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Package {gpcihybridII}

Type: Package
Title: Generalized Process Capability Indices under Hybrid Type-II Censoring
Version: 0.1.0
Description: A comprehensive, generalized framework for computing, estimating, and validating Generalized Process Capability Indices (GPCIs) under Hybrid Type-II censored lifetime data. Supports user-supplied probability density or mass functions (PDF/PMF), cumulative distribution functions (CDF), survival functions (SF), and quantile functions. Parameter estimation under Hybrid Type-II censoring is performed via Maximum Likelihood Estimation using the 'MleCensoR' package (Childs et al., 2003 <doi:10.1007/BF02517803>; Balakrishnan & Kundu, 2013 <doi:10.1002/nav.21545>). Computes classical and non-normal 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 percent, 95 percent, and 99 percent levels of significance 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. Integrates goodness-of-fit testing for Hybrid Type-II censored data via the 'gofPHCS' package.
License: MIT + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.3.3
Depends: R (≥ 4.0.0)
Imports: stats, numDeriv, MleCensoR, gofPHCS
Suggests: testthat (≥ 3.0.0), knitr, rmarkdown
VignetteBuilder: knitr
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2026-08-15 03:05:30 UTC; shikhar tyagi
Author: Shikhar Tyagi ORCID iD [aut, cre], Sumit Kumar [aut], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer: Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository: CRAN
Date/Publication: 2026-08-21 13:00:36 UTC

Bootstrap Confidence Intervals for Hybrid Type-II Censored Data

Description

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

Usage

boot_ci_hybrid2(
  fit,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCp", "BCa", "studentized"),
  type = c("parametric", "nonparametric"),
  parallel = FALSE,
  ncpus = 1
)

gpci_boot_hybrid2(
  fit,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCp", "BCa", "studentized"),
  type = c("parametric", "nonparametric"),
  parallel = FALSE,
  ncpus = 1
)

boot_ci(
  fit,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01),
  method = c("percentile", "normal", "basic", "BCp", "BCa", "studentized"),
  type = c("parametric", "nonparametric"),
  parallel = FALSE,
  ncpus = 1
)

Arguments

fit

A gpcifit_hybrid2 object returned by capability_hybrid2.

B

Positive integer scalar specifying number of bootstrap replicates. Defaults to 1000.

alpha

Numeric vector of significance levels. Defaults to c(0.10, 0.05, 0.01) corresponding to 90 percent, 95 percent, and 99 percent confidence levels.

method

Character string specifying confidence interval method. Choices are: "percentile" (default), "normal", "basic", "BCp" (Bias-Corrected Percentile), "BCa" (Bias-Corrected and Accelerated), or "studentized".

type

Character string specifying resampling type: "parametric" (default) or "nonparametric".

parallel

Logical scalar. If TRUE, bootstrap replicates are executed in parallel. Defaults to FALSE.

ncpus

Integer scalar specifying number of CPU cores to use if parallel = TRUE. Defaults to 1.

Value

An S3 object of class "gpci_ci_hybrid2" containing:

ci_table

Data frame of lower and upper confidence bounds, width, and confidence levels for all indices and parameters.

param_perf

Data frame summarizing parameter estimates, standard errors (SE), bias, and mean squared errors (MSE).

index_perf

Data frame summarizing capability index estimates, standard errors (SE), bias, and MSE.

param_reps

Matrix of bootstrap parameter replicates across all iterations.

index_reps

Matrix of bootstrap capability index replicates across all iterations.

fit

The original gpcifit_hybrid2 object.

B

Number of bootstrap replicates.

Examples

dist_exp <- dist_exponential(rate = 1)
x <- c(0.2, 0.5, 0.8, 1.1)
fit <- capability_hybrid2(x = x, r = 3, tc = 1.0, n = 10, distribution = dist_exp, USL = 3, LSL = 0)
ci <- boot_ci_hybrid2(fit, B = 50, alpha = c(0.10, 0.05, 0.01), method = "percentile")
print(ci)

Compute Process Capability Indices under Hybrid Type-II Censored Data

Description

Computes classical and generalized Process Capability Indices (GPCIs) under Hybrid Type-II censored lifetime data.

