Package {gpciIntCensor}

Type:	Package
Title:	Generalized Process Capability Indices for Interval-Censored Data
Version:	0.1.0
Description:	A comprehensive framework for computing, estimating, and validating Generalized Process Capability Indices (GPCIs) under interval-censored data. Supports user-supplied probability density functions (PDF/PMF), cumulative distribution functions (CDF), and survival functions (SF). Parameter estimation is performed using Maximum Likelihood Estimation for interval-censored data via the MleCensoR package. Computes classical and generalized 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. Provides parametric and non-parametric bootstrap confidence intervals at 90%, 95%, and 99% confidence levels using percentile, normal, basic, BCa, BCp, and studentized bootstrap methods. Computes standard errors, mean squared errors, and coverage probabilities for both distribution parameters and capability indices. References: Maiti, Saha & Nanda (2010) <doi:10.1080/16843703.2010.11673233>, Saha, Dey & Maiti (2018) <doi:10.1080/21681015.2018.1437793>, Dey & Saha (2019) <doi:10.1007/s41872-019-00081-4>, Saha, Dey & Maiti (2019) <doi:10.1007/s13198-019-00789-7>, Alotaibi, Dey & Saha (2022) <doi:10.1155/2022/3135264>, Saha, Dey & Nadarajah (2022) <doi:10.1080/02664763.2021.1971632>, Saha, Tripathi & Dey (2024) <doi:10.1142/S021853932450013X>.
License:	MIT + file LICENSE
Encoding:	UTF-8
RoxygenNote:	7.3.3
Depends:	R (≥ 4.0.0)
Imports:	stats, graphics, numDeriv, boot, MleCensoR
Suggests:	testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder:	knitr
Config/testthat/edition:	3
NeedsCompilation:	no
Packaged:	2026-08-03 19:18:25 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Sumit Kumar [aut], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-08 13:00:02 UTC

Autoplot Generic and Methods for Compatibility

Description

Autoplot Generic and Methods for Compatibility

Usage

autoplot(object, ...)

## S3 method for class 'gpcifit_censor'
autoplot(object, ...)

## S3 method for class 'gpci_ci_censor'
autoplot(object, ...)

## S3 method for class 'gpci_diagnostics_censor'
autoplot(object, ...)

Arguments

Value

Invisible plot object.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
fit <- capability_censor(left, right, dist_norm, USL = 13, LSL = 7)
autoplot(fit)

Compute Bootstrap Confidence Intervals for Process Capability Indices (Interval-Censored Data)

Description

Runs parametric or non-parametric bootstrapping to compute confidence intervals for generalized process capability indices at multiple significance levels (90%, 95%, 99%) under interval-censored data.

Usage

boot_ci_censor(
  fit,
  B = 2000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCa", "BCp", "studentized"),
  type = c("parametric", "nonparametric"),
  parallel = FALSE,
  ncpus = 1
)

gpci_boot_censor(
  fit,
  B = 2000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCa", "BCp", "studentized"),
  type = c("parametric", "nonparametric"),
  parallel = FALSE,
  ncpus = 1
)

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

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

Arguments

Value

An object of class gpci_ci_censor.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
fit <- capability_censor(left, right, dist_norm, USL = 13, LSL = 7)
ci <- boot_ci_censor(fit, B = 100, alpha = c(0.10, 0.05, 0.01), method = "percentile")
print(ci)

Built-in Process Distributions for Interval-Censored Analysis

Description

Convenience constructors for standard process probability distributions.

Usage

dist_normal(mean = 0, sd = 1)

dist_lognormal(meanlog = 0, sdlog = 1)

dist_gamma(shape = 1, scale = 1)

dist_weibull(shape = 1, scale = 1)

dist_beta(shape1 = 1, shape2 = 1)

dist_logistic_exponential(shape = 1, scale = 1)

Arguments

Value

An object of class gpci_dist_censor.

Examples

dist_n <- dist_normal(mean = 10, sd = 2)
dist_le <- dist_logistic_exponential(shape = 1.5, scale = 0.5)

Compute Process Capability Indices for Interval-Censored Data

Description

Computes classical and generalized Process Capability Indices (PCIs) for interval-censored data.

