Lindley Approximation for Capability Indices under Progressive Censoring

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.

gpciLindApproxProgII: Lindley Approximation for Generalized Process Capability Indices under Progressive Type-II Censoring

Overview

The gpciLindApproxProgII package implements Bayesian estimation and Generalized Process Capability Indices (GPCIs) evaluation under Progressive Type-II Censoring using Lindley's 3rd-order approximation method.

Features

• Lindley 3rd-Order Approximation: Evaluates Bayesian posterior expectations for model parameters and 14 Generalized Process Capability Indices (Cpy, Cp, Cpk, Cpu, Cpl, Cpm, Cpmk, CpTk, Spmk, Cpc, CNpk, CNpmc, CNpmkc, Cp_uv).
• Flexible Distributions: Built-in Normal, Weibull, Gamma, Logistic-Exponential, and Exponentiated-Exponential distributions, plus full support for custom user-supplied PDF, CDF, SF, and QF functions.
• Sampling & Diagnostics: MCMC-style chain generation with customizable burn-in and thinning, Highest Posterior Density (HPD) credible intervals at 90%, 95%, and 99% levels, and Heidelberger-Welch convergence diagnostics.
• Progressive Resampling: Parametric and non-parametric bootstrap confidence intervals (Percentile, Normal, Basic, BCp) at 90%, 95%, and 99% confidence levels.

Installation

# Install from source package archive (.tar.gz)
install.packages("gpciLindApproxProgII_0.1.0.tar.gz", repos = NULL, type = "source")

Quick Example

library(gpciLindApproxProgII)

# Observed failure times and progressive removal counts
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)

# Fit model using Lindley approximation and chain generator
fit <- lindley_prog_gpci(
  x = x,
  r_removals = r,
  distribution = dist_weibull(),
  USL = 6,
  LSL = 0,
  chain_length = 500,
  burn_in = 100,
  thinning = 1,
  B = 100
)

# Print and summary
print(fit)
summary(fit)

# Plot posterior distributions and trace plots
plot(fit)