Package 'gofPHCS'

Aluminum Coupon Fatigue Lifetimes Data

Description

Fatigue lifetimes (in 10^3 cycles) of 101 aluminum coupons under periodic stress loading.

Usage

aluminum_coupons

Format

A numeric vector of length 101.

Source

Birnbaum, Z. W., & Saunders, S. C. (1958). A statistical model for life-length of materials. JASA, 53(281), 151-160.

References

Banerjee, B., & Pradhan, B. (2018). Kolmogorov-Smirnov test for life test data with hybrid censoring. Communications in Statistics - Theory and Methods, 47(11), 2590-2604.

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Create a Censored Data Container

Description

Constructor for creating a structured censored dataset object of class "cens_data".

Usage

cens_data(
  x,
  scheme = c("complete", "typeII", "progtypeII", "hybridI", "hybridII", "hybridI_hcs",
    "hybridII_hcs"),
  n = length(x),
  r = NULL,
  R = NULL,
  T0 = NULL,
  verbose = FALSE
)

Arguments

x	Numeric vector of observed failure times. Must be finite.
scheme	Character string specifying the censoring scheme. Options are: "complete", "typeII", "progtypeII", "hybridI", "hybridII", "hybridI_hcs", and "hybridII_hcs".
n	Total sample size at the beginning of the experiment. Defaults to length(x).
r	Integer specifying the pre-fixed failure count for Type-II or hybrid censoring schemes.
R	Integer vector of progressive removals for "progtypeII", "hybridI_hcs", or "hybridII_hcs".
T0	Positive numeric value for pre-fixed time threshold in hybrid censoring schemes.
verbose	Logical; if TRUE, emits informative messages (e.g. when sorting unsorted x). Default is FALSE.

Value

An S3 object of class "cens_data" containing:

x	Numeric vector of sorted observed failure times.
scheme	Censoring scheme name.
n	Total initial sample size.
n_obs	Number of observed failure times length(x).
r	Pre-fixed failure count (if applicable).
R	Progressive removal vector (if applicable).
T0	Time threshold (if applicable).

References

Cramer, E., & Balakrishnan, N. (2023). Goodness-of-fit tests. In Hybrid Censoring Know-How (Chapter 11, pp. 321-329). Academic Press. doi:10.1016/B978-0-12-398387-9.00019-2

Examples

# Complete data
cd1 <- cens_data(x = c(0.5, 1.2, 2.1, 3.4), scheme = "complete")
print(cd1)

# Progressive Type-II censored data
cd2 <- cens_data(x = c(0.19, 0.78, 0.96, 1.31), scheme = "progtypeII", R = c(0, 1, 0, 2))
summary(cd2)

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Goodness-of-Fit Test Dispatcher for Censored Lifetime Data

Description

Main function for conducting goodness-of-fit tests on complete, progressively Type-II, and hybrid censored lifetime data.

Usage

gof_test(
  data,
  pdf = NULL,
  cdf = NULL,
  sf = NULL,
  pmf = NULL,
  distribution = NULL,
  params = NULL,
  statistic = "auto",
  p.method = c("auto", "asymptotic", "montecarlo"),
  nsim = 9999,
  seed = NULL,
  conf.level = 0.95,
  ...
)

Arguments

data	A "cens_data" object created by cens_data.
pdf	Optional probability density function f(x, ...).
cdf	Optional cumulative distribution function F(x, ...).
sf	Optional survival function S(x, ...).
pmf	Optional probability mass function P(x, ...).
distribution	Optional pre-constructed "gof_distribution" object created by make_distribution.
params	Parameter vector or named list for the null distribution.
statistic	Character string specifying test statistic name. Default "auto" selects default test for data$scheme. Use "all" to compute all applicable test statistics.
p.method	Character string specifying p-value calculation method ("auto", "asymptotic", or "montecarlo").
nsim	Integer specifying number of Monte Carlo replicates. Default is 9999.
seed	Optional integer seed for reproducible Monte Carlo simulation.
conf.level	Confidence level (default 0.95).
...	Additional arguments passed to specific statistic functions (e.g. mc_moments for "genT").

Value

An object of class c("gof_htest", "htest") containing:

statistic	Observed test statistic value.
p.value	Calculated p-value.
method	Character string describing the test.
data.name	Character string describing the dataset.
estimate	Parameter estimates / fitted values.

References

Balakrishnan, N., Ng, H. K. T., & Kannan, N. (2002). A test of exponentiality based on spacings for progressively type-II censored data. In Goodness-of-Fit Tests and Model Validity (pp. 89-111). Birkhauser.

