts is to practice applying them to realistic industrial process simulations.

INTRODUCTION

Why is it important to incorporate process improvement into manufacturing operations? Consider these 1991 remarks by D. Allan Bromley, assistant to President George Bush for science and technology in the Executive Office: "... In science and technology we tend to focus on the revolutionary types of discoveries, the ones for which people are awarded Nobel prizes, rather than on the evolutionary developments. Yet these evolutionary advances allow companies to bring products to the market a little faster, a little cheaper, and a little more reliably, thus gaining market share. In general, these evolutionary developments are not spectacular and attract none of the attention and media coverage -- not to mention professional recognition or reward -- that goes with the revolutionary developments. Yet I am convinced that they are as important -- if not more important -- in the competitiveness of American industry" [1]. Although these comments addressed the situation in the United States of America, they are pertinent to any modern business whose prosperity is contingent on successful globalization.

It must be recognized that there is a need to improve both new and mature manufacturing processes. Regardless of the extent of prior testing and conscientious design, every new installation requires some adjustment to find the best operating conditions for that particular facility. Even then the degree of fine-tuning is limited by striking a balance between the advantages to be gained by additional process explorations and the necessity to settle into an economically-viable operation as soon as possible. As a process matures it usually sustains changes in equipment, personnel, raw materials, and product specifications -- it is unlikely that it is operating as effectively as possible.

Process improvement at an industrial scale introduces three unique constraints not relevant to small-scale studies. First, most processes involve multiple steps or stages -- changes in a particular stage must be introduced cautiously to avoid disrupting normal operating procedures elsewhere in the process. Second, because of the large quantities involved, the production of off-specification product must be avoided. Finally, it is important that the product remains consistent -- even though the product may be improved, different properties might cause problems for customers relying on current product characteristics. Violation of any of these constraints usually results in an unnecessary economic penalty.

SYSTEMATIC TECHNIQUES

Intuition always has and probably always will play a role in process improvement. However, the intuitive approach often involves unacceptable economic risks (see above) and is particularly ineffectual for analyzing variable interactions. The importance of variable

interactions can be illustrated by observing how the selectivity for producing a desired product in a chemical reactor is affected by changing the reaction time and temperature (Figure 1). When the temperature is held at T₁ and the time increased from ₁ to ₂, the selectivity increases 2% (43% less 41%). Likewise, when the reaction time is held at ₁ and the temperature increased from T₁ to T₂, the selectivity decreases 3% (38% less 41%). Instinctively it seems that if the time and temperature were simultaneously increased that the change in selectivity could be predicted by combining the individual effects of each variable -- a 2% gain due to time less a 3% loss due to temperature should result in a net loss of 1%. However, it is obvious from Figure 1 that the actual effect would be a net gain of 31% (72% less 41%). Variable interactions can be detrimental as well as favorable; in either case, successful process improvement depends on recognizing how they affect production.

Systematic process improvement techniques include (1) experimental designs and (2) optimization methods -- they are attractive because they are both efficient and expansive. Experimental designs are efficient because they obtain the maximum amount of information from a given number of experiments and they are expansive due to their ability to detect the existence of favorable variable interactions. The efficiency of optimization methods is derived from the speed at which they can find the best operating conditions; expansivity is the result of their ability to incorporate any beneficial variable interactions.

Because the systematic techniques were developed for use with small-scale experimental facilities or for solving mathematical models, they usually violate the previously-noted constraints associated with improving processes at the industrial scale. However, in the 1950's G.E.P. Box introduced Evolutionary Operation (EVOP) -- a widely-accepted method for improving manufacturing processes. It must be emphasized that EVOP is a routine method for permanent process operation, not an experimental procedure that could interfere with efficient process operation and require special testing personnel. The significant characteristic of Box's EVOP is that it combines small variable perturbations and numerous replications of every process adjustment with statistical analysis. Every process contains random process fluctuations (noise) typically caused by such factors as raw-material variations, equipment deterioration, and instrument corrections. Because process responses to variable changes and the random noise may occasionally have comparable values, replication allows the effects of the noise to average out so the true effects of the variable changes can be determined. There is little risk in the EVOP approach because drastic effects on the process or product are avoided. The widespread success of Box's EVOP led to the generation of a number of new methods purported to be applicable to improving manufacturing-scale processes. In fact, EVOP has effectively become a generic term referring to methods used to improve manufacturing processes.

