Inference on the Process Capability Index CNpmk Under Modified Multiple Interval Type‐I Censoring Using the Fréchet Distribution

This study is devoted to the estimation of the process capability index (PCI), , within the framework of the Fréchet distribution in the purview of modified version of a multiple interval type‐I censoring scheme. The estimation of is approached through three distinct methodologies: maximum likelihood estimation, maximum product spacing estimation, and a Bayesian framework. In the Bayesian paradigm, independent gamma priors are specified, and Bayes estimators of are derived under the squared error loss, general entropy loss and the LINEX loss functions. Inference is further augmented by constructing asymptotic confidence intervals and highest posterior density intervals. A comprehensive simulation study is undertaken to evaluate the finite‐sample performance of the proposed estimators in terms of mean squared error. Moreover, an optimal censoring scheme from a collection of potential schemes under various censoring scenarios has been investigated. The practical efficacy of the proposed methodologies is illustrated through the analysis of a real‐world data set.