Modified estimation and confidence intervals of an asymmetric loss‐based process capability index Cpm′$\mathcal {C}^{\prime }_{pm}$

Abstract

Abstract In this article, we are interested to estimate a new capability index , which is based on asymmetric loss function (linear‐exponential) when the underlying process follows normal distribution. We estimate the parameters of the model using maximum likelihood method, bias‐corrected maximum likelihood method and bootstrap bias‐corrected maximum likelihood method and subsequently the process capability index (PCI) using the cited methods. Through extensive simulation studies, we compare the performances of the aforementioned methods of estimation for the PCI in terms of their absolute bias (AB) and MSEs. Besides, four bootstrap methods are employed for constructing the confidence intervals for the index by using the considered methods of estimation. The performances of the bootstrap confidence intervals (BCIs) are also compared in terms of average widths (AWs) and coverage probabilities (CPs) using Monte Carlo simulation. Finally, for illustrating the effectiveness of the proposed methods of estimation and BCIs, two real data sets from electronic industries are analyzed. All these data sets show that width of bias‐corrected accelerated bootstrap interval is minimum among all other considered BCIs.

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