Title: Reliability Growth Analysis
Version: 0.3
Description: Modeling and plotting functions for Reliability Growth Analysis (RGA). Models include the Duane (1962) <doi:10.1109/TA.1964.4319640>, Non-Homogeneous Poisson Process (NHPP) by Crow (1975) https://apps.dtic.mil/sti/citations/ADA020296, Piecewise Weibull NHPP by Guo et al. (2010) <doi:10.1109/RAMS.2010.5448029>, and Piecewise Weibull NHPP with Change Point Detection based on the 'segmented' package by Muggeo (2024) https://cran.r-project.org/package=segmented.
Imports: graphics, plumber, segmented, stats
License: CC BY 4.0
Encoding: UTF-8
Suggests: ellmer, knitr, rmarkdown, spelling, testthat (≥ 3.0.0), vdiffr
Language: en-US
URL: https://paulgovan.github.io/ReliaGrowR/, https://github.com/paulgovan/ReliaGrowR
Config/testthat/edition: 3
VignetteBuilder: knitr
BugReports: https://github.com/paulgovan/ReliaGrowR/issues
RoxygenNote: 7.3.3
Depends: R (≥ 3.5)
LazyData: true
NeedsCompilation: no
Packaged: 2025-11-07 01:17:35 UTC; paulgovan
Author: Paul Govan ORCID iD [aut, cre, cph]
Maintainer: Paul Govan <paul.govan2@gmail.com>
Repository: CRAN
Date/Publication: 2025-11-07 06:10:47 UTC

ReliaGrowR: Reliability Growth Analysis

Description

Modeling and plotting functions for Reliability Growth Analysis (RGA). Models include the Duane (1962) doi:10.1109/TA.1964.4319640, Non-Homogeneous Poisson Process (NHPP) by Crow (1975) https://apps.dtic.mil/sti/citations/ADA020296, Piecewise Weibull NHPP by Guo et al. (2010) doi:10.1109/RAMS.2010.5448029, and Piecewise Weibull NHPP with Change Point Detection based on the 'segmented' package by Muggeo (2024) https://cran.r-project.org/package=segmented.

Author(s)

Maintainer: Paul Govan paul.govan2@gmail.com (ORCID) [copyright holder]

See Also

Useful links:

Duane Analysis

Description

This function performs a Duane analysis (1962) doi:10.1109/TA.1964.4319640 on failure data by fitting a log-log linear regression of cumulative Mean Time Between Failures (MTBF) versus cumulative time. The function accepts either two numeric vectors (times, failures) or a data frame containing both.

Usage

duane(times, failures = NULL, conf.level = 0.95)

Arguments

times

Either:

  • A numeric vector of cumulative failure times, or

  • A data frame containing two columns: times and failures. The times column contains cumulative failure times, and the failures column contains the number of failures at each corresponding time.

failures

A numeric vector of the number of failures at each corresponding time in times. Ignored if times is a data frame. Must be the same length as times if both are vectors. All values must be positive and finite.

conf.level

Confidence level for the confidence bounds (default: 0.95). Must be between 0 and 1 (exclusive).

Details

The scaling relationship between the size of input data (numbers of observations) and speed of algorithm execution is approximately linear (O(n)). The function is efficient and can handle large data sets (e.g., thousands of observations) quickly. The function uses base R functions and does not require any additional packages. The function includes comprehensive input validation and error handling to ensure robustness. The function is tested with a standard data set from a published paper and includes unit tests to verify correctness and performance.

Value

A list of class "duane" containing:

times

The input cumulative failure times.

failures

The input number of failures.

n_obs

The number of observations (failures).

MTBF

The cumulative mean time between failures.

model

The fitted lm (linear model) object containing the regression results.

logLik

The log-likelihood of the fitted model.

AIC

Akaike Information Criterion (AIC).

BIC

Bayesian Information Criterion (BIC).

conf.level

The confidence level.

Cumulative_Time

The cumulative operating times.

Cumulative_MTBF

The cumulative mean time between failures.

Fitted_Values

The fitted values on the MTBF scale.

Confidence_Bounds

Matrix of fitted values and confidence bounds on the MTBF scale.

Residuals_Log

Residuals on the log(MTBF) scale (from the regression).

