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Regret Indices and Capability Quantification

distribution, with 23 out of 31 indices again being in the desirable "Iow" rangÄ™ less than 1.0.

Absolute Value The observed mean value of absolute value regret on the 31 samples was 5.87 ml, and this value was rounded up to set the quality standard at ER = 6 ml. The extreme observed fill-volume values of 51 and 98 ml are not accentuated here. For example, a fili value of 82 ml yields absolute value regret 7 ml, and the corresponding performance index would be 1=7/6=1.17. NotÄ™ that the histogram of absolute value indices has skewness intermediate between the inverted normal and logistic cases.

Fili volume summary statistics are given in Table 1.

AdyÄ…ntages and Disadyantages of Common Regret Functions The main distinction between the four fundamental forms of yariables-data regret discussed here (Ä…uadratic, inyerted normal, absolute value, and logistic) lies in their implied treatment of both outliers and inliers. Outliers are "maverick" yalues that deviate wildly from their intended target; like the 51 ml and 98 ml readings collected when 75 ml was our fill-volume target value. And inliers are the "cream-of-the-crop" of current production that fali close to their target.

Quadratic regret actually accentuates outliers. One or two outlying yalues are sufficient to ruin the overall rating of a very large batch of production when regret is Ä…uadratic. One absolutely must prevent wild outliers from occurring if one is to haye any hope of performance improvement under Ä…uadratic regret; nothing else counts nearly so much as avoiding those few "big mistakes."

Logistic regret focuses attention, instead, upon inliers...the obseryed yalues that are already most close to their intended target. Outliers have almost no effect because logistic regret is absolutely fiat in its tails. But logistic regret is steep [and comes to a sharp "point"! at its target. The only way to demonstrate a major performance improvement under logistic regret (at least when H is relatiyely smali) is to dramatically increase your proportion of production that are inliers; you must focus on making the very best part of your current production eyen better. When H is relatiyely large (ER is relatiyely smali), logistic regret tends to behave very much like absolute value regret.

Absolute yalue regret almost always represents a middle-ground position between the extremes represented by the Ä…uadratic and logistic regret options. Absolute value regret doesn’t create any new outliers that don’t already exist in a sample of X measurements. Quality improvements of any given magnitude then count eÄ…ually regardless of where they occur along the X axis.