Usage

capability_censor(
  data_left = NULL,
  data_right = NULL,
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = c("Cpy", "Cp", "Cpk", "Cpu", "Cpl", "Cpm", "Cpmk"),
  u = 1,
  v = 1,
  mode = c("moments", "quantile"),
  fit = TRUE,
  C0 = 1,
  C1 = 0,
  C2 = 1,
  tolerance_t = USL - LSL,
  P0 = 0.9973002,
  LDL = LSL,
  UDL = USL
)

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

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

## S3 method for class 'gpcifit_censor'
coef(object, what = c("indices", "parameters"), ...)

## S3 method for class 'gpcifit_censor'
vcov(object, ...)

## S3 method for class 'gpcifit_censor'
confint(
  object,
  parm = NULL,
  level = 0.95,
  B = 1000,
  method = "percentile",
  ...
)

Arguments

Value

An object of class gpcifit_censor.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
capability_censor(
  data_left = left, data_right = right,
  distribution = dist_norm,
  USL = 13, LSL = 7, target = 10,
  indices = c("Cpy", "Cp", "Cpk", "Cpm", "Cpmk"),
  mode = "moments"
)

Compute Standard Errors, MSE, and Coverage Probabilities for Interval-Censored Data

Description

Computes standard errors, mean squared errors, and coverage probabilities for distribution parameters and process capability indices using bootstrap results.

Usage

compute_diagnostics_censor(
  fit,
  true_params = NULL,
  true_indices = NULL,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01)
)

gpci_diagnostics_censor(
  fit,
  true_params = NULL,
  true_indices = NULL,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01)
)

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

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

Arguments

Value

A list of class gpci_diagnostics_censor.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
fit <- capability_censor(left, right, dist_norm, USL = 13, LSL = 7)
diagnostics <- compute_diagnostics_censor(fit, B = 100)
print(diagnostics)

Compute Theoretical Moments of an Interval-Censored Distribution

Description

Computes the theoretical mean and variance of a gpci_dist_censor object using numerical integration.

Usage

compute_theoretical_moments_censor(dist)

Arguments

Value

A list with mean and var.

Examples

dist_n <- dist_normal(mean = 5, sd = 1.5)
compute_theoretical_moments_censor(dist_n)

Define a Process Distribution for Interval-Censored Data

Description

Constructor to define a probability distribution for process capability analysis under interval-censored data.

Usage

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

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

Arguments

Value

An object of class gpci_dist_censor.

Examples

custom_weib <- define_distribution_censor(
  name = "custom_weibull",
  sf = function(x, shape, scale) pweibull(x, shape, scale, lower.tail = FALSE),
  params = list(shape = 2, scale = 10),
  support = c(0, Inf)
)

Fit Distribution Parameters under Interval-Censored Data

Description

Fits the parameters of a gpci_dist_censor distribution to interval-censored data using Maximum Likelihood Estimation (MLE) via the MleCensoR package.

Usage

fit_distribution_censor(data_left, data_right, dist, start = NULL)

gpci_fit_censor(data_left, data_right, dist, start = NULL)

Arguments

Value

A new gpci_dist_censor object containing fitted parameters.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
fit <- fit_distribution_censor(left, right, dist_norm)

Dispatcher for Single Index Computation under Interval Censoring

Description

Dispatcher for Single Index Computation under Interval Censoring

Usage

gpci_index(fit, index)

Arguments

Value

Numeric value of the specified index.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
fit <- capability_censor(left, right, dist_norm, USL = 13, LSL = 7)
gpci_index(fit, "Cpy")

Plot Method for gpci_ci_censor Objects

Description

Visualizes bootstrap confidence intervals across different significance levels.

Usage

## S3 method for class 'gpci_ci_censor'
plot(x, ...)

Arguments

Value

Invisible CI object x.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
fit <- capability_censor(left, right, dist_norm, USL = 13, LSL = 7)
ci <- boot_ci_censor(fit, B = 100, alpha = c(0.10, 0.05, 0.01), method = "percentile")
plot(ci)

Plot Method for gpci_diagnostics_censor Objects

Description

Visualizes standard errors for parameters and capability indices.

Usage

## S3 method for class 'gpci_diagnostics_censor'
plot(x, ...)

Arguments

Value

Invisible diagnostics object x.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
fit <- capability_censor(left, right, dist_norm, USL = 13, LSL = 7)
diag_obj <- compute_diagnostics_censor(fit, B = 100)
plot(diag_obj)

Plot Method for gpcifit_censor Objects

Description

Visualizes interval-censored observations, fitted distribution density curve, and specification limits.

Usage

## S3 method for class 'gpcifit_censor'
plot(x, main = "Process Capability Analysis (Interval-Censored)", ...)

Arguments

Value

Invisible fit object x.

Examples

dist_norm <- dist_normal()
left <- c(9.5, 10.2, 8.8, 11.1, 9.9)
right <- c(10.5, 11.2, 9.8, 12.1, 10.9)
fit <- capability_censor(left, right, dist_norm, USL = 13, LSL = 7)
plot(fit)