EVOP in the Curriculum

In engineering education a "capstone" design experience is usually relied upon to bind academic and industrial perspectives together. Process improvement using EVOP is another valuable approach for engaging students in practices pertinent to industrial practice. In the Department of Chemical Engineering at Montana State University, several EVOP methods are introduced following this sequence: (1) overview, (2) statistical methods, (3) definitions and nomenclature, (4) heuristics, (5) worksheets, (6) heuristics exercises, (7) comprehensive process study, and (8) wrap-up discussion.

The overview is used to emphasize the importance of continual process improvement and identify how a study of a manufacturing-scale process differs from that of a bench-scale or pilot plant operation. It is made clear that EVOP methods are applicable to both physical and chemical processes. A summary of an EVOP study as a process progresses from its normal operating condition to an improved situation is visually presented. In fact, visual explanations are used whenever possible to present any new information -- they are effective in providing comprehensible explanations. However, the number of process variables that can be visually represented is limited (in the overview a 2-variable study is used).

Simple statistical methods are used to calculate (1) the mean, variance, and standard deviation of a sample, (2) the effects associated with variables and variable interactions, (3) the standard errors of the effects, and (4) the error limits. The effects and error limits are compared to determine the significance of the results of the variable perturbations. Emphasis is placed on clarifying what the calculations represent rather than in just providing an algorithm to simplify their execution. Special attention is given to illustrating what is meant by variable interactions. Short assignments give the students practice in making these statistical calculations.

Definitions and nomenclature differ between EVOP methods; therefore, it is essential that the jargon peculiar to each method is made obvious. A list of this information is given to each student and the items are discussed.

The heuristics are the foundation upon which each method is based. A compilation of heuristics is given to each student organized relative to (1) global heuristics that apply throughout the method, to (2) decisions that must be made to select the size of a variable perturbation and whether to change the reference value of a variable, and to (3) alternate heuristics that apply depending on whether or not a range of variable levels has been established that brackets the best level. A justification is given for each heuristic and numerical examples of their application to a process are presented. It is emphasized that the heuristics are usually reliable and are based on experience gained by using the method. However, engineering judgment can be used to alter their application whenever their consequences on the process or product may be too uncertain or possibly unacceptable. Heuristics have been organized to form a decision strategy. The strategy is currently being converted into a decision tree that can be readily implemented as an expert system and/or programmed instruction. Beyond clarifying the EVOP methods and simplifying their application, the decision tree strategy could be integrated into process control software.

Although the individual heuristics are simple, their collective application can become confusing. As an example, the perturbation size for different variables may expand, contract, or remain constant -- different heuristics apply to each situation. It is important to organize the information being generated by an EVOP study so that it can be easily understood. Comprehensive worksheets have been developed to simplify the calculations required to invoke the heuristics; they also provide a record of the course the EVOP study has taken. Each student completes the worksheets as the results of a partial example of a process improvement study is introduced and discussed.

Because active student participation is a more effective learning alternative than passive observation, heuristics exercises are provided to involve each student in their application and to provide practice in situations that past experience has shown to cause difficulties. It is not necessary that every possible situation be explored because this usually occurs while completing the comprehensive process improvement study.

