On the bootstrap confidence intervals of the capability index Cpk for multiple process streams

Abstract

PurposeThe present paper aims to present the results of a simulation study on the behavior of the four 95 percent bootstrap confidence intervals for estimating Cpk when collected data are from a multiple streams process.Design/methodology/approachA computer simulation study is developed to present the behavior of four 95 percent bootstrap confidence intervals, i.e. standard bootstrap (SB), percentile bootstrap (PB), biased‐corrected percentile bootstrap (BCPB), and biased‐corrected and accelerated (BCa) bootstrap for estimating the capability index Cpk of a multiple streams process. An analysis of variance using two factorial and three‐stage nested designs is applied for experimental planning and data analysis.FindingsFor multiple process streams, the relationship between the true value of Cpk and the required sample size for effective experiment is presented. Based on the simulation study, the two‐stream process always gives a higher coverage percentage of bootstrap confidence interval than the four‐stream process. Meanwhile, BCPB and BCa intervals lead to better coverage percentage than SB and PB intervals.Practical implicationsSince a large number of process streams decreases the coverage percentage of the bootstrap confidence interval, it may be inappropriate to use the bootstrap method for constructing the confidence interval of a process capability index as the number of process streams is large.Originality/valueThe present paper is the first work to explore the behavior of bootstrap confidence intervals for estimating the capability index Cpk of a multiple streams process. It is concluded that the number of process streams definitively affects the performance of bootstrap methods.