Package 'OneShotEM'

Extract Akaike Information Criterion (AIC)

Description

Extract Akaike Information Criterion (AIC)

Usage

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

Arguments

object	an object of class "oneshot_em".
...	optional additional objects.
k	penalty per parameter (default: 2).

Value

A numeric scalar of class "numeric" containing the calculated Akaike Information Criterion (AIC) value for the fitted model.

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Extract Bayesian Information Criterion (BIC)

Description

Extract Bayesian Information Criterion (BIC)

Usage

## S3 method for class 'oneshot_em'
BIC(object, ...)

Arguments

object	an object of class "oneshot_em".
...	optional additional objects.

Value

A numeric scalar of class "numeric" containing the calculated Bayesian Information Criterion (BIC) value for the fitted model.

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Extract Model Coefficients

Description

Extract Model Coefficients

Usage

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

Arguments

object	an object of class "oneshot_em".
...	additional arguments (unused).

Value

A named numeric vector of class "numeric" containing the maximum likelihood estimates of the model parameters.

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Electro-Explosive Device Accelerated Life Test Data

Description

One-shot device accelerated life test (ALT) dataset reported by Fan, Balakrishnan, and Chang (2009) and analyzed by Zhu et al. (2026).

Usage

data(electro_explosive)

Format

A data frame with 9 rows and 4 variables:

temp

temperature stress setting in degrees Celsius (35, 45, 55)

it

inspection time in hours (10, 20, 30)

n

number of devices tested at the specified inspection time (10 per row, total 90)

r

number of observed device failures at inspection

Source

Fan, T., Balakrishnan, N., & Chang, C. (2009). The Bayesian approach for highly reliable electro-explosive devices using one-shot device testing. Journal of Statistical Computation and Simulation, 79(9), 1143–1154. doi:10.1080/00949650802142592

References

Zhu, X., Li, Y., Li, T., & Balakrishnan, N. (2026). A simple and efficient eM-algorithm for one-shot device data analysis. Communications in Statistics - Simulation and Computation, 55(3), 959–970. doi:10.1080/03610918.2025.2515193

Examples

data(electro_explosive)
head(electro_explosive)

---

Control Parameters for EM Algorithms

Description

Sets control parameters for the Expectation-Maximization algorithms.

Usage

em_control(
  maxit = 1000,
  tol = 1e-06,
  trace = FALSE,
  optimizer = c("nlm", "optim"),
  max_m_iter = 100,
  reltol = 1e-10
)

Arguments

maxit	maximum number of EM iterations (default: 1000).
tol	convergence tolerance based on maximum relative difference between parameter iterations (default: 1e-6).
trace	logical; if TRUE, iteration progress is printed (default: FALSE).
optimizer	optimization method for the M-step, either "nlm" or "optim" (default: "nlm").
max_m_iter	maximum iterations for the inner M-step optimization (default: 100).
reltol	relative tolerance for M-step optimizer (default: 1e-10).

Value

A list containing the control options.

Examples

ctrl <- em_control(maxit = 500, tol = 1e-5, trace = FALSE)

---

Extract Log-Likelihood

Description

Extract Log-Likelihood

Usage

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

Arguments

object	an object of class "oneshot_em".
...	additional arguments (unused).

Value

An object of class "logLik" representing the maximized log-likelihood value, with additional attributes "df" (degrees of freedom / number of estimated parameters) and "nobs" (total number of tested devices).

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Maximum Likelihood Estimation via New eM-Algorithm for One-Shot Device Data

Description

Fits lifetime models for one-shot device data using the new expectation-maximization (eM) algorithm proposed by Zhu et al. (2026).

Usage

oneshot_em(
  formula,
  data,
  it = "it",
  dist = c("exponential", "weibull", "lognormal", "gamma", "custom"),
  sf_fun = NULL,
  theta0 = NULL,
  control = em_control()
)

Arguments

formula	an object of class formula (e.g., cbind(r, n) ~ temp or r/n ~ temp).
data	a data frame containing the variables in the model.
it	character string or vector specifying inspection time variable. If data is supplied, can be the column name of inspection time.
dist	lifetime distribution name: "exponential", "weibull", "lognormal", "gamma", or custom. Default is "exponential".
sf_fun	custom survival function of signature function(t, theta, X). Required if dist = "custom".
theta0	numeric vector of initial parameter values. If omitted, calculated automatically.
control	list of control parameters from em_control.

