Bootstrap Confidence Intervals for Process Capability Indices Using Semiparametric Approach

ABSTRACT Process capability indices (PCIs) are widely used to evaluate how well a process performs, typically under the assumption of normality. However, when the data are non‐normal or include censoring, traditional PCIs may produce inaccurate results. This study focuses on estimating the capability indices and under a piecewise exponential (PWE) distribution, specifically for right‐censored data. Three estimation methods are compared: maximum likelihood estimation (MLE), ordinary least squares (OLS), and a hybrid method based on their bias and mean squared error (MSE), using the quantile‐based approach proposed by Pearn and Chen for indices and . Simulation results show that MLE consistently outperforms OLS and the hybrid method, especially for small samples. Estimates of were closer to the target values and more stable than estimates. For both and , we evaluated generalized (GCI), asymptotic (ACI), and bootstrap confidence intervals (BCI; SB, PB, and BCPB). Among bootstrap intervals, BCPB performed well for , while for , bootstrap performance depended on sample size and rate settings. Comparing all intervals using average width (AW) and coverage probability (CP), it is observed that GCI achieved coverage closest to the nominal level (0.95) with smaller widths, particularly for small samples, compared with other methods. ACI performed well for moderate‐to‐large samples, and bootstrap interval performance varied by setting. Overall, MLE combined with GCI provides accurate and stable results for PCIs, especially in small samples, while all methods converge asymptotically as the sample size increases. These results were also confirmed using two real‐life datasets. Future studies can extend the rate configurations, use powerful estimation methods, and can also expand the methodology to other indices like and .