Estimation of the generalized process capability index C_pyk based on bias-corrected maximum-likelihood estimators for the generalized inverse Lindley distribution and bootstrap confidence intervals

Abstract

In this paper, we are interested in estimating the generalized process capability index ($C_{pyk}$) proposed by Maiti et al. [On generalizing process capability indices. Qual Technol Quant Manag. 2010;7(3):279–300], when the underlying distribution is the generalized inverse Lindley (GIL) distribution. We estimate parameters of the GIL distribution using maximum likelihood (ML), bias-corrected maximum-likelihood (BCML) and bootstrap bias-corrected maximum-likelihood (BBCML) methodologies. $C_{pyk}$ are obtained using proposed estimators. Bootstrap confidence intervals called standard bootstrap (SB), percentile bootstrap (PB) and bias-corrected percentile bootstrap (BCPB) $95\mathrm{\%}$ are constructed based on the estimators of $C_{pyk}$. We compare efficiencies of the parameter estimators and the performance of ML, BCML and BBCML based Cpyk via an extensive Monte Carlo simulation study. A simulation study is also described to compare the coverage probabilities (CP) and average lengths (AL) of SB, PB and BCPB confidence intervals for proposed $C_{pyk}$. Finally, two real datasets are analysed for illustrative purposes.

Keywords:

• Process capability index
• Bias correction
• maximum-likelihood estimators
• generalized inverse Lindley distribution
• bootstrap confidence intervals

Disclosure statement

No potential conflict of interest was reported by the author(s).