Package 'gpciProgTyII' reference manual

Title:	Generalized Process Capability Indices under Progressive Type-II Censoring
Description:	Provides a comprehensive generalized framework for parameter estimation and Generalized Process Capability Indices (GPCIs) under Progressive Type-II censored data using the MleCensoR package. Accepts 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:10.1007/s41872-019-00081-4>), 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. Evaluates parametric and non-parametric bootstrap confidence intervals at 90%, 95%, and 99% levels of significance. Computes Standard Errors, Mean Squared Error (MSE), Bias, and Coverage Probabilities for model parameters and capability indices. References: Balakrishnan & Aggarwala (2000) <doi:10.1007/978-1-4612-1186-0>, 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), 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>.
Authors:	Shikhar Tyagi [aut, cre] (ORCID: <https://orcid.org/0000-0003-1606-0844>), Sumit Kumar [aut], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <[email protected]>
License:	MIT + file LICENSE
Version:	0.1.0
Built:	2026-10-11 12:31:40 UTC
Source:	https://github.com/cran/gpciProgTyII

Bootstrap Confidence Intervals and Performance Evaluation for Progressive Type-II GPCI

Description

Computes parametric and non-parametric bootstrap confidence intervals for Generalized Process Capability Indices (GPCIs) and model parameters under progressive Type-II censoring at 90%, 95%, and 99% significance levels.

Usage

boot_ci_prog(
  fit,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCp", "BCa", "studentized"),
  type = c("parametric", "nonparametric")
)

gpc_boot(
  fit,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCp", "BCa", "studentized"),
  type = c("parametric", "nonparametric")
)
boot_ci_prog(
  fit,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCp", "BCa", "studentized"),
  type = c("parametric", "nonparametric")
)

gpc_boot(
  fit,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCp", "BCa", "studentized"),
  type = c("parametric", "nonparametric")
)

Arguments

fit

A gpc_prog_fit object returned by capability_prog.

B

Number of bootstrap replicates (default 1000).

alpha

Vector of significance levels (default c(0.10, 0.05, 0.01) corresponding to 90%, 95%, and 99% confidence levels).

method

Confidence interval method. Options: "percentile", "normal", "basic", "BCp", "BCa", "studentized".

type

Resampling type: "parametric" (default) or "nonparametric".

Value

An object of class "gpc_prog_ci" containing confidence interval tables, standard errors, MSE, and bias.

Examples

dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- capability_prog(x = x, r_removals = r, distribution = dist_exp, USL = 6, LSL = 0)
ci <- boot_ci_prog(fit, B = 50, alpha = c(0.10, 0.05, 0.01), method = "percentile")
print(ci)
dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- capability_prog(x = x, r_removals = r, distribution = dist_exp, USL = 6, LSL = 0)
ci <- boot_ci_prog(fit, B = 50, alpha = c(0.10, 0.05, 0.01), method = "percentile")
print(ci)

Compute Generalized Process Capability Indices for Progressive Type-II Censored Data

Description

Computes classical and generalized Process Capability Indices (PCIs) for progressive Type-II censored data using model parameter estimates obtained from MleCensoR.

Usage

capability_prog(
  x = NULL,
  r_removals = NULL,
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = c("Cpy", "Cp", "Cpk", "Cpu", "Cpl", "Cpm", "Cpmk", "Spmk", "CpTk", "Cpc",
    "CNpmc"),
  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
)

gpc_fit(
  x = NULL,
  r_removals = NULL,
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = c("Cpy", "Cp", "Cpk", "Cpu", "Cpl", "Cpm", "Cpmk", "Spmk", "CpTk", "Cpc",
    "CNpmc"),
  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
)
capability_prog(
  x = NULL,
  r_removals = NULL,
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = c("Cpy", "Cp", "Cpk", "Cpu", "Cpl", "Cpm", "Cpmk", "Spmk", "CpTk", "Cpc",
    "CNpmc"),
  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
)

gpc_fit(
  x = NULL,
  r_removals = NULL,
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = c("Cpy", "Cp", "Cpk", "Cpu", "Cpl", "Cpm", "Cpmk", "Spmk", "CpTk", "Cpc",
    "CNpmc"),
  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
)

Arguments

x

Numeric vector of observed failure times under progressive Type-II censoring. Can be NULL if parameters are already fitted.

r_removals

Numeric vector of removal counts (censoring scheme R).

distribution

A gpc_dist distribution object.

USL

Upper Specification Limit.

LSL

Lower Specification Limit.

target

Process target (defaults to (USL + LSL) / 2).

indices

Vector of capability indices to compute. Choices include "Cpy", "Cp", "Cpk", "Cpu", "Cpl", "Cpm", "Cpmk", "Cp_uv", "Spmk", "CpTk", "Cpc", "CNpmc", "CNpmkc", "CNpk", "Cp_q", "Cpk_q".

u

Weight parameter u for Cp(u,v) family (default is 1).

v

Weight parameter v for Cp(u,v) family (default is 1).

mode

Mode of evaluation: "moments" (mean and variance) or "quantile" (quantiles).

fit

Logical. If TRUE (default), estimates distribution parameters using MleCensoR::mle_progressive_type2.