Value

An object of class "oneshot_em" containing:

coefficients	estimated model parameters
loglik	maximized log-likelihood value
iterations	number of EM iterations to convergence
converged	logical indicating successful convergence
vcov	variance-covariance matrix
std_err	standard errors of parameter estimates
dist	distribution used
method	"npm" (new proposed method)
data	input data frame
formula	model formula
terms	model terms object
control	control list

References

Zhu, X., Li, Y., Li, T., & Balakrishnan, N. (2026). A simple and efficient eM-algorithm for one-shot device data analysis. Communications in Statistics - Simulation and Computation, 55(3), 959–970. doi:10.1080/03610918.2025.2515193

Examples

data(electro_explosive)
fit_exp <- oneshot_em(cbind(r, n) ~ temp, data = electro_explosive,
                      it = "it", dist = "exponential")
summary(fit_exp)

---

Unified Wrapper for Fitting One-Shot Device ALT Models

Description

Unified high-level fitting interface for one-shot device accelerated life test data.

Usage

oneshot_fit(
  formula,
  data,
  it = "it",
  dist = c("exponential", "weibull", "lognormal", "gamma", "custom"),
  method = c("npm", "tm"),
  sf_fun = NULL,
  theta0 = NULL,
  control = em_control()
)

Arguments

formula	an object of class formula (e.g., cbind(r, n) ~ temp or r/n ~ temp).
data	a data frame containing the variables in the model.
it	character string or vector specifying inspection time variable. If data is supplied, can be the column name of inspection time.
dist	lifetime distribution name: "exponential", "weibull", "lognormal", "gamma", or custom. Default is "exponential".
method	estimation method: "npm" (new proposed eM-algorithm) or "tm" (traditional EM algorithm).
sf_fun	custom survival function of signature function(t, theta, X). Required if dist = "custom".
theta0	numeric vector of initial parameter values. If omitted, calculated automatically.
control	list of control parameters from em_control.

Value

An object of class "oneshot_em" containing model fitting results (see oneshot_em for full list of output elements).

Examples

data(electro_explosive)
fit <- oneshot_fit(cbind(r, n) ~ temp, data = electro_explosive,
                   it = "it", dist = "weibull", method = "npm")
print(fit)

---

Standardized and Generalized Residuals for One-Shot Device EM Fit

Description

Computes standardized Pearson residuals and randomized quantile residuals for one-shot device data models.

Usage

oneshot_residuals(fit)

Arguments

fit	an object of class "oneshot_em".

Value

A data frame containing:

observed	observed failure count
expected	expected failure count
pearson	standardized Pearson residual
quantile	randomized quantile residual

Examples

data(electro_explosive)
fit <- oneshot_em(cbind(r, n) ~ temp, data = electro_explosive, it = "it")
res <- oneshot_residuals(fit)
head(res)

---

Maximum Likelihood Estimation via Traditional EM-Algorithm for One-Shot Device Data

Description

Fits lifetime models for one-shot device data using the traditional failure-time expectation-maximization (EM) algorithm for comparison with the new eM-algorithm (oneshot_em).

Usage

oneshot_tm(
  formula,
  data,
  it = "it",
  dist = c("exponential", "weibull", "lognormal", "gamma", "custom"),
  sf_fun = NULL,
  theta0 = NULL,
  control = em_control()
)

Arguments

formula	an object of class formula (e.g., cbind(r, n) ~ temp or r/n ~ temp).
data	a data frame containing the variables in the model.
it	character string or vector specifying inspection time variable. If data is supplied, can be the column name of inspection time.
dist	lifetime distribution name: "exponential", "weibull", "lognormal", "gamma", or custom. Default is "exponential".
sf_fun	custom survival function of signature function(t, theta, X). Required if dist = "custom".
theta0	numeric vector of initial parameter values. If omitted, calculated automatically.
control	list of control parameters from em_control.

