Package 'gpciIntCensor'

Title: Generalized Process Capability Indices for Interval-Censored Data
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>.
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: 2026-10-08 10:14:51 UTC
Source: https://github.com/cran/gpciIntCensor

Help Index

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

object

Object to plot.
...

Additional 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

fit

A gpcifit_censor object returned by capability_censor.
B

Number of bootstrap replicates.
alpha

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

Confidence interval method ("percentile", "normal", "basic", "BCa", "BCp", "studentized").
type

Bootstrap type ("parametric" or "nonparametric").
parallel

Logical. If TRUE, parallel processing is used.
ncpus

Number of CPUs for parallel execution.
x, object

An object of class gpci_ci_censor.
...

Additional print/summary 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

mean, sd

Mean and standard deviation parameters for normal distribution.
meanlog, sdlog

Mean and standard deviation of the distribution on the log scale.
shape, scale

Shape and scale parameters.
shape1, shape2

Non-negative parameters of the Beta distribution.

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

data_left

Numeric vector of left interval bounds for interval-censored data.
data_right

Numeric vector of right interval bounds for interval-censored data.
distribution

A gpci_dist_censor distribution object.
USL

Numeric value of the Upper Specification Limit.
LSL

Numeric value of the Lower Specification Limit.
target

Numeric value of process target (default is midpoint of USL and LSL).
indices

Character vector of capability indices to compute.
u, v

Parameters for Vannman's Cp(u,v) family.
mode

Computation mode: "moments" or "quantile".
fit

Logical. If TRUE, parameters are estimated via MLE under interval censoring.
C0, C1, C2

Cost function parameters for CNpmc and CNpmkc.
tolerance_t

Tolerance parameter for CNpmc and CNpmkc.
P0

Desirable process yield for Cpy and Cpc.
LDL, UDL

Desired limits for CpTk.
x, object

An object of class gpcifit_censor.
what

Extraction target: "indices" or "parameters".
parm

Optional vector of index names.
level

Confidence level(s).
B

Number of bootstrap replicates.
method

Bootstrap CI method.
...

Additional 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

fit

A gpcifit_censor object returned by capability_censor.
true_params

Named list of true parameter values (if known).
true_indices

Named vector of true index values (if known).
B

Number of bootstrap replicates for SE computation.
alpha

Vector of significance levels for coverage probability.
x, object

An object of class gpci_diagnostics_censor.
...

Additional print/summary 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

dist

A gpci_dist_censor object.

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

name

Character string naming the distribution.
pdf

Function representing the probability density function (PDF/PMF).
cdf

Function representing the cumulative distribution function (CDF).
sf

Function representing the survival function (SF = 1 - CDF).
quantile

Function representing the quantile function.
params

Named list of parameters for the distribution.
support

Vector of length 2 defining lower and upper bounds of support.

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

data_left

Numeric vector of left interval bounds for interval-censored data.
data_right

Numeric vector of right interval bounds for interval-censored data.
dist

A gpci_dist_censor distribution object with initial parameters.
start

Optional named list of starting parameter values.

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

fit

A gpcifit_censor object.
index

Name of index to compute.

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

x

An object of class gpci_ci_censor.
...

Additional graphical parameters.

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

x

An object of class gpci_diagnostics_censor.
...

Additional graphical parameters.

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

x

An object of class gpcifit_censor.
main

Title of the plot.
...

Additional graphical parameters.

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)