Supplier selection by estimation and testing of differences between two process capability indices

Boyles (1994) proposed a measurement formula for the production yield of normal processes called S pk , which establishes the relationship between the manufacturing specifications and the actual process performance. In this article, we use this index to obtain the difference between two indices (S pk 1 −S pk 2 ) to select the better process capability of two processes or manufacturers (or suppliers). The difference between two process capability indices (S pk 1 −S pk 2 ), cannot be inferred statistically because of the complexity of the sampling probability theory. Thus, we utilize bootstrap methods namely, standard bootstrap ( SB ), percentile bootstrap ( PB ) and bias-corrected percentile bootstrap ( BCPB ) for the difference between two indices (S pk 1 −S pk 2 ) to obtain bootstrap confidence intervals (BCIs) through simulation study. In order to compare the proposed BCIs of (S pk 1 −S pk 2 ) in terms of coverage probabilities ( CPs ) and average width ( AW ) we carried out a Monte Carlo simulation study. Results of the simulation study show that the AW of the BCPB confidence interval performs better than other bootstrap methods. To illustrate the application of BCIs of (S pk 1 −S pk 2 ), one real data set is analyzed.