Banerjee, B., & Pradhan, B. (2018). Kolmogorov-Smirnov test for life test data with hybrid censoring. Communications in Statistics - Theory and Methods, 47(11), 2590-2604. doi:10.1080/03610926.2016.1205616

Cramer, E., & Balakrishnan, N. (2023). Goodness-of-fit tests. In Hybrid Censoring Know-How (Chapter 11). Academic Press. doi:10.1016/B978-0-12-398387-9.00019-2

Examples

set.seed(42)
x_data <- rexp(15, rate = 0.5)
cd <- cens_data(x = x_data, scheme = "complete")
dist <- make_distribution(cdf = function(x, rate) pexp(x, rate), params = c(rate = 0.5))
res <- gof_test(cd, distribution = dist, statistic = "KS", p.method = "montecarlo", nsim = 99)
print(res)

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Insulating Fluid Breakdown Times Data

Description

Times to breakdown (in minutes) of an insulating fluid subjected to high voltage stress.

Usage

insulating_fluid

Format

A numeric vector of length 18.

Source

Nelson, W. (1982). Applied Life Data Analysis. John Wiley & Sons.

References

Cramer, E., & Balakrishnan, N. (2023). Goodness-of-fit tests. In Hybrid Censoring Know-How (Chapter 11). Academic Press.

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Create a Unified Distribution Adapter

Description

Constructs a distribution object encapsulating probability density function (pdf), cumulative distribution function (cdf), survival function (sf), and quantile function (qdist). Missing functions are derived automatically using numerical calculus and root-finding.

Usage

make_distribution(
  pdf = NULL,
  cdf = NULL,
  sf = NULL,
  pmf = NULL,
  discrete = FALSE,
  support = c(-Inf, Inf),
  params = NULL
)

Arguments

pdf	Probability density function f(x, ...).
cdf	Cumulative distribution function F(x, ...).
sf	Survival function S(x, ...).
pmf	Probability mass function P(x, ...) for discrete models.
discrete	Logical indicating if the distribution is discrete. Default is FALSE.
support	Numeric vector of length 2 defining distribution support bounds c(lower, upper). Default is c(-Inf, Inf).
params	Named list or numeric vector of parameters passed to pdf, cdf, sf, or pmf.

Value

An S3 object of class "gof_distribution" containing:

pdf	Vectorized density function pdf(x).
cdf	Vectorized CDF function cdf(x).
sf	Vectorized survival function sf(x).
qdist	Vectorized quantile function qdist(p).
discrete	Logical flag.
support	Support interval.
params	User-supplied parameter vector or list.

Examples

# Create an Exponential distribution adapter
exp_dist <- make_distribution(
  cdf = function(x, rate) pexp(x, rate = rate),
  params = c(rate = 0.5),
  support = c(0, Inf)
)
exp_dist$cdf(1)
exp_dist$pdf(1)

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Random Generation Engine for Censored Data

Description

Generates simulated datasets under specified censoring schemes from a quantile function qdist.

Usage

rcens(
  scheme = c("complete", "progtypeII", "hybridI", "hybridII", "hybridI_hcs",
    "hybridII_hcs"),
  n,
  R = NULL,
  r = NULL,
  T0 = NULL,
  qdist,
  nsim = 1
)

Arguments

scheme	Character string specifying censoring scheme ("complete", "progtypeII", "hybridI", "hybridII", "hybridI_hcs", "hybridII_hcs").
n	Integer specifying initial sample size.
R	Integer vector of progressive removals.
r	Integer specifying target failure count for Type-II or hybrid schemes.
T0	Numeric value specifying time threshold for hybrid schemes.
qdist	Quantile function qdist(p) of the target distribution.
nsim	Integer specifying the number of datasets to simulate. Default is 1.

Value

If nsim = 1, returns a single "cens_data" object. If nsim > 1, returns a list of "cens_data" objects.

References

Balakrishnan, N., & Sandhu, R. A. (1995). A simple simulational algorithm for generating progressive Type-II censored samples. The American Statistician, 49(2), 229-230.

Banerjee, B., & Pradhan, B. (2018). Kolmogorov-Smirnov test for life test data with hybrid censoring. Communications in Statistics - Theory and Methods, 47(11), 2590-2604. doi:10.1080/03610926.2016.1205616

Examples

# Simulate a progressive Type-II censored sample from Standard Exponential
set.seed(123)
sim_data <- rcens(
  scheme = "progtypeII", n = 10, R = c(0, 1, 0, 1, 3),
  qdist = function(p) qexp(p, rate = 1)
)
print(sim_data)

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