Howard J. Blomquist

200 Woodland Rd.

Wyomissing, PA 19610

(610)678-3779

email:qualityinf@aol.com

As costs, competition, and consumer expectations increase, manufacturers are constantly looking for ways to improve their products. The philosophy of W. Edwards Deming has taken hold as an important basis for accomplishing this improvement.

The legacy of Deming on our manufacturing culture has been substantial during the few short years that he was finally heeded. Much attention has been focused on the major points that he made regarding needed changes in management styles and some of the deadly sins that perpetuated the inability to adapt to these needed management style changes.

However, somewhat lost in the discussion and appreciation of what he espoused was a reality, presented in statistical terms, that was more fully appreciated by the Japanese as early adherents of his philosophy. To quote Deming: "Our aim in production should be to improve the process to the point where its distribution is so narrow, the specifications are lost beyond the horizon." That is, we should learn enough about our processes to be able to set process target nominals such that the variation around those nominals is minimal. In fact, the variation should be so minimal that any tolerances set (for "tolerated" variation from the target) become irrelevant to that optimized process because the process is tightly centered around the target. No product is found near the tolerances in those cases.

The Japanese have done well in their attention to this central theme of Deming. In fact, data from many (but not all) Japanese manufactured products demonstrate tight dispersion around functional targets, well within advertised tolerances. The quality and reliability of such products has been demonstrated all too well in too many markets worldwide where others were unable to compete on a quality or even a price basis.

Not only have their products demonstrated this characteristic, but some of their written statements have implied the importance they have given to dispersion around some standard. To concentrate on this while gradually discontinuing the practice of quality by screening finished product to tolerances represents a major breakthrough that the Japanese have shown in adapting Deming principles.

The major challenge from this Deming quotation is the improvement process to accomplish this objective. We need to change from the practice of trial and error investigations to discover possible process variable influences after quality problems appear, no matter how statistically efficient it is done. We should instead be making systematic reviews of known process variables and operating conditions and their effect on variation right from the start.

In adopting the Deming objective, the Japanese already realized that screening product to tolerances is not a cost effective path to quality. Additionally, reducing variation by moving the screening upstream from the final product to tighter control tolerances of process inputs is also going to be a costly and less desirable way to achieve reduced product variation.

Rather, they have shown considerable attention to proactive (what we call preventive) quality and less reliance on reactive, or "after the fact," quality strategies. According to them, waiting for the process to tell us we have quality problems -- by observing excessive nonconformances or charts that are out-of-control -- is too late. Special attention must be paid to selecting the known inputs that determine a process and learning how they should be specified to obtain an optimum process, both in terms of being on target as well as with minimized dispersion around that target. Otherwise, we may be wasting our time looking for some strange variable that may have caused a perturbation to the process, while we ignore the nature of the fundamental relationships that determine how the known variable inputs achieve the desired process output.

Many solutions to quality problems, presumably traced to outside variables introduced into the process, become only temporary. The same quality problem reappears at a later date, now requiring a new solution because the process was not made tolerant of such perturbations.

The evidence is all too clear that the Japanese have been very successful in reaching the Deming objective. Why, we wonder? Maybe they understand more fully a missing step that is overlooked to a large extent in US manufacturing.

To better appreciate what this step might be, we need a fuller understanding of variation in the process. Product variation is quite natural and expected. It is not some mysterious characteristic of the process that is minimized only by continually tightening process controls at a higher cost, resulting in just marginal gains in quality.

Learning about variation and how it is passed on to the product becomes a priority in any attempt at cost effective variation reduction. That is, we need to learn how to deal with the inevitable daily variation that invades our process. In the past decades, we have decided that by implementing various SPC tools, we have a better insight on this variation and when we should react to it. However, using these tools does not automatically assure that we'll discover conditions resulting in product or processes on target with minimum variation. Many have been disappointed in not achieving the gains they expected from implementing SPC programs.

Cost effective variation reduction can only come from proactively determining what input causes have an influence on the nature and the amount of the inevitable daily variation that is passed on (transmitted) to the product. This is done best when designing the product or process and choosing the operating conditions to make that product. However, existing product or processes can also be improved by proactive studies to better understand functional relationships in the process.