Usage

capability_hybrid2(
  x = NULL,
  r = NULL,
  tc = NULL,
  n = NULL,
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = c("Cpy", "Spmk", "CpTk", "Cpc", "CNpmc", "CNpmkc", "CNpk", "Cp", "Cpk",
    "Cpm", "Cpmk"),
  u = 1,
  v = 1,
  mode = c("moments", "quantile"),
  fit = TRUE,
  start = NULL,
  C0 = 1,
  C1 = 0,
  C2 = 1,
  tolerance_t = USL - LSL,
  P0 = 0.9973002,
  LDL = LSL,
  UDL = USL,
  ...
)

gpci_fit_hybrid2(
  x = NULL,
  r = NULL,
  tc = NULL,
  n = NULL,
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = c("Cpy", "Spmk", "CpTk", "Cpc", "CNpmc", "CNpmkc", "CNpk", "Cp", "Cpk",
    "Cpm", "Cpmk"),
  u = 1,
  v = 1,
  mode = c("moments", "quantile"),
  fit = TRUE,
  start = NULL,
  C0 = 1,
  C1 = 0,
  C2 = 1,
  tolerance_t = USL - LSL,
  P0 = 0.9973002,
  LDL = LSL,
  UDL = USL,
  ...
)

capability(
  x = NULL,
  r = NULL,
  tc = NULL,
  n = NULL,
  distribution,
  USL,
  LSL,
  target = (USL + LSL)/2,
  indices = c("Cpy", "Spmk", "CpTk", "Cpc", "CNpmc", "CNpmkc", "CNpk", "Cp", "Cpk",
    "Cpm", "Cpmk"),
  u = 1,
  v = 1,
  mode = c("moments", "quantile"),
  fit = TRUE,
  start = NULL,
  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. Can be NULL (default) if distribution parameters are already estimated or fixed.

r

Positive integer target number of failures. Can be NULL (default) if not fitting raw data.

tc

Positive numeric fixed censoring time. Can be NULL (default) if not fitting raw data.

n

Positive integer total sample size placed on test. Can be NULL (default) if not fitting raw data.

distribution

A gpci_dist_hybrid2 distribution object.

USL

Numeric Upper Specification Limit. Must satisfy USL > LSL.

LSL

Numeric Lower Specification Limit. Must satisfy LSL < USL.

target

Numeric process target. Defaults to (USL + LSL) / 2.

indices

Character vector of capability indices to compute. Choices include: "Cpy", "Spmk", "CpTk", "Cpc", "CNpmc", "CNpmkc", "CNpk", "Cp", "Cpk", "Cpu", "Cpl", "Cpm", "Cpmk", "Cp_uv", "Cp_q", "Cpk_q", "Cpu_q", "Cpl_q", "Cpm_q", "Cpmk_q", "CNp_uv".

u

Non-negative numeric weight parameter u for the generalized Cp(u, v) family. Defaults to 1.

v

Non-negative numeric weight parameter v for the generalized Cp(u, v) family. Defaults to 1.

mode

Character string specifying mode of computation: "moments" (default; uses mean and variance) or "quantile" (uses robust quantiles).

fit

Logical scalar. If TRUE (default) and x is supplied, distribution parameters are estimated under Hybrid Type-II censoring. If FALSE, parameters in distribution are used directly without fitting.

start

Optional named list or numeric vector of starting parameter values for MLE. Defaults to NULL.

C0

Non-negative numeric coefficient for the tolerance cost function in CNpmc and CNpmkc. Defaults to 1.

C1

Non-negative numeric coefficient for the tolerance cost function in CNpmc and CNpmkc. Defaults to 0.

C2

Non-negative numeric coefficient for the tolerance cost function in CNpmc and CNpmkc. Defaults to 1.

tolerance_t

Positive numeric process tolerance t for the tolerance cost function. Defaults to USL - LSL.

P0

Desirable process yield for Cpc and Cpy. Defaults to 0.9973002.

LDL

Lower Desired Limit for CpTk. Defaults to LSL.

UDL

Upper Desired Limit for CpTk. Defaults to USL.

...

Additional arguments passed to fit_distribution_hybrid2.

Value

An S3 object of class "gpcifit_hybrid2" containing:

x

Observed failure times.

r

Target number of failures.

tc

Fixed censoring time.

n

Total sample size.

distribution

Fitted or supplied gpci_dist_hybrid2 distribution object.

