On the bootstrap confidence intervals of the capability index C_(pk) for multiple process streams

摘要

Purpose - The present paper aims to present the results of a simulation study on the behavior of thernfour 95 percent bootstrap confidence intervals for estimating C_(pk) when collected data are from arnmultiple streams process.rnDesign/methodology/approach - A computer simulation study is developed to present thernbehavior of four 95 percent bootstrap confidence intervals, i.e. standard bootstrap (SB), percentilernbootstrap (PB), biased-corrected percentile bootstrap (BCPB), and biased-corrected and acceleratedrn(BCa) bootstrap for estimating the capability index C_(pk) of a multiple streams process. An analysis ofrnvariance using two factorial and three-stage nested designs is applied for experimental planning andrndata analysis.rnFindings - For multiple process streams, the relationship between the true value of C_(pk) and thernrequired sample size for effective experiment is presented. Based on the simulation study, therntwo-stream process always gives a higher coverage percentage of bootstrap confidence interval thanrnthe four-stream process. Meanwhile, BCPB and BCa intervals lead to better coverage percentage thanrnSB and PB intervals.rnPractical implications - Since a large number of process streams decreases the coveragernpercentage of the bootstrap confidence interval, it may be inappropriate to use the bootstrap methodrnfor constructing the confidence interval of a process capability index as the number of process streamsrnis large.rnOriginality/value - The present paper is the first work to explore the behavior of bootstraprnconfidence intervals for estimating the capability index C_(pk) of a multiple streams process. It isrnconcluded that the number of process streams definitively affects the performance of bootstraprnmethods.