Package {gpciProgTyIIImpSam}

Type:	Package
Title:	Generalized Process Capability Indices for Progressive Type-II Censored Data using Importance Sampling
Version:	0.1.0
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Description:	Implements Importance Sampling (Sampling Importance Resampling, SIR) for Bayesian parameter estimation and Generalized Process Capability Indices (GPCIs) under progressive Type-II censored data. 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 uncensored estimates, parameter MCMC chains, GPCI posterior chains, point estimates, posterior means, bias, mean squared error (MSE), Bayes risk under loss functions, 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. Methods based on Balakrishnan and Aggarwala (2000) <doi:10.1007/978-1-4612-1186-0>, Maiti et al. (2010) <doi:10.1080/16843703.2010.11673233>, Dey and Saha (2019) <doi:10.1007/s41872-019-00081-4>, Alotaibi et al. (2022) <doi:10.1155/2022/3135264>, Saha et al. (2022) <doi:10.1080/02664763.2021.1971632>, and Saha et al. (2024) <doi:10.1142/S021853932450013X>.
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding:	UTF-8
RoxygenNote:	7.3.3
Imports:	stats, graphics
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder:	knitr
NeedsCompilation:	no
Packaged:	2026-07-31 01:45:46 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Sumit Kumar [aut], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Repository:	CRAN
Date/Publication:	2026-08-07 21:00:02 UTC

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

Description

Implements Importance Sampling (Sampling Importance Resampling, SIR) for Bayesian parameter estimation and Generalized Process Capability Indices (GPCIs) under progressive Type-II censored data. 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 uncensored estimates, parameter MCMC chains, GPCI posterior chains, point estimates, posterior means, bias, mean squared error (MSE), Bayes risk under loss functions, Highest Posterior Density (HPD) credible intervals at 90

Author(s)

Maintainer: Shikhar Tyagi shikhar1093tyagi@gmail.com (ORCID)

Authors:

• Sumit Kumar stats.sumitbhal@gmail.com

• Arvind Pandey arvindmzu@gmail.com

• Bhupendra Singh bhupendra.rana@gmail.com

• Vrijesh Tripathi vrijesh.tripathi@uwi.edu

Compute Process Capability Indices (GPCIs)

Description

Evaluates classical and generalized Process Capability Indices for specified process parameters and specification limits.

Usage

capability(
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = NULL,
  u = 1,
  v = 1,
  mode = c("moments", "quantile"),
  C0 = 1,
  C1 = 0,
  C2 = 1,
  tolerance_t = USL - LSL,
  P0 = 0.9973002
)

Arguments

Value

A named numeric vector of computed GPCI values.

Examples

dist_norm <- dist_normal(mean = 10, sd = 1.5)
capability(
  distribution = dist_norm,
  USL = 15, LSL = 5, target = 10
)

Compute Theoretical Moments of a Distribution

Description

Estimates theoretical mean and variance of a distribution object using numerical integration.

Usage

compute_theoretical_moments(distribution)

Arguments

Value

A list containing mean and var.

Define a Custom Distribution Object

Description

Creates a gpci_dist distribution object containing probability density/mass function (PDF/PMF), cumulative distribution function (CDF), survival function (SF), quantile function, parameter names, and support boundaries.

Usage

define_distribution(
  name = "Custom",
  pdf = NULL,
  cdf = NULL,
  sf = NULL,
  quantile = NULL,
  param_names = NULL,
  default_params = list(),
  support = c(-Inf, Inf)
)

Arguments

Value

An object of class "gpci_dist".

Examples

dist_custom <- define_distribution(
  name = "ExpCustom",
  pdf = function(x, rate = 1) dexp(x, rate = rate),
  cdf = function(q, rate = 1) pexp(q, rate = rate),
  sf = function(q, rate = 1) pexp(q, rate = rate, lower.tail = FALSE),
  param_names = "rate",
  default_params = list(rate = 1),
  support = c(0, Inf)
)

Exponential Distribution Object Constructor

Description

Exponential Distribution Object Constructor

Usage

dist_exponential(rate = 1)

Arguments

Value

A gpci_dist object.

Gamma Distribution Object Constructor

Description

Gamma Distribution Object Constructor

Usage

dist_gamma(shape = 1, rate = 1)

Arguments

Value

A gpci_dist object.

Logistic-Exponential Distribution Object Constructor

Description

Logistic-Exponential Distribution Object Constructor

Usage

dist_logistic_exp(alpha = 1, lambda = 1)

Arguments

Value

A gpci_dist object.

Normal Distribution Object Constructor

Description

Normal Distribution Object Constructor

Usage

dist_normal(mean = 0, sd = 1)

Arguments

Value

A gpci_dist object.

Weibull Distribution Object Constructor

Description

Weibull Distribution Object Constructor

Usage

dist_weibull(shape = 1, scale = 1)

Arguments

Value

A gpci_dist object.

