Bootstrap confidence intervals of CpTk for two parameter logistic exponential distribution with applications

Abstract

Process capability index is an important statistical technique that measures the ability of a process and hence it is used in quality control to quantify the relation between the actual performance of the process and the preset specification of the product. In this article bootstrap confidence intervals (BCIs) of generalized process capability index (GPCI) $$C_{pTk}$$ proposed by Maiti et al. (J Qual Technol Quant Manag 7(3):279–300, 2010) are studied through simulation when the underlying distribution is logistic-exponential (LE). The model parameters are estimated by the maximum likelihood method of estimation. Three non-parametric (NPR) as well as parametric (PR) BCIs, namely, percentile bootstrap ( $$\mathcal P$$ -boot), student’s t bootstrap ( $$\mathcal T$$ -boot) and bias-corrected percentile bootstrap ( $$\mathcal BC_p$$ -boot) are considered for obtaining confidence intervals (CIs) of GPCI $$C_{pTk}$$ . Through extensive Monte Carlo simulations, we examine the estimated coverage probabilities and average widths of the BCIs for two parameter LE distribution and in particular for exponential distribution. Simulation results show that the estimated coverage probabilities of the $$\mathcal P$$ -boot CI perform better than their counterparts. Finally, three real data sets are analyzed for illustrative purposes.