Package {gpciImpSam}

Type:	Package
Title:	Importance Sampling Estimation of Generalized Process Capability Indices
Version:	0.1.0
Description:	Provides a comprehensive generalized framework for parameter estimation and Generalized Process Capability Indices (GPCIs) under uncensored data using Importance Sampling (ImpSam). Supports user-supplied probability density functions (PDF/PMF), cumulative distribution functions (CDF), and survival functions (SF). Computes classical and generalized capability indices including Cpy (Maiti et al., 2010 <doi:10.1080/16843703.2010.11673233>), Spmk (Dey & Saha, 2019 <doi:10.1080/00949655.2019.1671980>), CpTk (Saha et al., 2019), Cpc (Saha et al., 2022 <doi:10.1080/02664763.2021.1971632>), CNpmc (Alotaibi et al., 2022 <doi:10.1155/2022/3135264>), CNpmkc (Saha et al., 2024 <doi:10.1142/S021853932450013X>), CNpk (Saha et al., 2018 <doi:10.1080/21681015.2018.1437793>), and Vannman's Cp(u,v) family. Generates parameter and GPCI MCMC chains via Sampling Importance Resampling (SIR) after burn-in and thinning. Provides point estimates, bias, MSE, risk values, Highest Posterior Density (HPD) intervals at 90, 95, and 99 percent levels of significance, Heidelberger and Welch MCMC convergence diagnostic, and convergence probability.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 4.0.0)
Imports:	stats, graphics, grDevices, numDeriv, boot
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder:	knitr
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-07-30 02:35:41 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-07 16:30:07 UTC

gpciImpSam: Importance Sampling Estimation of Generalized Process Capability Indices

Description

Provides a comprehensive generalized framework for parameter estimation and Generalized Process Capability Indices (GPCIs) under uncensored data using Importance Sampling (ImpSam). Supports user-supplied probability density functions (PDF/PMF), cumulative distribution functions (CDF), and survival functions (SF). Computes classical and generalized capability indices including Cpy (Maiti et al., 2010 doi:10.1080/16843703.2010.11673233), Spmk (Dey & Saha, 2019 doi:10.1080/00949655.2019.1671980), CpTk (Saha et al., 2019), Cpc (Saha et al., 2022 doi:10.1080/02664763.2021.1971632), CNpmc (Alotaibi et al., 2022 doi:10.1155/2022/3135264), CNpmkc (Saha et al., 2024 doi:10.1142/S021853932450013X), CNpk (Saha et al., 2018 doi:10.1080/21681015.2018.1437793), and Vannman's Cp(u,v) family. Generates parameter and GPCI MCMC chains via Sampling Importance Resampling (SIR) after burn-in and thinning. Provides point estimates, bias, MSE, risk values, Highest Posterior Density (HPD) intervals at 90, 95, and 99 percent levels of significance, Heidelberger and Welch MCMC convergence diagnostic, and convergence probability.

Author(s)

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

Compute Process Capability Indices (GPCIs)

Description

Computes classical and generalized Process Capability Indices for a given dataset or process distribution parameters under uncensored data.

Usage

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

Arguments

Value

A named numeric vector of evaluated GPCI values.

Examples

dist_n <- dist_normal(mean = 10, sd = 1.5)
capability(
  distribution = dist_n,
  USL = 15, LSL = 5, target = 10,
  indices = c("Cpy", "Cp", "Cpk", "Cpm", "Cpmk")
)

Theoretical Moments Computation for Process Distribution

Description

Computes numerical or analytical mean and variance for a gpci_dist object.

Usage

compute_theoretical_moments(distribution)

Arguments

Value

A list with mean and var.

Examples

compute_theoretical_moments(dist_normal(mean = 5, sd = 2))

Define a Process Distribution

Description

Constructor to define a probability distribution for process capability analysis. The distribution can be defined by specifying any one (or more) of its PDF/PMF, CDF, Survival Function (SF), or quantile function. Missing functions are numerically derived.

Usage

define_distribution(
  name,
  pdf = NULL,
  cdf = NULL,
  sf = NULL,
  quantile = NULL,
  params = list(),
  support = c(-Inf, Inf)
)

Arguments

Value

An object of class gpci_dist.

Examples

dist_norm <- define_distribution(
  name = "Normal",
  pdf = function(x, mean = 0, sd = 1) dnorm(x, mean, sd),
  cdf = function(x, mean = 0, sd = 1) pnorm(x, mean, sd),
  params = list(mean = 0, sd = 1),
  support = c(-Inf, Inf)
)

Standard Pre-defined Exponential Distribution

Description

Standard Pre-defined Exponential Distribution

Usage

dist_exponential(rate = 1)

Arguments

Value

A gpci_dist object.