USL

Upper Specification Limit.

LSL

Lower Specification Limit.

target

Target value.

indices

Character vector of requested capability index names.

estimates

Named numeric vector of capability index point estimates.

p_hat

Expected process non-conformance proportion.

mode

Computation mode used ("moments" or "quantile").

options

List of calculation options and parameters used.

Examples

dist_exp <- dist_exponential(rate = 1)
x <- c(0.2, 0.5, 0.8, 1.1)
res <- capability_hybrid2(
  x = x, r = 3, tc = 1.0, n = 10,
  distribution = dist_exp,
  USL = 3, LSL = 0, target = 1.5,
  indices = c("Cpy", "Spmk", "CpTk", "Cpc", "CNpmc", "CNpmkc", "Cp", "Cpk", "Cpm", "Cpmk")
)
print(res)

Coef Method for gpcifit_hybrid2

Description

Extract point estimates of capability indices or fitted distribution parameters.

Usage

## S3 method for class 'gpcifit_hybrid2'
coef(object, what = c("indices", "parameters"), ...)

Arguments

object

An object of class gpcifit_hybrid2.

what

Character string: "indices" (default) or "parameters".

...

Additional arguments.

Value

Named numeric vector of indices or parameters.

Compute Standard Errors, MSE, and Coverage Probabilities for Hybrid Type-II Censoring

Description

Evaluates standard errors, mean squared errors (MSE), bias, and empirical coverage probabilities for model parameters and Generalized Process Capability Indices (GPCIs) using bootstrap resampling.

Usage

compute_diagnostics_hybrid2(
  fit,
  true_params = NULL,
  true_indices = NULL,
  B = 1000,
  alpha = c(0.1, 0.05, 0.01)
)

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

Arguments

fit

A gpcifit_hybrid2 object returned by capability_hybrid2.

true_params

Optional named numeric list or vector of true parameter values. Defaults to NULL.

true_indices

Optional named numeric vector of true capability index values. Defaults to NULL.

B

Positive integer scalar specifying number of bootstrap replicates for estimation. Defaults to 1000.

alpha

Numeric vector of significance levels for coverage probabilities. Defaults to c(0.10, 0.05, 0.01).

Value

An S3 object of class "gpci_diagnostics_hybrid2" containing:

se_params

Named numeric vector of standard errors for model parameters.

bias_params

Named numeric vector of empirical bias for model parameters.

mse_params

Named numeric vector of mean squared errors for model parameters.

coverage_params

List of parameter empirical coverage probabilities across significance levels.

se_indices

Named numeric vector of standard errors for capability indices.

bias_indices

Named numeric vector of empirical bias for capability indices.

mse_indices

Named numeric vector of mean squared errors for capability indices.

coverage_indices

List of capability index empirical coverage probabilities across significance levels.

alpha_levels

Numeric vector of significance levels used.

bootstrap_replicates

Number of bootstrap replicates.

fit

The original gpcifit_hybrid2 object.

Examples

dist_exp <- dist_exponential(rate = 1)
x <- c(0.2, 0.5, 0.8, 1.1)
fit <- capability_hybrid2(x = x, r = 3, tc = 1.0, n = 10, distribution = dist_exp, USL = 3, LSL = 0)
diag <- compute_diagnostics_hybrid2(fit, B = 50, true_params = c(rate = 1))
print(diag)

Theoretical Moments of a Distribution

Description

Computes theoretical mean and variance of a distribution using adaptive numerical integration over effective quantile support.

Usage

compute_theoretical_moments_hybrid2(dist)

Arguments

dist

A gpci_dist_hybrid2 distribution object.

Value

A list with two numeric elements:

mean

Theoretical mean of the distribution.

var

Theoretical variance of the distribution.

Examples

dist_w <- dist_weibull(shape = 2, scale = 5)
compute_theoretical_moments_hybrid2(dist_w)

Confint Method for gpcifit_hybrid2

Description

Calculate bootstrap confidence intervals for capability indices at specified significance levels (e.g. 90 percent, 95 percent, 99 percent).

Usage

## S3 method for class 'gpcifit_hybrid2'
confint(
  object,
  parm = NULL,
  level = 0.95,
  B = 1000,
  method = "percentile",
  ...
)

Arguments

object

An object of class gpcifit_hybrid2.

parm

Optional vector of index names.

level

Confidence level (default is 0.95; can be 0.90, 0.95, 0.99 or a vector).

