00396 ‚90bd207e57c31bccb63bb276658de9

400

Obenchain

PROBGAM(x, p) = J* t^p_l e"* dt/r(p)    [28]

Then CC for the standardized gamma distribution of shape EE is simply CC(I) = PROBGAM(I • EE,EE). Similarly, using EÄ…uation (31) of Johnson and Kotz(1969, page 98), CC for the Poisson distribution of intensity EE is CC(I) = l-PROBGAM(EE,[I • EE]+1), where [pi here denotes the largest fuli integer in p. NotÄ™ in particular that, because the Poisson distribution is discrete, its CC(I) is not monotonie in EE; in fact, Poisson CC(1) is discontinuous at each integer value of EE.

Summary

A CC curve displays process yields (conformance fractions) for a spectrum of intervals indexed by their maximum relative cost and, thus, provides a complete Ä…uantification of process capability. CC curves are not only benchmarks against which we can measure Ä…uality improvement over time for a given process but also simple tools that enable (and, in fact, encourage) comparisons across diverse processes. CC methodology requires an initial parametric transformation of process measurements into regrets, but the remaining steps of a CC analysis can be non-parametric. Of possible methods for either smoothing an empirical CC curve or for forming composite indices (over time or across processes), the methods described here (based on Poisson or standardized gamma distributions) are not only straightforward but also seem to work well in actual practice.

Results from only the first two stages of CC analysis can form a basis for subseÄ…uent Ä…uality trend monitoring (with results displayed on the regret index scalÄ™) using Moving Average (finite window) methods. Powerful MA methods designed specilically for use with possibly composited ENs (i.e., the corresponding EEs may vary with reporting period) include QMP [Hoadley (1981,1986); Bellcore (1986,1987); Brush, Hoadley and Saperstein (1990)] and WAMOC [Obenchain (1993), Obenchain and Kenett (1993).]

Acknowledgments

I was introduced to several of the most basie concepts described here (e.g., the Index ScalÄ™, Poissonization, Composite Indices) by colleagues while I was working in the Quality Assurance Technology department of Bell Communications Research, 1983-1986. I must express my great indebtedness to Bruce Hoadley, John Healy, Debbie Guyton, Gary Brush, Rob Hausman, Jen