Bootstrap confidence intervals of the difference between two generalized process capability indices for inverse Lindley distribution

Abstract

A process capability index (PCI) meant for assessing the capability of the concerned manufacturing process to manufacturer’s products as per specifications pre-set by the product designers or customers. In this article, we utilize bootstrap re-sampling simulation method to construct bootstrap confidence intervals, namely, standard bootstrap (s-boot), percentile bootstrap (p-boot), and bias-corrected percentile bootstrap (BCp-boot) for the difference between two indices ( $$C_\mathrm{pyk1}-C_\mathrm{pyk2}$$ ) through simulation when the underlying distribution is inverse Lindley distribution. Maximum-likelihood method is used to estimate the parameter of the model. The proposed bootstrap confidence intervals can be effectively employed to determine which one of the two processes or manufacturer’s (or supplier’s) has a better process capability. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the bootstrap confidence intervals of ( $$C_\mathrm{pyk1}-C_\mathrm{pyk2}$$ ). Simulation results showed that the estimated coverage probabilities of the standard bootstrap confidence interval perform better than their counterparts. Finally, a simulated data and a real data are presented to illustrate the bootstrap confidence intervals of the difference between two PCIs.