B

Number of bootstrap replicates (default 1000).

method

Bootstrap CI method ("percentile", "normal", "basic", "BCp", "BCa", "studentized").

...

Additional arguments passed to boot_ci_hybrid2.

Value

A matrix containing lower and upper confidence limits.

Define a Process Distribution for Hybrid Type-II Censored Data

Description

Constructor to define a continuous or discrete probability distribution for process capability analysis under Hybrid Type-II censored data. The distribution can be defined by specifying any one (or more) of its Probability Density/Mass Function (PDF/PMF), Cumulative Distribution Function (CDF), Survival Function (SF), or Quantile Function. Missing functions are automatically and numerically derived using adaptive integration and root-finding algorithms.

Usage

define_distribution_hybrid2(
  name,
  pdf = NULL,
  cdf = NULL,
  sf = NULL,
  quantile = NULL,
  params = list(),
  support = c(-Inf, Inf)
)

gpci_dist_hybrid2(
  name,
  pdf = NULL,
  cdf = NULL,
  sf = NULL,
  quantile = NULL,
  params = list(),
  support = c(-Inf, Inf)
)

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

Arguments

name

Character string naming the distribution (e.g. "custom_weibull").

pdf

Optional function representing the probability density/mass function (PDF/PMF). Must be of the form function(x, ...). Defaults to NULL.

cdf

Optional function representing the cumulative distribution function (CDF). Must be of the form function(x, ...). Defaults to NULL.

sf

Optional function representing the survival function (SF = 1 - CDF). Must be of the form function(x, ...). Defaults to NULL.

quantile

Optional function representing the quantile function. Must be of the form function(p, ...). Defaults to NULL.

params

Named list of numeric parameter values for the distribution. Defaults to list().

support

Numeric vector of length 2 defining the lower and upper support bounds. Defaults to c(-Inf, Inf).

Value

An S3 object of class "gpci_dist_hybrid2" containing:

name

Character string of the distribution name.

pdf

The probability density function.

cdf

The cumulative distribution function.

sf

The survival function.

quantile

The quantile function.

params

Named list of numeric parameter values.

param_names

Character vector of parameter names.

support

Numeric vector of length 2 specifying support limits.

Examples

# Define custom Weibull distribution using only the survival function
custom_weib <- define_distribution_hybrid2(
  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)
)
print(custom_weib)

Exponential Distribution Constructor

Description

Exponential Distribution Constructor

Usage

dist_exponential(rate = 1)

Arguments

rate

Rate parameter.

Value

A gpci_dist_hybrid2 object for Exponential distribution.

Examples

dist_e <- dist_exponential(rate = 0.5)

Gamma Distribution Constructor

Description

Gamma Distribution Constructor

Usage

dist_gamma(shape = 1, scale = 1)

Arguments

shape

Shape parameter.

scale

Scale parameter.

Value

A gpci_dist_hybrid2 object for Gamma distribution.

Examples

dist_g <- dist_gamma(shape = 3, scale = 2)

Logistic Distribution Constructor

Description

Logistic Distribution Constructor

Usage

dist_logistic(location = 0, scale = 1)

Arguments

location

Location parameter.

scale

Scale parameter.

Value

A gpci_dist_hybrid2 object for Logistic distribution.

Examples

dist_l <- dist_logistic(location = 0, scale = 1)

Log-Logistic Distribution Constructor

Description

Log-Logistic Distribution Constructor

Usage

dist_loglogistic(shape = 1, scale = 1)

Arguments

shape

Shape parameter.

scale

Scale parameter.

Value

A gpci_dist_hybrid2 object for Log-Logistic distribution.

Examples

dist_ll <- dist_loglogistic(shape = 2, scale = 3)

Lognormal Distribution Constructor

Description

Lognormal Distribution Constructor

Usage

dist_lognormal(meanlog = 0, sdlog = 1)

Arguments

meanlog

Mean of the logarithm.

sdlog

Standard deviation of the logarithm.

Value

A gpci_dist_hybrid2 object for Lognormal distribution.

