Bootstrap Lower Confidence Limits for Capability Indices

Abstract

The indices Cp, Cpk, and Cpm are widely used to estimate whether a process is capable. Recently, techniques and tables were developed to construct lower 95% confidence limits for each index. These techniques, however, assume the underlying process is normally distributed, and processes that are modestly nonnormal do occur and can be hard to detect. Therefore, three nonparametric bootstrap lower confidence limits are proposed for each of these indices. A simulation using three distributions (one normal and two nonnormal) was conducted, and a comparison was made of the performances of the bootstrap and the parametric estimates. The simulation demonstrated that in the normal process environment the bootstrap confidence limits perform comparably to confidence limits based on normality and in nonnormal process environments the bootstrap estimates perform significantly better.

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