C0, C1, C2

Parameters for loss/tolerance cost function in CNpmc and CNpmkc (default: C0 = 1, C1 = 0, C2 = 1).

tolerance_t

Tolerance length t (defaults to USL - LSL).

P0

Desired conformance level for Cpy and Cpc (default is 0.9973002).

LDL, UDL

Lower and Upper Desired Limits for CpTk (default to LSL and USL).

Value

An object of class c("gpc_prog_fit", "gpcifit").

Examples

dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
cap <- capability_prog(x = x, r_removals = r, distribution = dist_exp, USL = 6, LSL = 0)
print(cap)
dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
cap <- capability_prog(x = x, r_removals = r, distribution = dist_exp, USL = 6, LSL = 0)
print(cap)

Monte Carlo Simulation and Coverage Probability Evaluation

Description

Evaluates standard error, MSE, bias, and empirical coverage probability for parameters and GPCIs under progressive Type-II censoring.

Usage

eval_performance(
  distribution,
  r_removals,
  USL,
  LSL,
  target = (USL + LSL)/2,
  true_indices = NULL,
  M = 100,
  B = 200,
  alpha = c(0.1, 0.05, 0.01)
)

gpc_sim(
  distribution,
  r_removals,
  USL,
  LSL,
  target = (USL + LSL)/2,
  true_indices = NULL,
  M = 100,
  B = 200,
  alpha = c(0.1, 0.05, 0.01)
)
eval_performance(
  distribution,
  r_removals,
  USL,
  LSL,
  target = (USL + LSL)/2,
  true_indices = NULL,
  M = 100,
  B = 200,
  alpha = c(0.1, 0.05, 0.01)
)

gpc_sim(
  distribution,
  r_removals,
  USL,
  LSL,
  target = (USL + LSL)/2,
  true_indices = NULL,
  M = 100,
  B = 200,
  alpha = c(0.1, 0.05, 0.01)
)

Arguments

distribution

A gpc_dist distribution object with true parameters.

r_removals

Progressive censoring scheme vector R.

USL

Upper Specification Limit.

LSL

Lower Specification Limit.

target

Process target.

true_indices

Optional named vector of true index values.

M

Number of Monte Carlo simulation runs (default 100).

B

Number of bootstrap iterations per run (default 200).

alpha

Vector of significance levels (default c(0.10, 0.05, 0.01)).

Value

A list containing performance tables and coverage probabilities.

Examples

dist_true <- dist_weibull(shape = 2, scale = 5)
r_scheme <- c(2, 0, 3, 0, 1)
eval_res <- eval_performance(dist_true, r_scheme, USL = 10, LSL = 0, M = 5, B = 20)
print(eval_res)
dist_true <- dist_weibull(shape = 2, scale = 5)
r_scheme <- c(2, 0, 3, 0, 1)
eval_res <- eval_performance(dist_true, r_scheme, USL = 10, LSL = 0, M = 5, B = 20)
print(eval_res)

Parameter Estimation for Progressive Type-II Censored Data using MleCensoR

Description

Fits process distribution parameters to progressive Type-II censored data using the MleCensoR package (mle_progressive_type2).

Usage

fit_prog_ty2(
  x,
  r_removals,
  distribution,
  start = NULL,
  method = NULL,
  lower = NULL,
  upper = NULL,
  ...
)
fit_prog_ty2(
  x,
  r_removals,
  distribution,
  start = NULL,
  method = NULL,
  lower = NULL,
  upper = NULL,
  ...
)

Arguments

x

Numeric vector of observed failure times (must be sorted in ascending order).

r_removals

Numeric vector of progressive removal counts (censoring scheme R).

distribution

A gpc_dist distribution object or function specifications.

start

Vector of initial parameter values.

method

Optimization method (e.g. "L-BFGS-B", "BFGS", "NR").

lower

Optional lower bounds for parameters.

upper

Optional upper bounds for parameters.

...

Additional arguments passed to MleCensoR::mle_progressive_type2.

Value

A fitted gpc_dist object with updated parameters, log-likelihood, standard errors, and covariance matrix.

Examples

dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- fit_prog_ty2(x = x, r_removals = r, distribution = dist_exp)
dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- fit_prog_ty2(x = x, r_removals = r, distribution = dist_exp)

Dispatcher for Index Value Retrieval

Description

Dispatcher for Index Value Retrieval

Usage

gpc_index(fit, index)
gpc_index(fit, index)

Arguments

fit

A gpc_prog_fit object.

index

Name of index to extract or compute.

Value

Numeric value of the specified index.

Examples

dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- capability_prog(x = x, r_removals = r, distribution = dist_exp, USL = 6, LSL = 0)
gpc_index(fit, "Cpy")
dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- capability_prog(x = x, r_removals = r, distribution = dist_exp, USL = 6, LSL = 0)
gpc_index(fit, "Cpy")

Custom Distribution Object Builder for Progressive Type-II GPCI

Description

Builds a distribution specification object for parameter estimation and Generalized Process Capability Indices (GPCIs) under Progressive Type-II Censored Data.