Examples

dist_ln <- dist_lognormal(meanlog = 1, sdlog = 0.5)

Normal Distribution Constructor

Description

Normal Distribution Constructor

Usage

dist_normal(mean = 0, sd = 1)

Arguments

mean

Mean parameter.

sd

Standard deviation parameter.

Value

A gpci_dist_hybrid2 object for Normal distribution.

Examples

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

Weibull Distribution Constructor

Description

Weibull Distribution Constructor

Usage

dist_weibull(shape = 1, scale = 1)

Arguments

shape

Shape parameter.

scale

Scale parameter.

Value

A gpci_dist_hybrid2 object for Weibull distribution.

Examples

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

Monte Carlo Simulation Framework for Hybrid Type-II Censoring

Description

Evaluates empirical standard errors, bias, MSE, and coverage probabilities for model parameters and Generalized Process Capability Indices (GPCIs) across Monte Carlo simulation runs.

Usage

eval_performance_hybrid2(
  distribution,
  r,
  tc,
  n,
  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,
  tc,
  n,
  USL,
  LSL,
  target = (USL + LSL)/2,
  true_indices = NULL,
  M = 100,
  B = 200,
  alpha = c(0.1, 0.05, 0.01)
)

gpci_sim_hybrid2(
  distribution,
  r,
  tc,
  n,
  USL,
  LSL,
  target = (USL + LSL)/2,
  true_indices = NULL,
  M = 100,
  B = 200,
  alpha = c(0.1, 0.05, 0.01)
)

Arguments

distribution

A gpci_dist_hybrid2 distribution object with known true parameters.

r

Positive integer target number of failures.

tc

Positive numeric fixed censoring time.

n

Positive integer total number of initial units placed on life test.

USL

Numeric Upper Specification Limit.

LSL

Numeric Lower Specification Limit.

target

Numeric process target. Defaults to (USL + LSL) / 2.

true_indices

Optional named numeric vector of true capability index values. If NULL (default), derived from distribution.

M

Positive integer scalar specifying number of Monte Carlo simulation runs. Defaults to 100.

B

Positive integer scalar specifying number of bootstrap iterations per simulation run. Defaults to 200.

alpha

Numeric vector of significance levels. Defaults to c(0.10, 0.05, 0.01).

Value

An S3 object of class "gpci_sim_hybrid2" containing:

param_summary

Data frame of true values, mean estimates, standard errors (SE), bias, and MSE for model parameters.

index_summary

Data frame of true values, mean estimates, standard errors (SE), bias, and MSE for capability indices.

coverage_probabilities

Matrix of empirical coverage probabilities across all significance levels.

M

Total number of simulation runs requested.

valid_runs

Number of successfully converged simulation runs.

B

Number of bootstrap replicates per run.

true_parameters

Vector of true parameter values.

true_indices

Vector of true capability index values.

Examples

dist_true <- dist_weibull(shape = 2, scale = 5)
sim_res <- eval_performance_hybrid2(
  distribution = dist_true, r = 5, tc = 4.0, n = 12,
  USL = 8, LSL = 1, M = 5, B = 20
)
print(sim_res)

Parameter Estimation for Hybrid Type-II Censored Data using MleCensoR

Description

Fits process distribution parameters under Hybrid Type-II censored data using the MleCensoR package (MleCensoR::mle_hybrid_type2) with robust numerical optimization fallbacks.

Usage

fit_distribution_hybrid2(
  x,
  r,
  tc,
  n,
  distribution,
  start = NULL,
  method = NULL,
  lower = NULL,
  upper = NULL,
  ...
)

gpci_fit_hybrid2_dist(
  x,
  r,
  tc,
  n,
  distribution,
  start = NULL,
  method = NULL,
  lower = NULL,
  upper = NULL,
  ...
)

fit_hybrid2(
  x,
  r,
  tc,
  n,
  distribution,
  start = NULL,
  method = NULL,
  lower = NULL,
  upper = NULL,
  ...
)

Arguments

x

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

r

Positive integer scalar specifying the target number of failures.

tc

Positive numeric scalar specifying the fixed censoring time.

n

Positive integer scalar specifying the total initial sample size placed on test.

distribution

A gpci_dist_hybrid2 distribution object specifying the target model.

start

Optional named numeric vector or list of starting parameter values. If NULL (default), uses distribution$params.

method

Character string specifying optimization method (e.g. "L-BFGS-B", "BFGS", "Nelder-Mead"). If NULL (default), chosen automatically.

lower

Optional numeric vector of lower bounds for parameters under bounded optimization. Defaults to NULL.

upper

Optional numeric vector of upper bounds for parameters under bounded optimization. Defaults to NULL.

