Generalized Process Capability Indices for Progressive Type-II Censored Data using Importance Sampling

Shikhar Tyagi

2026-07-31

Introduction

The gpciProgTyIIImpSam package provides Bayesian parameter estimation and Generalized Process Capability Indices (GPCIs) under Progressive Type-II Censoring using Importance Sampling (Sampling Importance Resampling, SIR).

Supported capability indices include \(C_{py}\), \(C_p\), \(C_{pk}\), \(C_{pu}\), \(C_{pl}\), \(C_{pm}\), \(C_{pmk}\), \(S_{pmk}\), \(C_{pTk}\), \(C_{pc}\), \(C_{Np}\), \(C_{Npk}\), \(C_{Npm}\), \(C_{Npmk}\), \(C_{Npmc}\), \(C_{Npmkc}\), and Vännman’s \(C_p(u,v)\) family.

Example: Custom Exponential Distribution

library(gpciProgTyIIImpSam)

# 1. User-defined PDF, CDF, and Survival functions
my_pdf <- function(x, rate = 1) dexp(x, rate = rate)
my_cdf <- function(q, rate = 1) pexp(q, rate = rate)
my_surv <- function(q, rate = 1) pexp(q, rate = rate, lower.tail = FALSE)

# 2. Progressive Type-II Censored Failure Times and Removals
x_data <- c(0.8, 1.5, 2.3, 3.1, 4.2)
removals <- c(1, 0, 1, 0, 1)

# 3. Fit Importance Sampling GPCI Model
fit <- gpci_prog_ty2_impsam(
  x = x_data,
  r_removals = removals,
  pdf = my_pdf,
  cdf = my_cdf,
  surv = my_surv,
  start = c(rate = 0.5),
  chain_length = 500,
  burn_in = 100,
  thinning = 1,
  USL = 8,
  LSL = 0
)

# 4. View Results and Diagnostic Summary
print(fit)
summary(fit)