Lindley Approximation for Capability Indices under Hybrid Censoring

Provides a comprehensive framework for estimating Generalized Process Capability Indices (GPCIs) under Hybrid Type-II censored lifetime data using Lindley's 3rd-order approximation method (Lindley, 1980 ). Supports user-supplied probability density/mass functions (PDF/PMF), cumulative distribution functions (CDF), survival functions (SF), and quantile functions. Computes Maximum Likelihood Estimates (MLE) using the 'MleCensoR' package (Childs et al., 2003 ; Balakrishnan & Kundu, 2013 ) and Bayesian posterior expectations for classical and non-normal capability indices, including Cpy (Maiti et al., 2010 ), Spmk (Dey & Saha, 2019 ), CpTk (Saha et al., 2019), Cpc (Saha et al., 2022 ), CNpmc (Alotaibi et al., 2022 ), CNpmkc (Saha et al., 2024 ), CNpk (Saha et al., 2018 ), and Vannman's Cp(u,v) family. Generates posterior parameter and GPCI chains via sampling with burn-in and thinning, calculating Bias, Mean Squared Error (MSE), Bayes Risk (SEL and Linex), Highest Posterior Density (HPD) credible intervals at 90%, 95%, and 99% levels, and Heidelberger and Welch's MCMC Convergence Diagnostics (Heidelberger & Welch, 1983 ) with convergence probabilities. Evaluates parametric and non-parametric bootstrap confidence intervals (Percentile, Normal, Basic, BCp, BCa) at 90%, 95%, and 99% levels of significance. Integrates goodness-of-fit testing for Hybrid Type-II censored data via the 'gofPHCS' package.