Abstract
In this paper, we are interested in estimating the generalized process capability index () 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.
are obtained using proposed estimators. Bootstrap confidence intervals called standard bootstrap (SB), percentile bootstrap (PB) and bias-corrected percentile bootstrap (BCPB)
are constructed based on the estimators of
. 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
. Finally, two real datasets are analysed for illustrative purposes.
Disclosure statement
No potential conflict of interest was reported by the author(s).