Bootstrap Confidence Interval of the Difference Between Two Process Capability Indices

The process capability index, C_pk, is extensively used to assess process performance in manufacturing industry. Statistical hypothesis testing or an interval estimation of a single C_pk had been derived under a normally distributed process. However, the difference between two process capability indices, C_pk

₁ - C _{pk 2} , cannot be inferred statistically because of the complexity of the sampling probability theory. This study proposes a bootstrap resampling simulation method to construct the biased corrected percentile bootstrap (BCPB) confidence interval of (C _{pk 1} - C _{pk 2} ), which can be used to select the better of two suppliers. The various simulation results indicate that the bootstrap confidence interval of (C _{pk 1} - C _{pk 2} ) can be employed to evaluate effectively the difference between the performance of two suppliers.