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)