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Regret Indices and Capability Quantification

capability before the start of a process improvement program. New results would then unąuestionably represent an improvement if (when plotted using the same R function and ER and VR values) the new curve lies strictly above the historical CC curve. One obvious way this could happen would be for the new process distribution to yield smaller expected regret than the historical ER.

As time passes, you could update your historical database by (i) adding in recently observed results and, possibly, also by (ii) deleting some of the oldest results that are now least relevant to current operations. The numerical values of ER, VR, and EE would then also need to be updated, usually without changing the functional form or parameter settings of your regret function. This updating is likely to decrease ER (and possibly to decrease EE) when process improvements have indeed occurred. Notę that the numerical values of regret that lie strictly between the old and new values of ER will now have discordant new/old regret index values; if the new index value is greater than one because ER decreased, then the old index was less than one. In other words, the new and old CC(I) curves would cross if both were drawn on the same plot. Changes in the overall shape of the updated CC(I) curve will usually reveal whether or not EE decreased (index skewness and/or kurtosis increased), but changes in ER can be somewhat obfuscated when CC(I) is reparameterized. Therefore, process improvement programs should monitor decreases in ER as well as changes in the CC(I) curve over time.

EXAMPLE:    When regret is quadratic and the process distribution is

normal with mean on target as in an earlier example, the process improvement objective might be simply to reduce ER by decreasing <j².

On the other hand, there will be no change in EE = 0.5 as long as the process distribution remains normal. To decrease EE below 0.5, the process distribution must become morę leptokurtic than normal (fourth central moment morę than three times the square of the second central moment).

Other Capability Quantification Methodologies

Taguchi-like process capability indices, Cp , Cp^ and Cp_m, are summary statistics that provide much less complete characterizations of a process than does the fuli cumulative capability curve, but these sorts of summary statistics are widely used and prescribed; see Taguchi and Wu (1979), Hsiang and Taguchi (1985), Montgomery (1985), and Kane (1986). ANSI/ASQC Al-1987 States on page 16 that "standard measures of process capability have not achieved consensus at this time." But this publication also