...

Additional arguments passed to MleCensoR::mle_hybrid_type2 or stats::optim.

Value

A fitted gpci_dist_hybrid2 distribution object with updated parameters and attributes:

vcov

Asymptotic variance-covariance matrix of estimated parameters.

se

Numeric vector of standard errors for estimated parameters.

std_errs

Alias for se.

loglik

Scalar log-likelihood value at the optimum.

vdata

Validated Hybrid Type-II censoring data summary list.

Examples

dist_exp <- dist_exponential(rate = 1)
x <- c(0.2, 0.5, 0.8, 1.1)
fit <- fit_distribution_hybrid2(x = x, r = 3, tc = 1.0, n = 10, distribution = dist_exp)
print(fit)

Goodness-of-Fit Testing for Hybrid Type-II Censored Data using gofPHCS

Description

Performs goodness-of-fit testing for Hybrid Type-II censored lifetime data using the gofPHCS package (gofPHCS::gof_test).

Usage

gof_test_hybrid2(
  fit = NULL,
  x = NULL,
  r = NULL,
  tc = NULL,
  n = NULL,
  distribution = NULL,
  statistic = "auto",
  p.method = c("auto", "asymptotic", "montecarlo"),
  nsim = 999,
  seed = NULL,
  conf.level = 0.95,
  ...
)

gof_test(
  fit = NULL,
  x = NULL,
  r = NULL,
  tc = NULL,
  n = NULL,
  distribution = NULL,
  statistic = "auto",
  p.method = c("auto", "asymptotic", "montecarlo"),
  nsim = 999,
  seed = NULL,
  conf.level = 0.95,
  ...
)

Arguments

fit

Optional gpcifit_hybrid2 object returned by capability_hybrid2. If supplied, x, r, tc, n, and distribution are extracted automatically. Defaults to NULL.

x

Numeric vector of observed failure times (required if fit is not supplied). Defaults to NULL.

r

Positive integer target number of failures (required if fit is not supplied). Defaults to NULL.

tc

Positive numeric fixed censoring time (required if fit is not supplied). Defaults to NULL.

n

Positive integer total sample size (required if fit is not supplied). Defaults to NULL.

distribution

A gpci_dist_hybrid2 distribution object (required if fit is not supplied). Defaults to NULL.

statistic

Character string specifying the test statistic (e.g. "auto", "AD", "CvM", "KS"). Defaults to "auto".

p.method

Character string specifying method for calculating p-values: "auto" (default), "asymptotic", or "montecarlo".

nsim

Positive integer scalar specifying number of Monte Carlo replicates. Defaults to 999.

seed

Optional integer seed for reproducibility. Defaults to NULL.

conf.level

Numeric confidence level for test. Defaults to 0.95.

...

Additional arguments passed to gofPHCS::gof_test.

Value

An S3 object of class "gpci_gof_hybrid2" containing:

fit

The original gpcifit_hybrid2 object, or NULL if raw data was passed.

cens_data

The gofPHCS censored data structure.

gof_result

The returned test result object from gofPHCS::gof_test.

distribution

The tested gpci_dist_hybrid2 distribution object.

Examples

dist_exp <- dist_exponential(rate = 0.5)
x <- c(0.2, 0.5, 0.8, 1.1)
fit <- capability_hybrid2(x = x, r = 3, tc = 1.0, n = 10, distribution = dist_exp, USL = 3, LSL = 0)
gof_res <- gof_test_hybrid2(fit, p.method = "montecarlo", nsim = 50)
print(gof_res)

Extract a Specific Capability Index

Description

Extract a Specific Capability Index

Usage

gpci_index_hybrid2(fit, index)

Arguments

fit

A gpcifit_hybrid2 object.

index

Name of the capability index to retrieve or compute.

Value

Numeric scalar value of the index.