In a classroom environment, a comprehensive process study necessitates the availability of a realistic process simulation. A FORTRAN simulation has been developed that includes the effect of random process noise on the process responses. In addition to providing process responses for replicate runs, the simulation calculates the necessary variable effects and their associated error limits. Several industrial processes have already been modeled. It is a straightforward procedure to generate new industrial simulations by modifying the FORTRAN program -- only the mathematical model for a process and its standard deviation have to be known. A significant improvement recently initiated has been to provide students with a simulation executable file for PC use instead of only having it available on a mainframe computer. Each student is given an initial and different operating condition providing a reasonable process response but allowing room for improvement. The objective is for the student to better the process response as much as possible by changing the levels of the process variables. Two different types of comprehensive studies have been assigned: complete and partial studies. A complete process study usually requires that the EVOP method be repeated many times and invokes practically all of the heuristics before identifying the best variable levels that can be determined using the method. A quicker partial process study is more appropriate for workshop settings. The EVOP method is applied for only a certain number of times after starting from the initial operating condition. Subsequently, each student is provided with another unique operating condition along with suggested variable perturbations that will most likely bracket or enclose the best level for each variable -- this allows practice in recognizing when the best conditions have been attained within the limitations of the EVOP method. Although the complete process study is more time-consuming, the students come to the realization that EVOP is deliberate and long-term program -- it requires patience to improve a process while simultaneously satisfying product and process specifications. The self-correcting properties of EVOP also become apparent -- if a poor decision is made in selecting the size and/or direction of a variable perturbation, this will become obvious and can be subsequently corrected.

A wrap-up discussion is the final step in presenting each EVOP method. Completion of the comprehensive process study assures that the heuristics and strategy for employing them are fairly-well assimilated. The wrap-up provides an opportunity to identify situations where heuristics may be confusing or contradictory. In fact, suggestions generated by such discussions have influenced the maturation of each EVOP method. Perhaps the most beneficial result of this step is the realization by the students of the validity of the EVOP approach; a comparison of their process studies shows they generally finish with similar variable levels and process responses even though they started from substantially different initial operating conditions.

Factorial EVOP

Factorial EVOP was the initial evolutionary operation adaptation developed by Box [2]. It uses 2-level factorial experimental designs to simultaneously consider the effects of up to three variables. No optimization method is employed. A factorial design consists of every combination of all the variables at their two levels. In addition, a reference point is added to the center of the factorial design -- it is recommended that the current operating conditions be selected for this reference point. The purposes of the reference point are (1) to identify any curvature effects associated with the variables and (2) to provide a baseline for estimating the "cost" of the study by comparing the factorial design process responses with that at the normal operating conditions. Judgment is used to determine the reference point and variable perturbations for succeeding factorials -- it is recommended that these decisions be made by an advisory committee including personnel with a broad range of expertise.

Figure 2 concisely illustrates the factorial EVOP method: the open circles identify the initial factorial experimental design and the solid circles indicate the reference points at the center of the initial and subsequent factorial designs. The variable levels for a 2-variable factorial design are represented by the four corners of a rectangle -- the dimensions of the rectangles change as the study progresses and the effects of variable changes become different. Judgment was used to select subsequent factorial designs until the best operating conditions were reached. The reference point was not changed unless a significant improvement of the process response had been realized; the sizes of the variable perturbations were adjusted so that they had significant, but not excessive, effects. The 2-variable study shown in Figure 2 was made using a simulation developed for maximizing the modulus of elasticity of a propellant by adjusting its binder, oxidizer, and fuel compositions [3].

The choice of the factorial experimental design does, however, have some drawbacks. Because the variables are simultaneously changed for every run, the entire design must be completed before individual variable effects and interactions can be identified. The practical limit of considering only up to three variables is due to a combination of (1) the necessity to complete the entire design before the data can be analyzed and (2) the fact that the number of runs doubles for each additional variable considered. Unfortunately, the choice of the current operating conditions for a reference point results in about half the runs in the experimental design having responses inferior to that at normal operation. Because of process constraints it is occasionally impossible to operate at all the combinations of variable levels required by the factorial design. Factorial designs also limit flexibility in that it is difficult to (1) add or delete variables and to (2) consider variables with only discrete rather than continuous levels.

Because of the reference point and replications included in factorial EVOP, the statistical calculations differ from those used to analyze standard factorial designs; however, a thorough explanation of the simple procedures is available [4]. The calculation of the standard errors of the effects is simplified by estimating them from the range of differences between current and average process responses. A cycle is defined as one replication of all the runs required for all the variable level combinations in the factorial design plus the reference point. A phase consists of all the replications of the cycle for a particular factorial design. From seven to ten cycles are recommended for every phase.

