On the bootstrap confidence intervals of the capability index C-pk for multiple process streams
Purpose - The present paper aims to present the results of a simulation study on the behavior of the four 95 percent bootstrap confidence intervals for estimating C-pk when collected data are from a multiple streams process. Design/methodology/approach - A 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 C-pk 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. Findings - For multiple process streams, the relationship between the true value Of C-pk 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 implications - Since 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/value - The present paper is the first work to explore the behavior of bootstrap confidence intervals for estimating the capability index C-pk of a multiple streams process. It is concluded that the number of process streams definitively affects the performance of bootstrap methods.
simulation analysis of variance process analysis