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Obenchain

A regret function can only hope to characterize the long-term costs that would collapse to zero if the distribution of X were to became concentrated precisely at the target, T. For example, regret can be thought of as representing not only intemal rework/scrap costs but also extemally motivated losses in market-share resulting from customer dissatisfaction, regulatory disapproval, product recall and/or inventory shortage.

The freedom to express a regret function in terms of any convenient, arbitrary units of measure is a major advantage of the performance index approach described here. Later, we will argue that one's choice of the constant factor, K, used in defining regrets above turns out to be totally unimportant. Thus we can take K = 1 so that the maximum value for a bounded regret will be 1 Just as in the goal-posts regret case of [2],

In other words, one's chosen regret parametrization need only provide a reasonable measure of relative long-term costs for all pairs of X values. Specifically, if Xj and X2 are any pair of quality measurements with R(X2) > 0, then a sufficient condition for adequacy of a regret parametrization is that the ratio of R(Xj) to R(X2) be a reasonable proxy or surrogate for the corresponding ratio of true long-term costs. NotÄ™ that this ratio may depend only upon the relative probabilities of customer rejection or regulatory disapproval at Xj and X2; the total economic impact of rejection/disapproval does not need to be known as long as it would always be the same at all X values.

What Other Functional Forms of Regret Can Be Usefiil in Practice? Inaddition to the five basie "symmetric-about-the-target" shapes illustrated above, variations that I have found usefiil include:

-    regrets that are asymmetric in the sense that they use different X scaling to the left and right of the target (but the same basie shape on both sides); or

-    regrets that use different basie shapes to the left and right of the target (for example, regret may be identically zero on one side of the target.)

For example, my personal Computer capability quantification software (see Appendix) allows the user to select his/her regret function from any of 10 parametric families each requiring either one or two X inputs.

How Does One Get Started Using Regret Concepts? Given a set of X data, our primary stage-one CC task is to convert the observed X values into regrets. This step requires us to pick a target value, T, and specify a functional form for