Residuals_MTBF

Residuals on the MTBF scale (observed - fitted).

See Also

Other Duane functions: plot.duane(), print.duane()

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit1 <- duane(times, failures, conf.level = 0.90)
print(fit1)

df <- data.frame(times = times, failures = failures)
fit2 <- duane(df, conf.level = 0.95)
print(fit2)

ReliaGrowR API

Description

This function provides an interface to the ReliaGrowR API.#' This function provides an interface to the ReliaGrowR API.

Usage

grwr_api()

Examples

## Not run: 
grwr_api()#' grwr_api()

## End(Not run)

Plot Method for Duane Analysis

Description

Generates a Duane plot (log-log or linear scale) with fitted regression line and optional confidence bounds.

Usage

## S3 method for class 'duane'
plot(
  x,
  log = TRUE,
  conf.int = TRUE,
  legend = TRUE,
  legend.pos = "topleft",
  ...
)

Arguments

x

An object of class "duane".

log

Logical; whether to use logarithmic scales for axes (default: TRUE).

conf.int

Logical; whether to plot confidence bounds (default: TRUE).

legend

Logical; whether to include a legend (default: TRUE).

legend.pos

Position of the legend (default: "topleft").

...

Further arguments passed to plot().

Value

Invisibly returns NULL.

See Also

Other Duane functions: duane(), print.duane()

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit <- duane(times, failures)
plot(fit, main = "Duane Plot", xlab = "Cumulative Time", ylab = "Cumulative MTBF")

Plot Method for RGA Objects

Description

This function generates plots for objects of class rga.

Usage

## S3 method for class 'rga'
plot(
  x,
  conf_bounds = TRUE,
  legend = TRUE,
  log = FALSE,
  legend_pos = "bottomright",
  ...
)

Arguments

x

An object of class rga, which contains the results from the RGA model.

conf_bounds

Logical; include confidence bounds (default: TRUE).

legend

Logical; show the legend (default: TRUE).

log

Logical; use a log-log scale (default: FALSE).

legend_pos

Position of the legend (default: "bottomright").

...

Additional arguments passed to plot().

Value

Invisibly returns NULL.

See Also

Other Reliability Growth Analysis: print.rga(), rga()

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
result <- rga(times, failures)
plot(result,
  main = "Reliability Growth Analysis",
  xlab = "Cumulative Time", ylab = "Cumulative Failures"
)

P-P Plot for RGA Objects

Description

This function creates a P-P plot for a fitted Reliability Growth Analysis (RGA) model. Currently only supports the Crow-AMSAA model. A P-P plot compares the empirical cumulative distribution function (CDF) to the theoretical CDF specified by the model. If the model fits well, the points should fall approximately along a straight line.

Usage

ppplot.rga(x, main = "P-P Plot", ...)

Arguments

x

An object of class rga.

main

Title of the plot.

...

Additional arguments passed to plot().

Value

A P-P plot comparing empirical and theoretical CDFs.

See Also

Other goodness-of-fit: qqplot.rga()

Examples

times <- c(5, 10, 15, 20, 25)
failures <- c(1, 2, 1, 3, 2)
fit <- rga(times, failures)
ppplot.rga(fit)

Print method for duane objects.

Description

This function prints a summary of the Duane analysis result.

Usage

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

Arguments

x

An object of class "duane" returned by the duane_plot function.

...

Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

Other Duane functions: duane(), plot.duane()

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit <- duane(times, failures)
print(fit)

Print method for rdt objects

Description

This function provides a formatted print method for objects of class rdt.

Usage

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

Arguments

x

An object of class rdt.

...

Additional arguments (not used).

Value

Invisibly returns the input object.

Examples

plan <- rdt(target = 0.9, mission_time = 1000, conf_level = 0.9, beta = 1, n = 10)
print(plan)

Print method for rga objects.

Description

This function prints a summary of the results from an object of class rga.

Usage

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

Arguments

x

An object of class rga, which contains the results from the RGA model.

...

Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

Other Reliability Growth Analysis: plot.rga(), rga()

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
result <- rga(times, failures)
print(result)

Q-Q Plot for RGA Objects

Description

This function creates a Q-Q plot for a fitted Reliability Growth Analysis (RGA) model Currently only supports the Crow-AMSAA model. A Q-Q plot compares the quantiles of the empirical data to the quantiles of the theoretical distribution specified by the model. If the model fits well, the points should fall approximately along a straight line.

