Package {StressCensoR}

Type:	Package
Title:	Generalized Stress-Strength Reliability Estimation Under Censoring Schemes
Version:	0.1.0
Description:	Generalized framework for data generation, Maximum Likelihood Estimation, and Bayesian estimation of stress-strength reliability R = P(Y < X) for arbitrary continuous distributions under censoring schemes based on Chapter 9 of 'Balakrishnan', 'Cramer', and 'Kundu' (2023) <ISBN:978-0-12-398387-9>. Users provide probability density functions, cumulative distribution functions, survival functions, support bounds, parameter ranges, and sample sizes. Implements data generation under Type-I, Type-II, progressive Type-II, Type-I hybrid, Type-II hybrid, generalized hybrid, progressive hybrid, joint, block random, middle, and truncation censoring schemes, accompanied by diagnostic histograms, dot plots, and autocorrelation plots. Maximum Likelihood Estimation supports optimization routines including 'Newton-Raphson', 'Broyden'-'Fletcher'-'Goldfarb'-'Shanno' ('BFGS'), 'BFGS' in R ('BFGSR'), 'Berndt'-'Hall'-'Hall'-'Hausman' ('BHHH'), Simulated Annealing ('SANN'), Conjugate Gradients ('CG'), and 'Nelder'-'Mead' ('NM'), returning summaries ('AIC', 'coef', 'logLik', 'nIter', 'stdEr', summary, 'vcov'). Bayesian estimation of stress-strength reliability R = P(Y < X) is performed via Gibbs sampling, Metropolis-Hastings algorithm, Importance Sampling, and 'Lindley' approximation (1980). Methods and censoring schemes are described in 'Balakrishnan', 'Cramer', and 'Kundu' (2023, ISBN:978-0-12-398387-9), 'Lindley' (1980) <doi:10.1111/j.2517-6161.1980.tb01102.x>, 'Geweke' (1989) <doi:10.2307/2290062>, 'Metropolis' (1953) <doi:10.1063/1.1699114>, 'Hastings' (1970) <doi:10.1093/biomet/57.1.97>, 'Geman' and 'Geman' (1984) <doi:10.1109/TPAMI.1984.4767596>, 'Kundu' and 'Gupta' (2005) <doi:10.1016/j.jspi.2004.09.006>, 'Kundu' and 'Gupta' (2006) <doi:10.1016/j.csda.2005.02.007>, 'Berndt', 'Hall', 'Hall', and 'Hausman' (1974) <doi:10.3386/t0003>, 'Fletcher' (1987, ISBN:978-0-471-91547-8), and 'Nelder' and 'Mead' (1965) <doi:10.1093/comjnl/7.4.308>.
License:	GPL-3
Encoding:	UTF-8
Language:	en-US
Depends:	R (≥ 4.0.0)
Imports:	graphics, stats
Suggests:	testthat (≥ 3.0.0)
Config/testthat/edition:	3
RoxygenNote:	7.3.3
NeedsCompilation:	no
Packaged:	2026-07-25 16:47:34 UTC; shikhar tyagi
Author:	Shikhar Tyagi [aut, cre], Arvind Pandey [aut], Bhupendra Singh [aut], Vrijesh Tripathi [aut]
Maintainer:	Shikhar Tyagi <shikhar1093tyagi@gmail.com>
Repository:	CRAN
Date/Publication:	2026-08-05 06:40:23 UTC

Master Function for Bayesian Stress-Strength Reliability Estimation

Description

Fits Bayesian stress-strength reliability R = P(Y < X) using Gibbs sampling, Metropolis-Hastings, Importance Sampling, or Lindley Approximation.

Usage

bayes_stress_strength(
  data_x,
  data_y,
  pdf_x,
  cdf_y,
  method = "gibbs",
  start_x = 1,
  start_y = 1,
  ...
)

Arguments

Value

List of Bayesian estimation results.

S3 Methods for mle_censored Objects

Description

S3 Methods for mle_censored Objects

Usage

## S3 method for class 'mle_censored'
coef(object, ...)

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

## S3 method for class 'mle_censored'
logLik(object, ...)

## S3 method for class 'mle_censored'
AIC(object, ..., k = 2)

## S3 method for class 'mle_censored'
stdEr(object, ...)

## S3 method for class 'mle_censored'
nIter(object, ...)

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

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

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

Arguments

Value

Extracted method values (coefficients, vcov matrix, logLik, AIC, stdEr, nIter, summary, or printed output).

Compute Stress-Strength Reliability R = P(Y < X)

Description

Computes R = P(Y < X) given PDF/CDF functions and parameter vectors.

