Comparison of Two Generalized Process Capability Indices by using Bootstrap Confidence Intervals

Process capability index (PCI) is used to quantify the relation between the actual performance of the process and the pre-set specifications of the product. In this article, we utilize bootstrap re-sampling simulation method to construct bootstrap confidence intervals, namely, standard bootstrap (SB) and percentile bootstrap (PB) of the difference between two generalized process capability indices (   to select the better of two processes or manufacturer’s/supplier’s through simulation when the underlying distribution is normal distribution. The distribution of  difference between two processes or manufacturer’s/supplier’s capability indices cannot be inferred statistically. Thus, we use bootstrap re- sampling simulation technique to construct bootstrap confidence intervals of . Maximum likelihood method of estimation is used to estimate the parameters of the model. The proposed two bootstrap confidence intervals can be effectively employed to determine which one between the two processes or manufacturer’s/supplier’s has a better process capability. Monte Carlo simulations are performed to compare the performances of the proposed bootstrap confidence intervals for δ in terms of their estimated average widths and corresponding coverage probabilities. Simulation results showed that the average widths of the PB confidence interval perform better than their counterparts.  Finally, two real data sets are presented to illustrate the bootstrap confidence intervals of the difference between two process capability indices.