Usage

qqplot.rga(x, main = "Q-Q Plot", ...)

Arguments

x

An object of class rga.

main

Title of the plot.

...

Additional arguments passed to stats::qqplot().

Value

A Q-Q plot comparing empirical and theoretical quantiles.

See Also

Other goodness-of-fit: ppplot.rga()

Examples

times <- c(5, 10, 15, 20, 25)
failures <- c(1, 2, 1, 3, 2)
fit <- rga(times, failures)
qqplot.rga(fit)

Reliability Demonstration Test (RDT) Plan Calculator

Description

This function calculates the required test time or sample size for a Reliability Demonstration Test (RDT) based on specified reliability, mission time, confidence level, and Weibull shape parameter.

Usage

rdt(target, mission_time, conf_level, beta = 1, n = NULL, test_time = NULL)

Arguments

target

Required reliability at mission time (0 < target < 1).

mission_time

Mission duration (time units). Must be greater than 0.

conf_level

Desired confidence level (e.g., 0.9 for 90% confidence). The confidence level must be between 0 and 1 (exclusive).

beta

Weibull shape parameter (beta=1 corresponds to exponential distribution). Must be greater than 0. Default is 1.

n

Sample size (optional, supply if solving for test_time). Must be a positive integer.

test_time

Test time per unit (optional, supply if solving for n). Must be greater than 0.

Value

The function returns an object of class rdt that contains:

Distribution

Type of distribution used (Exponential or Weibull).

Beta

Weibull shape parameter.

Target_Reliability

Specified target reliability.

Mission_Time

Specified mission time.

Required_Test_Time

Calculated required test time (if n is provided).

Input_Sample_Size

Provided sample size (if test_time is calculated).

Required_Sample_Size

Calculated required sample size (if test_time is provided).

Input_Test_Time

Provided test time (if n is calculated).

Examples

#' # Example 1: Calculate required test time
plan1 <- rdt(target = 0.9, mission_time = 1000, conf_level = 0.9, beta = 1, n = 10)
print(plan1)
# Example 2: Calculate required sample size
plan2 <- rdt(target = 0.9, mission_time = 1000, conf_level = 0.9, beta = 1, test_time = 2000)
print(plan2)

Reliability Growth Analysis.

Description

This function performs reliability growth analysis using the Crow-AMSAA model by Crow (1975) https://apps.dtic.mil/sti/citations/ADA020296 or piecewise NHPP model by Guo et al. (2010) doi:10.1109/RAMS.2010.5448029. It fits a log-log linear regression of cumulative failures versus cumulative time. The function accepts either two numeric vectors (times, failures) or a data frame containing both. The ⁠Piecewise NHPP⁠ model can automatically detect change points or use user-specified breakpoints.

Usage

rga(
  times,
  failures,
  model_type = "Crow-AMSAA",
  breaks = NULL,
  conf_level = 0.95
)

Arguments

times

Either a numeric vector of cumulative failure times or a data frame containing both failure times and failure counts. If a data frame is provided, it must contain two columns: times and failures. The times column contains cumulative failure times, and the failures column contains the number of failures at each corresponding time.

failures

A numeric vector of the number of failures at each corresponding time in times. Must be the same length as times if both are vectors. All values must be positive and finite. Ignored if times is a data frame.

model_type

The model type. Either Crow-AMSAA (default) or ⁠Piecewise NHPP⁠ with change point detection.

breaks

An optional vector of breakpoints for the ⁠Piecewise NHPP⁠ model.

conf_level

The desired confidence level, which defaults to 95%. The confidence level is the probability that the confidence interval contains the true mean response.

Details

The scaling relationship between the size of input data (numbers of observations) and speed of algorithm execution is approximately linear (O(n)). The function is efficient and can handle large data sets (e.g., thousands of observations) quickly. The function uses the segmented package for piecewise regression, which employs an iterative algorithm to estimate breakpoints. The number of iterations required for convergence may vary depending on the data and initial values. In practice, the function typically converges within a few iterations for most data sets. However, in some cases, especially with complex data or poor initial values, it may take more iterations.

