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Obenchain

Introduction

We describe ways to use cost-of-poor-quality concepts in ąuality improvement programs by construction of Cumulative Capability (CC) curves. Three simple steps are required to construct empirical CC curves (such as those in Figures 8 and 14) from samples of observations on almost any quantitative process characteristic.

1.    Use a parametric loss function to convert the observed values into surrogate measures of cost-of-poor-quality.

2.    Rescale the observed losses so that they have expected value one.

3.    Construct the empirical distribution function of the rescaled losses.

CC curves constructed in this way quantify process yields (conformance fractions) corresponding to a entire class of intervals. These intervals are commonly all those with equal, maximum loss at their two end-points. For example, when one's loss function is both 2-to-l (as defined below) and symmetric about the target, the CC curve quantifies observed yields for all intervals symmetric about that target.

CC curves provide a much morę relevant and complete characterization of capability than can be conveyed by any single, summary statistic such as the Cp-type indices in common use today. Rodriguez (1992) summarizes many wefi-known problems with Cp , Cp^ and Cp_m indices; distinctions between Cp -type indices and CC curves are discussed nere. We do not give new advice on how to detect special causes or how to identify uncontrolled factors that have inflated common cause variation. Rather, we assume that standard capability/process improvement study methods, as described in Gunter (1991a,b,c,d,e) say, have already been applied.

The Three Staees of CC Implementation In the flrst stage, our task is to convert any observed deviation in a quantitative process characteristic from its intended target value into a measure of economic loss. These loss values are proxy or surrogate measures of cost-of-poor-quality (dissatisfaction) from the point-of-view of customers and/or regulators. Several simple but versatile forms of loss functions are illustrated below in our section on "Loss/Regret Concepts." Thus, we start out by deliberately making a (parametric) transformation of observed data in order to express their deviations from target in the "language of money," Faltin (1993).

In the second stage, we examine (and possibly smooth) the observed marginal distribution of loss in order to set quality standards. In other words,