Our historic assumption of the nature of variation has been intuitive: any variation encountered in the process on a daily basis is passed on to the product as a constant. We have assumed that regardless of where a cause is set to achieve the desired effect, the variation passed on during the process is relatively the same. Yet this is not always the case. In fact, it can be demonstrated that some causes not only determine the level of their effect (by definition of a cause), but also can influence greatly just how much of their daily variation they pass on to the product.

With the goal of optimizing product and processes, sophisticated models and techniques have been developed in many cases to try to achieve the best optimum of level and minimized variation simultaneously. Response surface analysis is one such technique. However, in our desire to transfer technology from empirical or theoretical models (which describe the relationships) to actual production, we have overlooked the important consideration of variation transmission when it occurs in the process. Most of us can agree that there are differences in the nature of functions describing the cause and effect relationships used in this transfer. However, have we stopped to consider how these differences in functions pass along the inevitable daily variation mentioned earlier that is encountered in normal production?

A comparison of scatter plot linear and nonlinear functions can quickly demonstrate this difference.

The linear function curve will pass along a relatively constant amount of variation to the output when comparing "y1 out" to "y2 out." That is, with the same amount of variation of the input at "x2 in" as at "x1 in," equal amounts of variation occur at the output regardless of where the input is set.

However, the nonlinear function curve shows a definite difference in the amount of variation passed on to the output. In this case, having the input "x4 in" set near the flat part of the function curve will result in a dramatically reduced amount of variation passed on to the "y4 out" output when compared with "x3 in" vs. "y3 out." This is in spite of the fact that the variation of x3 equals x4.

What does the above curve comparison mean? It means that we should carefully consider that not all input causes are appropriate candidates for adjustment when setting the process on target. Those nonlinear inputs that might pass on excessive variation (compared with remaining inputs) should be identified and set to minimize this effect before the remaining linear input set points are selected. After this is done, the nonlinear functions should not be used as control parameters to adjust the process back on target. (If they were to be adjusted, we may be reintroducing greater variation transmission—a plausible explanation of why processes seem sometimes to be worse with greater variation after adjusting known inputs to restore the process on target.) By doing this with nonlinear inputs, we have exploited the nonlinear effect of transmitted variation to the output. We have taken advantage of the fact that nonlinear functions transmit far less variation at the flat part of their curves than at the steep part. Such action allows us to design products and processes that are much more immune to inevitable daily variation because we are minimizing any variation passed on by the nonlinear input to the output. We can call this important strategy Nonlinear Exploitation.

When choosing product feature target specifications and process set points to give us desired product feature targets, we must consider whether some of the product or process inputs are nonlinear to the output over a broad range of input values. That is, while it may appear that a given input seems to be linear in the region of current operating tolerances, that relationship might eventually be nonlinear at some other region of the curve.

If the slope for that input in the current operating region is high, then a greater amount of daily variation will be transmitted to the output. If the input set point were moved to a flat part of the curve, as we are doing with Nonlinear Exploitation, then less variation would be transmitted to the output.

We will never find that point if we experiment with the process within the existing specified tolerances. There is much to be gained in improved future quality by temporarily studying, with limited experimentation, beyond current tolerances to discover regions of minimized variation transmission. Such experimentation requires confident determination on the part of engineers (and support by their management) because of the potential to be realized.

We have been traditionally selecting process set points and product features assuming that the selected operating region for the relationship is linear. Even in cases where the relationship appears nonlinear, often times the relationship is transformed by taking the log or reciprocal, etc. to generate a linear relationship, presumably for a better way of presenting the relationship. Doing this obscures the opportunity for exploitation. While those relationships could appear linear, at some other settings for the input, the relationship could be discovered to be nonlinear.

The tendency has been to set the process on target, and then minimize the variation around that target by either tightening input specifications or screening final product to tighter tolerances. In the first case we have had limited success in reducing variation while also increasing the cost of processing. In the second case, any decrease in variation comes at a high cost and does not result in cost competitive quality. It also can result in questionable reliability.