Examples

dist_exp <- dist_exponential(rate = 1)
x <- c(0.2, 0.5, 0.8, 1.1)
fit <- capability_hybrid2(x = x, r = 3, tc = 1.0, n = 10, distribution = dist_exp, USL = 3, LSL = 0)
gpci_index_hybrid2(fit, "Cpy")

Print Method for Hybrid Type-II Bootstrap CIs

Description

Print Method for Hybrid Type-II Bootstrap CIs

Usage

## S3 method for class 'gpci_ci_hybrid2'
print(x, ...)

Arguments

x

An object of class gpci_ci_hybrid2.

...

Additional print arguments.

Value

The invisible object x.

Print Method for Hybrid Type-II Diagnostics

Description

Print Method for Hybrid Type-II Diagnostics

Usage

## S3 method for class 'gpci_diagnostics_hybrid2'
print(x, ...)

Arguments

x

An object of class gpci_diagnostics_hybrid2.

...

Additional print arguments.

Value

The invisible object x.

Print Method for gpci_dist_hybrid2

Description

Print Method for gpci_dist_hybrid2

Usage

## S3 method for class 'gpci_dist_hybrid2'
print(x, ...)

Arguments

x

An object of class gpci_dist_hybrid2.

...

Additional print arguments.

Value

The invisible object x.

Print Method for gpci_gof_hybrid2

Description

Print Method for gpci_gof_hybrid2

Usage

## S3 method for class 'gpci_gof_hybrid2'
print(x, ...)

Arguments

x

An object of class gpci_gof_hybrid2.

...

Additional print arguments.

Value

The invisible object x.

Print Method for Hybrid Type-II Monte Carlo Simulation

Description

Print Method for Hybrid Type-II Monte Carlo Simulation

Usage

## S3 method for class 'gpci_sim_hybrid2'
print(x, ...)

Arguments

x

An object of class gpci_sim_hybrid2.

...

Additional print arguments.

Value

The invisible object x.

Print Method for gpcifit_hybrid2

Description

Print Method for gpcifit_hybrid2

Usage

## S3 method for class 'gpcifit_hybrid2'
print(x, ...)

Arguments

x

An object of class gpcifit_hybrid2.

...

Additional print arguments.

Value

The invisible object x.

Summary Method for Hybrid Type-II Bootstrap CIs

Description

Summary Method for Hybrid Type-II Bootstrap CIs

Usage

## S3 method for class 'gpci_ci_hybrid2'
summary(object, ...)

Arguments

object

An object of class gpci_ci_hybrid2.

...

Additional arguments.

Value

The invisible object object.

Summary Method for Hybrid Type-II Diagnostics

Description

Summary Method for Hybrid Type-II Diagnostics

Usage

## S3 method for class 'gpci_diagnostics_hybrid2'
summary(object, ...)

Arguments

object

An object of class gpci_diagnostics_hybrid2.

...

Additional arguments.

Value

The invisible object object.

Summary Method for gpci_dist_hybrid2

Description

Summary Method for gpci_dist_hybrid2

Usage

## S3 method for class 'gpci_dist_hybrid2'
summary(object, ...)

Arguments

object

An object of class gpci_dist_hybrid2.

...

Additional arguments.

Value

The invisible object object.

Summary Method for gpci_gof_hybrid2

Description

Summary Method for gpci_gof_hybrid2

Usage

## S3 method for class 'gpci_gof_hybrid2'
summary(object, ...)

Arguments

object

An object of class gpci_gof_hybrid2.

...

Additional arguments.

Value

The invisible object object.

Summary Method for Hybrid Type-II Monte Carlo Simulation

Description

Summary Method for Hybrid Type-II Monte Carlo Simulation

Usage

## S3 method for class 'gpci_sim_hybrid2'
summary(object, ...)

Arguments

object

An object of class gpci_sim_hybrid2.

...

Additional arguments.

Value

The invisible object object.

Summary Method for gpcifit_hybrid2

Description

Summary Method for gpcifit_hybrid2

Usage

## S3 method for class 'gpcifit_hybrid2'
summary(object, ...)

Arguments

object

An object of class gpcifit_hybrid2.

...

Additional arguments.

Value

The invisible object object.

Vcov Method for gpcifit_hybrid2

Description

Extract asymptotic variance-covariance matrix of fitted distribution parameters.

Usage

## S3 method for class 'gpcifit_hybrid2'
vcov(object, ...)

Arguments

object

An object of class gpcifit_hybrid2.

...

Additional arguments.

Value

Variance-covariance matrix.

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