Value

An object of class "oneshot_em" fitted via the traditional EM approach, containing:

coefficients	estimated model parameters
loglik	maximized log-likelihood value
iterations	number of EM iterations to convergence
converged	logical indicating successful convergence
vcov	variance-covariance matrix
std_err	standard errors of parameter estimates
dist	distribution used
method	"tm" (traditional method)
data	input data frame
formula	model formula
terms	model terms object
control	control list

References

Balakrishnan, N., & Ling, M. (2012). EM algorithm for one-shot device testing under the exponential distribution. Computational Statistics & Data Analysis, 56(3), 502–509.

Examples

data(electro_explosive)
fit_tm <- oneshot_tm(cbind(r, n) ~ temp, data = electro_explosive,
                     it = "it", dist = "exponential")
summary(fit_tm)

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Diagnostic Plots for One-Shot Device EM Fit

Description

Generates fitted survival curves, empirical vs fitted failure proportions, or residual plots.

Usage

## S3 method for class 'oneshot_em'
plot(x, type = c("fitted", "survival", "residuals"), ...)

Arguments

x	an object of class "oneshot_em".
type	plot type: "fitted" (fitted vs observed failure rates), "survival" (fitted survival curves over time), or "residuals".
...	additional graphical parameters.

Value

Invisibly returns the original input object x of class "oneshot_em". This function is called for its side effect of producing graphical diagnostic plots (fitted vs observed failure rates, survival curves, or standardized residuals).

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Predict Survival Probability or Mean Time To Failure

Description

Predicts survival probability $S(t)$ or Mean Time To Failure (MTTF) under specified stress levels.

Usage

## S3 method for class 'oneshot_em'
predict(object, newdata = NULL, time = NULL, type = c("survival", "mttf"), ...)

Arguments

object	an object of class "oneshot_em".
newdata	data frame containing new stress levels.
time	numeric vector of inspection times for survival prediction.
type	prediction type: "survival" or "mttf".
...	additional arguments (unused).

Value

A numeric vector or matrix of class "numeric" containing predicted survival probabilities (when type = "survival") or Mean Time To Failure (MTTF) values (when type = "mttf") calculated under the specified stress levels and times.

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Print Method for One-Shot Device EM Fit

Description

Print Method for One-Shot Device EM Fit

Usage

## S3 method for class 'oneshot_em'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x	an object of class "oneshot_em".
digits	number of significant digits to print.
...	additional arguments (unused).

Value

Invisibly returns the original input object x of class "oneshot_em". This function is called primarily for its side effect of printing model fit summary information (distribution, convergence status, estimated coefficients, log-likelihood) to the console.

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Print Method for Summary of One-Shot Device EM Fit

Description

Print Method for Summary of One-Shot Device EM Fit

Usage

## S3 method for class 'summary.oneshot_em'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

Arguments

x	an object of class "summary.oneshot_em".
digits	number of significant digits to print.
...	additional arguments (unused).

Value

Invisibly returns the summary object x of class "summary.oneshot_em". This function is called primarily for its side effect of formatting and printing model summary results, coefficient matrices, and information criteria to the console.

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Summary Method for One-Shot Device EM Fit

Description

Computes summary statistics including standard errors, z-values, p-values, 95% Wald confidence intervals, and model selection criteria.

Usage

## S3 method for class 'oneshot_em'
summary(object, level = 0.95, ...)

Arguments

object	an object of class "oneshot_em".
level	confidence level for confidence intervals (default: 0.95).
...	additional arguments (unused).

Value

An object of class "summary.oneshot_em", which is a list containing the following components:

coefficients	a matrix of parameter estimates, standard errors, z-values, p-values, and confidence intervals
loglik	maximized log-likelihood value
npar	number of estimated parameters
nobs	total number of tested devices
aic	Akaike Information Criterion
bic	Bayesian Information Criterion
aicc	corrected Akaike Information Criterion
hqic	Hannan-Quinn Information Criterion
iterations	number of EM iterations executed
converged	logical flag indicating convergence status
dist	fitted lifetime distribution name
method	estimation algorithm name ("npm" or "tm")
call_object	original fitted "oneshot_em" object

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Extract Variance-Covariance Matrix

Description

Extract Variance-Covariance Matrix

Usage

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

Arguments

object	an object of class "oneshot_em".
...	additional arguments (unused).

Value

A symmetric numeric matrix of class "matrix" representing the estimated variance-covariance matrix of the parameter estimates.

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