When one considers the very nature of variation transmission by functional relationships, it can be seen that it is impossible to find regions of optimum output with minimized variation simultaneously. Can the sophisticated modeling tools achieve this objective? They may be able to discover operating conditions where the variation is less for near optimum output than the variation at other conditions of near optimum output, but that resulting lower variation will still be greater than the minimum possible if the nonlinear inputs were properly exploited in the first place.

An Exploration of Popular Methods

Several strategies have been introduced and widely used to focus on variation reduction. Despite their popularity, their usefulness is limited without nonlinear exploitation.

• Taguchi’s Parameter Design

The robust methods of Taguchi’s parameter design are in contrast to the more traditional techniques that have been used to try reaching the Deming objective. Although Taguchi methods have become quite popular, nevertheless, some writers prior to Taguchi warned of the consequences of variation transmission. Unfortunately, to the extent that Taguchi’s parameter design methods use existing tolerances as a starting point for minimizing variation, they very likely will miss the opportunities for discovering and exploiting those relationships that appear linear under current operating tolerances but are eventually nonlinear. The effect of parameter design "Noise Factors" could possibly be reduced or discounted if the design criteria were initially picked based on minimizing variation transmission of any nonlinears in the original design. The result would be a product or process tolerant of such influences.

If the objectives of minimizing variation around the process target that Deming highlighted were clearly defined and promoted in Taguchi parameter design methods, the impact of parameter design to achieve the Deming objective might have been far greater. However, the use of arcane statistics (signal to noise ratios) to characterize what is happening when minimizing variation in parameter design serves only to obfuscate the overall objective of variation reduction around the target that Deming clearly emphasized. In fact, signal to noise ratios (S/N) imply finding optimum mean level and variation simultaneously, which is not logically possible if true exploitation takes place as discussed earlier. It would come as no surprise to learn that a number of Japanese manufacturers achieved the Deming objective without knowledge or application of Taguchi methods.

• The Six Sigma View of Quality

The six sigma quality program articulates well the advantages of seeking the Deming goal and is very helpful in defining the statistical basis for such a goal. However, as a quality improvement program, it does not define specific strategies for accomplishing such goals and basically leaves it up to the individual organization to discover what methods might help achieve them. It also has somewhat diminished the impact of the Deming objective by translating its goals so that it is expressed in terms of parts per million defects, rather than minimized variation around the target. While this might seem more helpful to those who are not familiar with statistical distributions, it has a negative effect in the sense that those same persons may think that they can achieve six sigma objectives by merely screening and re-screening product until the p.p.m. goals have been achieved. This is clearly impossible for a number of reasons, not the least of which is the sample size necessary to assure that the p.p.m. goal has been met.

Six sigma quality will only be achieved by making appropriate changes to process inputs so that variation is reduced while maintaining the process on target (i.e. proactive quality). It can never be accomplished by screening (i.e. reactive quality) alone.

• The Scatter Plot Tool

Real quality improvement to reach the Deming objective by reducing variation around the target nominal requires a fundamental change in how the classic scatter plot quality tool is used. Traditionally, process targets have been set from curves derived by plotting each input vs. the output, while holding the remaining inputs constant. This tends to ignore the additive and possible interactive effects of these inputs. (The additivity of input effects to the process output becomes intuitive, however, as combinations of inputs are set to establish the process.)

After the scatter plot has been used to establish causation, we must determine whether that relationship is linear or nonlinear throughout the total function curve. By looking across the entire range of experimental values where measurements of cause and effect can be made (probably beyond the currently specified operating range), we may be able to discover a nonlinear function that might not have been observed within a more limited range.

Once nonlinear functions have been discovered in this manner, we can then exploit their tendency to minimized variation transmission at the flat part of their curve. Limited experimentation to establish this information should provide significant direction in determining where nonlinearity exists and could be exploited. Alternative strategies are available to minimize experimentation during this search for nonlinearity.

Empirical scatter plots should be used to first identify potential nonlinear functions in the product or process. After these have been identified and set to where variation transmission is minimized, the remaining input vs. output scatter plots can be used to set the product or process on target.