Value

The function returns an object of class rga that contains:

times

The input cumulative failure times.

failures

The input number of failures.

n_obs

The number of observations (failures).

cum_failures

Cumulative failures.

model

The fitted model object (lm (linear model) or segmented).

residuals

Model residuals on the log-log scale. These represent deviations of the observed log cumulative failures from the fitted values and are useful for diagnostic checking.

logLik

The log-likelihood of the fitted model. The log-likelihood is a measure of model fit, with higher values indicating a better fit.

AIC

Akaike Information Criterion (AIC). AIC is a measure used for model selection, with lower values indicating a better fit.

BIC

Bayesian Information Criterion(BIC). BIC is another criterion for model selection

breakpoints

Breakpoints (log scale) if applicable.

fitted_values

Fitted cumulative failures on the original scale.

lower_bounds

Lower confidence bounds (original scale).

upper_bounds

Upper confidence bounds (original scale).

betas

Estimated beta(s). Betas are the slopes of the log-log plot.

betas_se

Standard error(s) of the estimated beta(s).

growth_rate

Estimated growth rate(s). Growth rates are calculated as 1 - beta.

lambdas

Estimated lambda(s). Lambdas are the intercepts of the log-log plot.

See Also

Other Reliability Growth Analysis: plot.rga(), print.rga()

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
result1 <- rga(times, failures)
print(result1)

df <- data.frame(times = times, failures = failures)
result2 <- rga(df)
print(result2)

result3 <- rga(times, failures, model_type = "Piecewise NHPP")
print(result3)

result4 <- rga(times, failures, model_type = "Piecewise NHPP", breaks = c(450))
print(result4)

Reliability Test Data

Description

A dataset containing example reliability test data from the military report "Reliability Growth Prediction" (1986) by The Analytical Sciences Corporation. This dataset includes cumulative ETI, failure counts, cumulative MTBF, report numbers, flags, and causes for two different LRUs (G1 and G2).

Usage

testdata

Format

@format ## testdata A data frame with 25 rows and 6 variables:

LRU

The Line Replaceable Unit identifier (G1 or G2).

Cum_ETI

Cumulative Equivalent Test Hours (ETI).

Failure_Count

Cumulative number of failures observed.

Cum_MTBF

Cumulative Mean Time Between Failures (MTBF).

Report_No

Report number associated with the failure.

Flag

A flag indicating special conditions or notes.

Cause

Cause of the failure (e.g., D for Design, M for Manufacturing, R for Random, NR for No Report).

@usage data(testdata)

Source

https://apps.dtic.mil/sti/tr/pdf/ADA176128.pdf

Examples

data(testdata)
head(testdata)
summary(testdata)
str(testdata)

Weibull to RGA

Description

Converts Weibull data (failure, suspension, and interval-censored times) into a format suitable for reliability growth analysis (RGA). The function handles exact failure times, right-censored suspensions, and interval-censored data. It approximates interval-censored failures by placing them at the midpoint of the interval. The output is a data frame with cumulative time and failure counts. This format can be used with RGA models such as Crow-AMSAA.

Usage

weibull_to_rga(
  failures,
  suspensions = NULL,
  interval_starts = NULL,
  interval_ends = NULL
)

Arguments

failures

A numeric vector of exact failure times. Each failure time indicates when an item failed during the observation period.

suspensions

A numeric vector of suspension (right-censored) times. A suspension indicates that the item was removed from observation at that time without failure. This parameter is optional and can be NULL if there are no suspensions.

interval_starts

A numeric vector of interval start times (lower bound of censoring). This parameter is optional and can be NULL if there are no interval-censored data. If provided, it must be the same length as interval_ends.

interval_ends

A numeric vector of interval end times (upper bound of censoring). This parameter is optional and can be NULL if there are no interval-censored data. If provided, it must be the same length as interval_starts.

Value

The data frame contains two columns:

CumulativeTime

Cumulative time at each failure event.

Failures

Number of failures at each cumulative time point.

The function approximates interval-censored failures by placing them at the midpoint of the interval.

Examples

failures <- c(100, 200, 200, 400)
suspensions <- c(250, 350, 450)
interval_starts <- c(150, 300)
interval_ends <- c(180, 320)
result <- weibull_to_rga(failures, suspensions, interval_starts, interval_ends)
print(result)