Although Box suggested that the progression of a his EVOP method be based on human judgment, experience with the approach at Montana State University has generated some effective heuristics useful in guiding a factorial EVOP study. The worksheets provided by Box and Draper [4] use Yates' algorithm -- an efficient scheme that unfortunately obscures the meaning of the calculations. Earlier worksheets that clearly indicate what the calculations represent have been found to be superior for student use [5].

The comprehensive process study consists of an assignment to maximize the extraction yield of a pharmaceutical product as a function of three variables -- two additives and the pH [6]. An example of the information provided for a factorial EVOP phase by the process simulation is shown in Figure 3. Note that all three variables were perturbed simultaneously. Analytical information provided after each cycle includes the average responses for every run, the variable effects and interaction effects, and the change-in-mean or cost of the study along with the error limits for all of the quantities.

Advantages of factorial EVOP include:

• widespread industrial acceptance
• avoidance of drastic process or product effects
• multiple measurements of effects
• simplified standard error calculations
• quantitative measurements of variable interactions
• a simple decision strategy relying on judgment

Singular EVOP

The generation of singular EVOP over the past five years has been based on the author's experience in industrial process improvement and the development of academic courses in optimization and process engineering. Both a simple experimental design and a simple optimization method are employed. The experimental design consists of seven measurements of the process response at both the normal (reference) level and a perturbed (exploratory) level of a process variable; these are statistically analyzed as paired observations. It must be emphasized that only one variable at a time is perturbed so that there is a direct relationship between changes in that variable and the resulting process response. The optimization method determines the size and direction of the variable perturbation. Although the Hooke-Jeeves optimization method [7] was not conservative enough to be used with manufacturing operations, it provided the inspiration for the optimization method that has been developed. Depending on the effect a variable has on a process response, it is classified as belonging to one of three stages: expansion, moderation, or contraction. Heuristics guide the transfer of a variable between stages, the selection of the size and direction of a variable perturbation, and the decision to change the reference level of a variable. The reference level of a variable is changed only if there is a significant improvement in the process response. An earlier article provided a general outline of the singular EVOP approach, but it has been substantially improved since that time [8].

An illustration of the singular EVOP method is shown in Figure 4; the open circles again represent the original experimental design and the solid circles the progression of the reference points until the best operating conditions were determined. The experimental design consists of investigating each variable separately -- the variable is perturbed and the process response at the reference and exploratory levels compared. If a significant improvement is observed, the study of that variable is stopped and an intermediate reference point is established at the exploratory level. Otherwise, both positive and negative perturbations can be explored and sometimes a single adjustment in the perturbation size can be made. The experimental design is completed after all the variables have been studied. Figure 4 shows that an increase in the binder mole fraction diminished the response while a decrease improved it; the same result was obtained when perturbing the oxidizer mole fraction. Therefore, the final reference point for the experimental design was moved to the low levels of both the binder and the oxidizer. Heuristics guide the direction and size of variable perturbations for subsequent experimental designs. As in the factorial EVOP study (Figure 2), the sizes of the variable perturbations were adjusted to be significant but not excessive. A comparison of Figures 2 and 4 shows that singular EVOP reference points move toward the best operating conditions much more quickly than the factorial EVOP reference points even though the successive changes in process responses were comparable using both methods. The explanation is that about half the perturbations in a factorial EVOP experimental design are in directions giving poorer responses while singular EVOP usually proceeds only in the the directions giving better responses.

The expansion stage is used to determine initial bounds within which the level of a variable can fluctuate without significantly diminishing the process response. At the beginning of a singular EVOP investigation, it is likely that a variable can be perturbed in either direction, i.e., its value can both decrease and increase. It is also probable that the largest changes in a variable's level will occur early in a study because (1) process changes that normally evolve have not been thoroughly evaluated or (2) variable interactions have not been explored. Provision is made to transfer a variable forward to the "moderation" stage after it has been enclosed, i.e., both upper and lower bounds have been identified. The defining characteristic of this stage is that the size of the perturbation can be expanded on one or both directions.