Logic shows that it must be a two step process. We cannot set nonlinear inputs to minimize variation while at the same time setting the remaining inputs to set the process on target. This is because resetting nonlinear inputs will move the output off target from where it is specified. Therefore, the remaining inputs should be set to compensate for the changes in the nonlinear inputs so that the output can be restored to its target value. This compensation should take place without increasing the minimized variation transmission achieved through the exploitation strategy. The end result will be having the output near or on target with minimized dispersion around that target, as specified by Deming.

It is noteworthy that this strategy proceeds from intuitive consideration of the basic functional relationships illustrated by simple scatter plots. While they may be helpful at some point in the application of the strategy, elegant statistical techniques and methods are not required to accomplish the objectives outlined here. Just as scatter plot techniques were used long before regression and other statistical methods were devised, so also the intuitive interpretation of those scatter plots can be made to discover the nature of variation transmission without sophisticated solutions.

This illustrates the fact that in our long journey to understand and discover how to characterize variation and to define it using the statistical sciences, we have overlooked an important aspect of just how variation is passed on from a cause to its effect. Since this is extremely important when transferring technology to production, much of the journey to optimization might have been shortened by recognition of this fact.

A Missing Step to Better Quality

We have, in fact, missed an important step in the application of the knowledge of quantifiable cause and effect relationships. We should not be predicting outcomes or selecting set points before we recognize the importance of variation transmission from the input to the output. We must first minimize this effect of variation transmission, and only then should we set remaining inputs for the output target selected. Any process optimization program that does not include as a first step the identification, isolation, and exploitation of nonlinear functions is missing an important step to better quality. Such a program will have to constantly deal with adjusting the process to correct for the "built in" nature of process variation due to the decisions made when establishing the process.

Important Questions for Exploitation

In seeking to achieve the Deming objective, we should be first asking some important questions:

1. Have we categorized all our known process inputs into either linear or nonlinear relationships throughout a broad enough range of quantifiable measurements so that nonlinearity can be discovered?
2. As a first step to establishing a process from such relationships, have we sought to exploit the nonlinears by setting them where they minimize variation transmission?
3. Last, have we compensated for the resulting shift in output level by resetting linear inputs so that the output is restored to its target level?

With processes already demonstrating the Deming objective (high C_pk’s), the strategy suggested here would be unnecessary. However, with quality problems in processes not centered on target that do demonstrate large dispersion, then considering these questions would be appropriate. If questions are raised that this technique is too time consuming or costly, some methods are available to help simplify the categorizing task implied in question #1 and the exploitation indicated in question #2. These methods will help reduce the experimentation necessary to answer the above questions.

We may now be at a pivotal moment with respect to our ability to compete on a global scale with the re-emergence of the Japanese economy. They have not been treading water while waiting for their revitalized economy to get stronger. This discussion is a call to all who are concerned with improving their manufacturing processes.

We need to better understand just how to more effectively transfer technology to the real world of manufacturing. We must recognize that we can no longer afford to ignore the implications of variation transmission. We must consider how the issue of variation transmission can be dealt with to improve quality in our process.

We who are concerned with optimizing manufacturing should not allow this issue to be obscured by complicated or highly technical approaches. As indicated earlier, the intuitive nature and simplicity of the exploitation strategy after examining scatter plots allows it to be implemented at a basic level without need of sophisticated techniques. (Such techniques serve their purpose for efficiently achieving the final optimization goals of the strategy.)

We no longer have the luxury of assuming that we can optimize the process through a time consuming learning curve that may or may not deal with the issues of nonlinear exploitation. In addition, the economic advantage from the exploitation strategy is substantial. That is, not only is output variation reduced giving higher production yields, but the opportunity is presented at the same time to relax input specifications, resulting in lower input costs to the process. The result is a double-barreled improvement in process productivity and quality and a win-win scenario for both producers and suppliers. This strategy, applied even in its most simple and intuitive form, can make significant strides in meeting the challenge of the Deming objective.

Ó Quality Information Systems 1997