Importance Sampling Estimation of GPCIs under Progressive Type-II Censoring

Description

Main high-level user interface function to compute Generalized Process Capability Indices (GPCIs) under Progressive Type-II Censored Data using Importance Sampling (Sampling Importance Resampling, SIR). Fits parameter estimates under uncensored and progressive censoring, generates parameter and GPCI chains, and evaluates point estimates, posterior means, bias, MSE, Linex/SEL Bayes risk, 90 percent, 95 percent, and 99 percent HPD credible intervals, Heidelberger and Welch MCMC convergence diagnostics, and convergence probabilities.

Usage

gpci_prog_ty2_impsam(
  x,
  r_removals = NULL,
  distribution = NULL,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  quantile = NULL,
  param_names = NULL,
  start = NULL,
  prior = NULL,
  chain_length = 1000,
  burn_in = 200,
  thinning = 1,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = NULL,
  u = 1,
  v = 1,
  C0 = 1,
  C1 = 0,
  C2 = 1,
  P0 = 0.9973002
)

Arguments

Value

An object of class "gpciProgTyIIImpSam" containing fit details and diagnostic metrics.

Examples

# Example using custom functions for Exponential distribution
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)
data_x <- c(0.8, 1.5, 2.3, 3.1, 4.2)
removals <- c(1, 0, 1, 0, 1)
fit <- gpci_prog_ty2_impsam(
  x = data_x, 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
)
print(fit)

Heidelberger and Welch's MCMC Convergence Diagnostic

Description

Conducts stationarity and relative half-width tests under Heidelberger and Welch's MCMC convergence diagnostic, returning test statistics, status, and convergence probability.

Usage

heidelberger_welch(x, alpha = 0.05, eps = 0.1)

Arguments

Value

A list containing Cramér-von Mises statistic (stat), p-value (pvalue), stationarity test status (passed), half-width test status (hw_passed), half-width statistic (hw_stat), and convergence probability (convergence_prob).

Examples

samples <- rnorm(1000)
heidelberger_welch(samples)

Highest Posterior Density (HPD) Interval Calculation

Description

Computes Highest Posterior Density (HPD) credible interval for posterior draws at specified confidence / significance levels (e.g., 90 percent, 95 percent, 99 percent).

Usage

hpd_interval(x, prob = 0.95)

Arguments

Value

A named numeric vector of length 2 containing lower and upper bounds.

Examples

samples <- rnorm(1000, mean = 5, sd = 1)
hpd_interval(samples, prob = 0.95)

Importance Sampling for Progressive Type-II Censored Data

Description

Generates posterior parameter draws and Generalized Process Capability Index (GPCI) chains using Importance Sampling (Sampling Importance Resampling, SIR) for progressive Type-II censored data.

Usage

impsam_prog_ty2(
  x,
  r_removals = NULL,
  distribution,
  start = NULL,
  prior = NULL,
  chain_length = 1000,
  burn_in = 200,
  thinning = 1,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = NULL,
  u = 1,
  v = 1,
  C0 = 1,
  C1 = 0,
  C2 = 1,
  P0 = 0.9973002
)

Arguments

Value

A list of class "gpciProgTyIIImpSam" containing parameter chain, GPCI chain, and point estimates.

Examples

dist_exp <- dist_exponential(rate = 0.5)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- impsam_prog_ty2(
  x = x,
  r_removals = r,
  distribution = dist_exp,
  chain_length = 500,
  burn_in = 100,
  thinning = 1,
  USL = 8,
  LSL = 0
)

Plot Method for gpciProgTyIIImpSam Objects

Description

Visualizes diagnostic traceplots, posterior probability density functions, and Highest Posterior Density (HPD) credibility intervals for evaluated Generalized Process Capability Indices (GPCIs).

Usage

## S3 method for class 'gpciProgTyIIImpSam'
plot(x, type = c("density", "trace", "hpd"), indices = NULL, ...)

Arguments

Value

No return value, called for side effects.

Examples

dist_exp <- dist_exponential(rate = 0.5)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- impsam_prog_ty2(x = x, r_removals = r, distribution = dist_exp, USL = 8, LSL = 0)
plot(fit, type = "density")

Print Method for gpciProgTyIIImpSam Objects

Description

Print Method for gpciProgTyIIImpSam Objects

Usage

## S3 method for class 'gpciProgTyIIImpSam'
print(x, ...)

Arguments

Value

Invisibly returns x.

Summary and Diagnostics for gpciProgTyIIImpSam Objects

Description

Computes estimated value, bias, MSE, Risk value, HPD intervals at 90 percent, 95 percent, and 99 percent significance levels, Heidelberger and Welch MCMC convergence diagnostics, and convergence probabilities for each evaluated GPCI.

Usage

## S3 method for class 'gpciProgTyIIImpSam'
summary(object, ...)

Arguments

Value

A data frame containing diagnostic metrics for each evaluated GPCI.

Examples

dist_exp <- dist_exponential(rate = 0.5)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- impsam_prog_ty2(x = x, r_removals = r, distribution = dist_exp, USL = 8, LSL = 0)
summary(fit)

Validate Progressive Type-II Censored Data

Description

Validate Progressive Type-II Censored Data

Usage

validate_prog_data(x, r_removals = NULL)

Arguments

Value

A list containing cleaned x and r_removals.