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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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Notes on contributors
Leroy A. Franklin
Dr. Franklin is a Professor of Statistics and Decision Sciences in the Department of Systems and Decision Sciences in the School of Business. He is a Senior Member of ASQC.
Gary S. Wasserman
Dr. Wasserman is an Associate Professor in the Department of Industrial and Manufacturing Engineering. He is a Member of ASQC.