Shikhar Tyagi

Fits and compares shared, correlated, additive, zero-inflated promotion cure-rate, and k-out-of-M one-shot device frailty survival models under Bayesian Markov chain Monte Carlo (MCMC) and Maximum Likelihood Estimation (MLE) frameworks. Supports ten baseline hazard distributions (Weibull, Exponential, Generalized Exponential, Exponential Power, Linear Failure Rate, Generalized Log-Logistic, Generalized Weibull, Generalized Rayleigh, Weighted Exponential, Extended Weibull) and eight frailty distributions (Gamma, Inverse Gaussian, Positive Stable, Compound Poisson, Compound Negative Binomial, Generalized Lindley, Weighted Lindley, Mixture of Inverse Gaussians). Implements reversed hazard rate (RHR) models for bivariate left-censored survival data, additive shared frailty models under random right censoring, and one-shot device reliability analysis. Provides goodness-of-fit testing, information criteria (AIC, BIC, AICc, HQIC, DIC, EAIC, EBIC, LPML), convergence diagnostics (Geweke, Gelman-Rubin, Heidelberger-Welch), Bayes factors, residual analyses, and diagnostic visualizations. Methodologies are based on Hanagal and Dabade (2013) , Hanagal and Dabade (2013) , Hanagal and Dabade (2015) , Hanagal and Bhambure (2015) , Hanagal and Bhambure (2016) , Hanagal, Pandey, and Ganguly (2017) , Hanagal and Pandey (2018) , Hanagal (2020) , Tyagi et al. (2021) , Pandey, Hanagal, Tyagi, and Gupta (2021) , Tyagi, Pandey, and Chesneau (2022) , Pandey, Hanagal, and Tyagi (2022) , Tyagi, Pandey, and Chesneau (2022) , Tyagi, Pandey, Hanagal, and Chesneau (2024) , Kiprotich et al. (2025) , Assuncao et al. (2026) , Chen et al. (1999) , Dunn and Smyth (1996) , Ling et al. (2021) , Yu, So, and Balakrishnan (2025) , Balakrishnan, Ling, and So (2021, ISBN:978-1-119-77795-3), and McGilchrist and Aisbett (1991) .

A comprehensive, generalized framework for computing, estimating, and validating Generalized Process Capability Indices (GPCIs). Supports user-supplied probability density functions (PDF/PMF), cumulative distribution functions (CDF), survival functions (SF), and quantile functions with uncensored data parameter estimation via Maximum Likelihood Estimation (MLE). Provides classical and non-normal capability indices, including Cpy (Maiti, Saha and Nanda, 2010) , Spmk (Dey and Saha, 2019) , CpTk (Saha, Dey and Maiti, 2019) , Cpc (Saha, Dey and Nadarajah, 2022) , CNpmc (Alotaibi, Dey and Saha, 2022) , CNpmkc (Saha, Tripathi and Dey, 2024) , CNpk (Saha, Dey and Maiti, 2018) , and Vannman capability indices. Computes parametric and non-parametric bootstrap confidence intervals at 90%, 95%, and 99% confidence levels using percentile, normal, basic, BCa, BCp, and studentized bootstrap methods. Evaluates Highest Posterior Density (HPD) intervals and Heidelberger-Welch convergence diagnostics. References: Maiti, Saha and Nanda (2010) , Saha, Dey and Maiti (2018) , Dey and Saha (2019) , Saha, Dey and Maiti (2019) , Alotaibi, Dey and Saha (2022) , Saha, Dey and Nadarajah (2022) , Saha, Tripathi and Dey (2024) .

Implements Bayesian parameter and Generalized Process Capability Indices (GPCIs) estimation using the Lindley approximation method (Lindley, 1980 ) under progressive Type-II censored data (Balakrishnan & Aggarwala, 2000 ). Evaluates point estimates and 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 (Vannman, 1995 ). Calculates point estimates, bias, mean squared error (MSE), Bayes risk under Linex and squared error loss, 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. Accommodates user-defined probability density/mass functions, cumulative distribution functions, and survival functions. Supports progressive parametric and non-parametric bootstrap confidence intervals (Efron, 1987 ) at 90%, 95%, and 99% significance levels.