Usage

compute_stress_strength_R(
  pdf_x,
  cdf_y,
  param_x,
  param_y,
  lower = 0,
  upper = Inf
)

Arguments

Value

Numeric scalar value of R in [0, 1].

Solved Example 11.3: Aluminum Coupons Lifetime Data Under Hybrid Censoring

Description

Solves Example 11.3 from Chapter 9 of Balakrishnan, Cramer, and Kundu (2023) using Type-I and Type-II Hybrid Censoring schemes (Birnbaum & Saunders 1958 dataset).

Usage

example_aluminum_coupons()

Value

A list containing dataset, hybrid censoring limits, MLEs, and Bayesian estimates.

Examples

res <- example_aluminum_coupons()
print(res$mle_hybrid1)
print(res$mle_hybrid2)

Solved Example 11.2: Insulating Fluid Breakdown Data Under Progressive Censoring

Description

Solves Example 11.2 from Chapter 9 of Balakrishnan, Cramer, and Kundu (2023) using progressive Type-II censoring estimation (MLE and Bayesian methods).

Usage

example_insulating_fluid()

Value

A list containing dataset, MLE estimates, and Bayesian stress-strength reliability estimates.

Examples

res <- example_insulating_fluid()
print(res$mle_fit)
print(res$bayes_fit)

Solved Example: Stress-Strength Reliability Under Hybrid Censoring

Description

Solves Stress-Strength Reliability R = P(Y < X) for stress X and strength Y under Chapter 9 hybrid censoring schemes using MLE and Bayesian methods.

Usage

example_stress_strength()

Value

A list containing stress/strength datasets, MLE, Gibbs, M-H, IS, and Lindley estimates.

Examples

res <- example_stress_strength()
print(res$R_mle)
print(res$R_lindley)

Bayesian Stress-Strength Reliability Estimation via Gibbs Sampling

Description

Bayesian Stress-Strength Reliability Estimation via Gibbs Sampling

Usage

gibbs_stress_strength(
  data_x,
  data_y,
  pdf_x,
  cdf_y,
  prior_x = NULL,
  prior_y = NULL,
  start_x = 1,
  start_y = 1,
  iter = 5000,
  burnin = 1000
)

Arguments

Value

A list containing posterior samples of parameters and R, and point estimates.

Bayesian Stress-Strength Reliability Estimation via Importance Sampling

Description

Bayesian Stress-Strength Reliability Estimation via Importance Sampling

Usage

is_stress_strength(
  data_x,
  data_y,
  pdf_x,
  cdf_y,
  proposal_sampler = NULL,
  proposal_density = NULL,
  n_samples = 2000
)

Arguments

Value

A list containing importance weights, R estimate, and standard error.

Bayesian Stress-Strength Reliability Estimation via Lindley's Approximation (1980)

Description

Bayesian Stress-Strength Reliability Estimation via Lindley's Approximation (1980)

Usage

lindley_stress_strength(data_x, data_y, pdf_x, cdf_y, start_x = 1, start_y = 1)

Arguments

Value

A list containing Lindley approximation estimate of R.

Bayesian Stress-Strength Reliability Estimation via Metropolis-Hastings Algorithm

Description

Bayesian Stress-Strength Reliability Estimation via Metropolis-Hastings Algorithm

Usage

mh_stress_strength(
  data_x,
  data_y,
  pdf_x,
  cdf_y,
  prior_x = NULL,
  prior_y = NULL,
  start_x = 1,
  start_y = 1,
  iter = 5000,
  burnin = 1000
)

Arguments

Value

A list containing posterior samples of parameters and R, and point estimates.

Generalized Maximum Likelihood Estimation Under Censoring Schemes

Description

Fits parameter estimates and calculates stress-strength reliability R = P(Y < X) under user-specified censoring schemes and optimization algorithms.

Usage

mle_censored(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  scheme = "Type-I",
  method = "NR",
  data_y = NULL,
  pdf_y = NULL,
  cdf_y = NULL,
  start_y = NULL,
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Generalized Hybrid Censoring

Description

MLE Under Generalized Hybrid Censoring

Usage

mle_genhybrid(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Type-I Hybrid Censoring

Description

MLE Under Type-I Hybrid Censoring

Usage

mle_hybrid1(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Type-II Hybrid Censoring

Description

MLE Under Type-II Hybrid Censoring

Usage

mle_hybrid2(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Interval Censoring

Description

MLE Under Interval Censoring

Usage

mle_interval(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Joint Censoring

Description

MLE Under Joint Censoring

Usage

mle_joint(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Middle Censoring

Description

MLE Under Middle Censoring

Usage

mle_middle(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Progressive Type-II Censoring

