Generalized interval estimation of process capability indices for the Birnbaum–Saunders distribution

Abstract

Abstract Since sampling variation would lead to the inaccurate assessment of process capability indices (PCIs), the interval estimation of PCIs has received considerable attention recently. The coverage probabilities (CPs) of the widely used bootstrap confidence intervals (BCIs) of PCIs are not sufficiently close to their nominal confidence level. Moreover, the bootstrap method is time‐consuming. This paper develops a procedure for constructing generalized confidence intervals (GCIs) of two widely used percentile‐based PCIs for the Birnbaum–Saunders (BS) distribution. A simulation study is conducted and the results indicate that the proposed GCI outperforms its bootstrap counterparts in terms of the CPs, the average widths (AWs) of the confidence intervals, and the variability of the interval widths. Finally, two real examples are used to illustrate the implementation of the proposed procedure.

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