Maximum likelihood estimation and reliability inference for Inverse Gaussian Process (IGP) degradation models with gamma and inverse Gaussian frailty terms, as formulated by Morita et al. (2021) . Classical IGP degradation models are described in Wasan (1968) and Meeker and Escobar (1998, ISBN:978-0471143284). The package provides tools for calculating lifetime cumulative distribution functions, probability density functions, lifetime quantiles with confidence intervals, posterior individual unit frailties, and goodness-of-fit diagnostics.

Evaluates Generalized Process Capability Indices (GPCIs) under Hybrid Type-II censored lifetime data using Importance Sampling (Sampling Importance Resampling, SIR). Implements Bayesian parameter estimation and evaluates classical and generalized capability indices including Cpy, Cp, Cpk, Cpu, Cpl, Cpm, Cpmk, Spmk, CpTk, Cpc, CNp, CNpk, CNpm, CNpmk, CNpmc, CNpmkc, and Vannman's Cp(u,v) family. Computes initial maximum likelihood estimates under Hybrid Type-II censoring, parameter MCMC chains, GPCI posterior chains, posterior point estimates, bias, mean squared error (MSE), Bayes risk, Highest Posterior Density (HPD) credible intervals at 90%, 95%, and 99% levels, Heidelberger and Welch's MCMC convergence diagnostics, and convergence probabilities. Accommodates user-defined probability density/mass functions, cumulative distribution functions, and survival functions. Goodness-of-fit testing for Hybrid Type-II censored data is supported via 'gofPHCS'. Methods are based on Childs et al. (2003) , Kundu and Pradhan (2009) , Maiti et al. (2010) , Dey and Saha (2019) , Alotaibi et al. (2022) , Saha et al. (2022) , and Saha et al. (2024) .

A comprehensive, generalized framework for computing, estimating, and validating Generalized Process Capability Indices (GPCIs) under Hybrid Type-II censored lifetime data. Supports user-supplied probability density or mass functions (PDF/PMF), cumulative distribution functions (CDF), survival functions (SF), and quantile functions. Parameter estimation under Hybrid Type-II censoring is performed via Maximum Likelihood Estimation using the 'MleCensoR' package (Childs et al., 2003 ; Balakrishnan & Kundu, 2013 ). Computes 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. Evaluates parametric and non-parametric bootstrap confidence intervals at 90 percent, 95 percent, and 99 percent levels of significance using percentile, normal, basic, BCa, BCp, and studentized bootstrap methods. Computes standard errors, mean squared errors, and coverage probabilities for both distribution parameters and capability indices. Integrates goodness-of-fit testing for Hybrid Type-II censored data via the 'gofPHCS' package.

Implements Random Forest regression under the Power Xgamma distribution error model. Provides core distribution functions (density, cumulative distribution, quantile, random generation, hazard, survival), parameter estimation via Expectation-Maximization (EM) and Markov Chain Monte Carlo (MCMC), non-parametric bootstrap confidence intervals (at 90%, 95%, and 99% levels), Highest Posterior Density (HPD) intervals, Heidelberger and Welch's MCMC convergence diagnostic, convergence probability, model evaluation metrics (estimated values, bias, mean squared error, risk value), homoscedastic prediction intervals, and goodness-of-fit diagnostic tests (Kolmogorov-Smirnov and Anderson-Darling tests, Akaike Information Criterion, and Bayesian Information Criterion). References: Tyagi et al. (2022, Int. J. Stat. Reliab. Eng., 9(1), 51-60); Breiman (2001) ; Wright and Ziegler (2017) ; Heidelberger and Welch (1983) ; Sen et al. (2016) .