After a variable has been enclosed, the range between the lower and upper bounds may be quite broad. The purpose of the moderation stage is to approximate the best variable level within this interval. Because of variable interactions, the allowable range of a variable may change -- provision is made to transfer the variable back to the "expansion" stage or ahead to the "contraction" stage when appropriate. The defining characteristic of this stage is that a single, conservatively-sized perturbation is used in one or both directions.

The contraction stage is used for "fine-tuning" to find the best level for each variable. This stage is not invoked until all the variables are simultaneously transferred into it. The defining characteristic of this stage is that the size of the variable perturbation can be reduced in one or both directions. The perturbation size of each variable will be reduced to at least 25% of that used in the "moderation" stage with larger reductions possible when appropriate.

The significance of the difference between the reference and exploratory level responses is resolved using the standard statistical analysis for paired observations [9]. A factorial EVOP cycle consists of one set of seven replicates of a pair of exploratory and reference levels for a variable; one to four cycles may be required to determine the effect of each variable. A phase includes all the cycles required to investigate all the variables in a particular singular experimental design.

Because of the complexity introduced by the different heuristics applicable in each singular EVOP stage, a great deal of effort has been devoted to generating worksheets that organize the resulting information so that it can be easily understood and used. The worksheets include two sections -- an experimental design and results section and an analysis and action section. The first section is used to record the variable levels and the resulting effect on the process for each cycle. The second section is used determine the size and direction of the next perturbation for that variable as well as summarize clearly the decisions that were made.

The same simulation is used for both the singular EVOP and factorial EVOP comprehensive process studies. Figure 5 is an example of the process simulation information provided for a factorial EVOP cycle (note that only one variable was perturbed).

Advantages of singular EVOP are:

• avoidance of drastic process or product effects
• process responses directly related to variable perturbations
• a decision strategy guided by tested heuristics
• incorporation of favorable variable interactions
• no limitation on the number of variables that can be included
• avoidance of unattainable combinations of variable levels
• predictably inferior runs are not included in the experimental design
• variables can be added or deleted at any time
• discrete-valued variables can be easily accommodated

Product quality and process efficiency can be expected to improve if EVOP is introduced into a manufacturing process. Incorporation of EVOP as a normal operating practice will provide timely detection of, and quick recovery from, inferior process performance caused by gradual process changes. Although small improvements may lack glamour, they provide a means for remaining competitive in today's world market.

REFERENCES

1. Bromley, D.A., "Engineering's Renaissance," ASEE Prism, Dec. 1991, p.14.

2. Box, G.E.P., "Evolutionary Operation: a Method for Increasing Industrial Productivity," Applied Statistics, Vol. VI, No. 2, pp. 81-101, 1957.

3. Snee, R.D., "Experimenting with Mixtures," Chemtech, Vol. 9, No.11, pp. 702-710, 1979.

4. Box, G.E.P., and Draper, N.R., Evolutionary Operation, John Wiley & Sons, New York, 1969.

5. Box, G.E.P., and Hunter, J.S., "Condensed Calculations for Evolutionary Operation Programs," Technometrics, Vol.1, No. 1, pp. 77-95, 1959.

6. Lind, E.E., Goldin, J., and Hickman, J.B., "Fitting Yield and Cost Response Surfaces," Chem. Eng. Progress, Vol. 56, No. 11, pp. 62-68, 1960.

7. Hooke, R., and Jeeves, T.A., "Direct Search Solution of Numerical and Statistical Problems," J. Assoc. Computing Machinery, Vol. 8, No.2, pp. 212-229, 1961.

8. Scarrah, W.P., "The Evolutionary Route to Process Improvement," Chem. Eng., Vol.99, No.5, pp. 122-125, 1992.

9. Montgomery, D.C., Design and Analysis of Experiments (4th ed.), John Wiley & Sons, New York, 1997.

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