Examples

d_exp <- dist_exponential(rate = 0.5)

Standard Pre-defined Gamma Distribution

Description

Standard Pre-defined Gamma Distribution

Usage

dist_gamma(shape = 1, rate = 1)

Arguments

Value

A gpci_dist object.

Examples

d_gam <- dist_gamma(shape = 2, rate = 1)

Pre-defined Logistic-Exponential Distribution

Description

Pre-defined Logistic-Exponential Distribution

Usage

dist_logistic_exponential(alpha = 1, lambda = 1)

Arguments

Value

A gpci_dist object.

Examples

d_le <- dist_logistic_exponential(alpha = 1, lambda = 1)

Standard Pre-defined Normal Distribution

Description

Standard Pre-defined Normal Distribution

Usage

dist_normal(mean = 0, sd = 1)

Arguments

Value

A gpci_dist object.

Examples

d_norm <- dist_normal(mean = 10, sd = 2)

Standard Pre-defined Weibull Distribution

Description

Standard Pre-defined Weibull Distribution

Usage

dist_weibull(shape = 1, scale = 1)

Arguments

Value

A gpci_dist object.

Examples

d_weib <- dist_weibull(shape = 2, scale = 5)

Uncensored Data Parameter Estimation via Maximum Likelihood

Description

Fits process distribution parameters to observed uncensored numeric data using Maximum Likelihood Estimation (MLE).

Usage

fit_distribution(data, distribution, method = "mle", initial = NULL)

Arguments

Value

An updated gpci_dist object with estimated parameters.

Examples

data_sample <- rnorm(100, mean = 10, sd = 2)
dist_fitted <- fit_distribution(data_sample, dist_normal())
dist_fitted$params

High-Level User Interface Function for Importance Sampling GPCIs

Description

Main user interface to fit uncensored data under Importance Sampling and evaluate GPCIs, returning point estimates, parameter chains, GPCI chains, HPD intervals, and convergence diagnostics.

Usage

gpci_impsam(
  data,
  pdf = NULL,
  cdf = NULL,
  sf = NULL,
  prior = NULL,
  chain_length = 1000,
  burn_in = 200,
  thinning = 1,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = NULL
)

Arguments

Value

A list of class "gpciImpSam" with full summary results.

Examples

gpci_impsam(
  data = rnorm(50, 10, 1),
  pdf = function(x, mean = 0, sd = 1) dnorm(x, mean, sd),
  cdf = function(x, mean = 0, sd = 1) pnorm(x, mean, sd),
  chain_length = 300, burn_in = 50,
  USL = 13, LSL = 7
)

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 the Highest Posterior Density (HPD) interval for MCMC posterior samples at specified confidence / significance levels (e.g., 90%, 95%, 99%).

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 MCMC Chain Generator for Process Capability Indices

Description

Generates posterior parameter draws and Generalized Process Capability Index (GPCI) chains using Importance Sampling (Sampling Importance Resampling, SIR) for uncensored data.

Usage

impsam_gpci(
  data,
  distribution,
  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 "gpciImpSam" containing:

Examples

data_x <- rnorm(50, mean = 10, sd = 1)
dist_norm <- dist_normal()
fit_imp <- impsam_gpci(
  data = data_x,
  distribution = dist_norm,
  chain_length = 500,
  burn_in = 100,
  thinning = 1,
  USL = 13, LSL = 7
)

Plot Method for gpciImpSam Objects

Description

Visualizes GPCI posterior density distributions, trace plots, and HPD intervals.

Usage

## S3 method for class 'gpciImpSam'
plot(x, type = c("density", "trace"), index = NULL, ...)

Arguments

Value

Invisible NULL.

Examples

data_x <- rnorm(40, mean = 10, sd = 1)
fit <- impsam_gpci(data = data_x, distribution = dist_normal(), USL = 13, LSL = 7)
plot(fit, type = "density", index = "Cpy")

Safe Numerical Integration Helper

Description

Evaluates definite integral of a 1D function safely with error handling and fallback bounds.

Usage

safe_integrate(f, lower, upper, ...)

Arguments

Value

Numeric scalar representing the integral value.

Safe Root Finder Helper

Description

Solves 1D non-linear equation f(x) = 0 safely within given interval.

Usage

safe_uniroot(f, interval, ...)

Arguments

Value

Numeric scalar solution.

Summary and Diagnostics for gpciImpSam Objects

Description

Computes estimated value, bias, MSE, Risk value, HPD intervals at 90%, 95%, and 99% significance levels, Heidelberger and Welch MCMC convergence diagnostic, and convergence probability.

Usage

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

Arguments

Value

A data frame containing diagnostic metrics for each evaluated GPCI.

Examples

data_x <- rnorm(40, mean = 10, sd = 1)
fit_imp <- impsam_gpci(data = data_x, distribution = dist_normal(), USL = 13, LSL = 7)
summary(fit_imp)