Description

MLE Under Progressive Type-II Censoring

Usage

mle_prog2(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Progressive Hybrid Censoring

Description

MLE Under Progressive Hybrid Censoring

Usage

mle_proghybrid(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Random Censoring

Description

MLE Under Random Censoring

Usage

mle_random(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Truncated Distribution

Description

MLE Under Truncated Distribution

Usage

mle_trunc(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Type-I Censoring

Description

MLE Under Type-I Censoring

Usage

mle_type1(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

MLE Under Type-II Censoring

Description

MLE Under Type-II Censoring

Usage

mle_type2(
  data,
  pdf = NULL,
  cdf = NULL,
  surv = NULL,
  start = NULL,
  method = "NR",
  ...
)

Arguments

Value

An object of class mle_censored.

Number of Iterations Generic Function

Description

Number of Iterations Generic Function

Usage

nIter(object, ...)

Arguments

Value

Number of optimization iterations.

Plot Method for Diagnostic Verification of Censored Samples

Description

Produces diagnostic plots including Histogram with PDF overlay, Dot Plot, and Autocorrelation (ACF) plot for generated samples.

Usage

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

Arguments

Value

Invisibly returns x.

Data Generation Under Generalized Hybrid Censoring

Description

Data Generation Under Generalized Hybrid Censoring

Usage

rcensor_genhybrid(
  n,
  k,
  r,
  T0,
  cdf = NULL,
  pdf = NULL,
  surv = NULL,
  param = NULL,
  lower = 0,
  upper = Inf,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Type-I Hybrid Censoring

Description

Data Generation Under Type-I Hybrid Censoring

Usage

rcensor_hybrid1(
  n,
  r,
  T0,
  cdf = NULL,
  pdf = NULL,
  surv = NULL,
  param = NULL,
  lower = 0,
  upper = Inf,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Type-II Hybrid Censoring

Description

Data Generation Under Type-II Hybrid Censoring

Usage

rcensor_hybrid2(
  n,
  r,
  T0,
  cdf = NULL,
  pdf = NULL,
  surv = NULL,
  param = NULL,
  lower = 0,
  upper = Inf,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Interval Censoring

Description

Data Generation Under Interval Censoring

Usage

rcensor_interval(n, cdf = NULL, pdf = NULL, param = NULL, seed = NULL)

Arguments

Value

An object of class rcensored.

Data Generation Under Joint Censoring Scheme

Description

Data Generation Under Joint Censoring Scheme

Usage

rcensor_joint(
  n1,
  n2,
  r,
  cdf_x = NULL,
  cdf_y = NULL,
  param_x = NULL,
  param_y = NULL,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Middle Censoring

Description

Data Generation Under Middle Censoring

Usage

rcensor_middle(n, cdf = NULL, pdf = NULL, param = NULL, seed = NULL)

Arguments

Value

An object of class rcensored.

Data Generation Under Progressive Type-II Censoring

Description

Data Generation Under Progressive Type-II Censoring

Usage

rcensor_prog2(
  n,
  r,
  R,
  cdf = NULL,
  pdf = NULL,
  surv = NULL,
  param = NULL,
  lower = 0,
  upper = Inf,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Progressive Hybrid Censoring

Description

Data Generation Under Progressive Hybrid Censoring

Usage

rcensor_proghybrid(
  n,
  r,
  R,
  T0,
  cdf = NULL,
  pdf = NULL,
  surv = NULL,
  param = NULL,
  lower = 0,
  upper = Inf,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Random Censoring

Description

Data Generation Under Random Censoring

Usage

rcensor_random(
  n,
  cdf = NULL,
  pdf = NULL,
  param = NULL,
  cen_cdf = NULL,
  cen_param = NULL,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Truncated Distribution

Description

Data Generation Under Truncated Distribution

Usage

rcensor_trunc(
  n,
  cdf = NULL,
  pdf = NULL,
  param = NULL,
  left_trunc = -Inf,
  right_trunc = Inf,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Type-I Censoring

Description

Data Generation Under Type-I Censoring

Usage

rcensor_type1(
  n,
  T0,
  cdf = NULL,
  pdf = NULL,
  surv = NULL,
  param = NULL,
  lower = 0,
  upper = Inf,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Data Generation Under Type-II Censoring

Description

Data Generation Under Type-II Censoring

Usage

rcensor_type2(
  n,
  r,
  cdf = NULL,
  pdf = NULL,
  surv = NULL,
  param = NULL,
  lower = 0,
  upper = Inf,
  seed = NULL
)

Arguments

Value

An object of class rcensored.

Standard Error Generic Function

Description

Standard Error Generic Function

Usage

stdEr(object, ...)

Arguments

Value

Vector of standard errors.