Usage

make_gpc_dist(
  name,
  pdf,
  cdf,
  surv = NULL,
  quantile = NULL,
  start,
  param_names = paste0("param", seq_along(start)),
  support = c(0, Inf)
)
make_gpc_dist(
  name,
  pdf,
  cdf,
  surv = NULL,
  quantile = NULL,
  start,
  param_names = paste0("param", seq_along(start)),
  support = c(0, Inf)
)

Arguments

name

Character string giving the name of the distribution.

pdf

Function f(x, theta, ...) for the Probability Density Function.

cdf

Function F(x, theta, ...) for the Cumulative Distribution Function.

surv

Function S(x, theta, ...) for the Survival Function (defaults to 1 - cdf(x, theta)).

quantile

Optional function Q(p, theta, ...) for the Quantile Function.

start

Vector of initial parameter values for estimation.

param_names

Character vector of parameter names.

support

Numeric vector of length 2 giving domain support of the distribution.

Value

An object of class "gpc_dist".

Examples

pdf_exp <- function(x, theta) dexp(x, rate = theta[1])
cdf_exp <- function(x, theta) pexp(x, rate = theta[1])
surv_exp <- function(x, theta) 1 - pexp(x, rate = theta[1])
dist <- make_gpc_dist("Exponential", pdf_exp, cdf_exp, surv_exp, start = c(1), param_names = "rate")
pdf_exp <- function(x, theta) dexp(x, rate = theta[1])
cdf_exp <- function(x, theta) pexp(x, rate = theta[1])
surv_exp <- function(x, theta) 1 - pexp(x, rate = theta[1])
dist <- make_gpc_dist("Exponential", pdf_exp, cdf_exp, surv_exp, start = c(1), param_names = "rate")

Visualization Functions for Progressive Type-II GPCI

Description

Provides plot S3 methods for fitted progressive Type-II capability objects and bootstrap confidence interval results.

Usage

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

## S3 method for class 'gpc_prog_ci'
plot(x, index = NULL, ...)
## S3 method for class 'gpc_prog_fit'
plot(x, ...)

## S3 method for class 'gpc_prog_ci'
plot(x, index = NULL, ...)

Arguments

x

Object of class gpc_prog_fit or gpc_prog_ci.

...

Additional plot parameters.

index

Name of index or parameter to plot for gpc_prog_ci.

Value

Invisibly returns the input object.

Examples

dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- capability_prog(x = x, r_removals = r, distribution = dist_exp, USL = 6, LSL = 0)
plot(fit)
dist_exp <- dist_weibull(shape = 1, scale = 1)
x <- c(0.5, 1.2, 2.1, 3.4, 4.8)
r <- c(1, 0, 2, 0, 1)
fit <- capability_prog(x = x, r_removals = r, distribution = dist_exp, USL = 6, LSL = 0)
plot(fit)

Predefined Distribution Specifications

Description

Built-in helper functions creating "gpc_dist" objects for standard process distributions.

Usage

dist_normal(mean = 0, sd = 1)

dist_weibull(shape = 1, scale = 1)

dist_gamma(shape = 1, rate = 1)

dist_exp_exp(alpha = 1, lambda = 1)

dist_logistic_exp(alpha = 1, lambda = 1)
dist_normal(mean = 0, sd = 1)

dist_weibull(shape = 1, scale = 1)

dist_gamma(shape = 1, rate = 1)

dist_exp_exp(alpha = 1, lambda = 1)

dist_logistic_exp(alpha = 1, lambda = 1)

Arguments

mean

Initial mean for Normal distribution.

sd

Initial standard deviation for Normal distribution.

shape

Initial shape parameter.

scale

Initial scale parameter.

rate

Initial rate parameter.

alpha

Initial alpha shape parameter.

lambda

Initial lambda scale parameter.

Value

A "gpc_dist" object.

Examples

d_norm <- dist_normal()
d_weib <- dist_weibull()
d_norm <- dist_normal()
d_weib <- dist_weibull()

Package 'gpciProgTyII'

Help Index

Bootstrap Confidence Intervals and Performance Evaluation for Progressive Type-II GPCI

Description

Usage

Arguments

Value

Examples

Compute Generalized Process Capability Indices for Progressive Type-II Censored Data

Description

Usage

Arguments

Value

Examples

Monte Carlo Simulation and Coverage Probability Evaluation

Description

Usage

Arguments

Value

Examples

Parameter Estimation for Progressive Type-II Censored Data using MleCensoR

Description

Usage

Arguments

Value

Examples

Dispatcher for Index Value Retrieval

Description

Usage

Arguments

Value

Examples

Custom Distribution Object Builder for Progressive Type-II GPCI

Description

Usage

Arguments

Value

Examples

Visualization Functions for Progressive Type-II GPCI

Description

Usage

Arguments

Value

Examples

Predefined Distribution Specifications

Description

Usage

Arguments

Value

Examples