A Unified Approach for Predicting Long- and Short-Term Capability Indices with Dependence on Manufacturing Target Bias

It is shown that the exact solution for the capability index (CPI) for Gaussian-distributed process with target bias can be expressed in terms of an unbiased CPI and a normalized target bias. The principal advantage of this specific formulation is that it facilitates evaluation of the degradation of the capability of the process due to bias between process mean and the process target. It is shown how this formalism, initially developed for the short-term process, is readily extended to long-term process for which the distribution is Gaussian. Readily isolated in the latter case are the two long-term CPI degrading effects, namely, process instability and target bias. Sufficient conditions to guarantee that long-term processes are distributed as Gaussian are discussed. Within the context of these assumed conditions, a new paradigm for a long-term locator ‘‘k’’ is proposed. For a three sigma process the results indicate that the exact CPI model is a less pessimistic predictor than both of the industry CPI models tested.