Title:	Reliability Growth Analysis
Version:	0.4
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) (No. AMSAATR138), 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, pkgload, rmarkdown, spelling, testthat (≥ 3.0.0), vdiffr, WeibullR
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:	2026-03-31 14:02:01 UTC; paulgovan
Author:	Paul Govan [aut, cre, cph]
Maintainer:	Paul Govan <paul.govan2@gmail.com>
Repository:	CRAN
Date/Publication:	2026-03-31 14:30:02 UTC

ReliaGrowR: Reliability Growth Analysis

Description

Modeling and plotting functions for Reliability Growth Analysis (RGA). The package implements three families of models and provides a REST API interface via plumber.

Reliability Growth Models

Crow-AMSAA (NHPP power-law)

The core model fits a Non-Homogeneous Poisson Process (NHPP) with a Weibull intensity function to cumulative failure data. Parameters are estimated by least-squares log-log regression (default) or maximum likelihood. A growth rate > 0 indicates reliability improvement.

Piecewise NHPP

Extends Crow-AMSAA by fitting separate NHPP segments separated by change points. Change points can be detected automatically via the segmented package or supplied by the user.

Duane

Log-log regression of cumulative MTBF versus cumulative time, providing a graphical and analytical representation of reliability growth.

Main Functions

S3 Classes and Methods

References

Crow, L. H. (1975). Reliability Analysis for Complex Repairable Systems. AMSAA Technical Report No. 138. US Army Materiel Systems Analysis Activity.

Duane, J. T. (1964). Learning curve approach to reliability monitoring. IEEE Transactions on Aerospace, 2(2), 563–566. doi:10.1109/TA.1964.4319640

Guo, H., Mettas, A., Sarakakis, G., & Niu, P. (2010). Piecewise NHPP models with maximum likelihood estimation for repairable systems. In Proceedings of the 2010 Annual Reliability and Maintainability Symposium (pp. 1–6). IEEE. doi:10.1109/RAMS.2010.5448029

Muggeo, V. M. R. (2024). segmented: Regression Models with Break-Points / Change-Points Estimation. R package. https://cran.r-project.org/package=segmented

Author(s)

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

See Also

Useful links:

• https://paulgovan.github.io/ReliaGrowR/

• https://github.com/paulgovan/ReliaGrowR

• Report bugs at https://github.com/paulgovan/ReliaGrowR/issues

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

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:

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()

Value

Launches the ReliaGrowR API on a local server.

Examples

## Not run: 
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

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

Value

Invisibly returns NULL.

See Also

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

Plot Method for rga_predict Objects

Description

Plots observed data, the fitted reliability growth curve, and the forecast with optional confidence bounds for an rga_predict object.

Usage

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

Arguments

Value

Invisibly returns NULL.

See Also

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

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit <- rga(times, failures)
fc <- predict_rga(fit, times = c(1500, 2000))
plot(fc, main = "RGA Forecast", 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

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)

Forecast Cumulative Failures from a Reliability Growth Model

Description

Takes a fitted rga object and a vector of cumulative times, returning predicted cumulative failures with confidence bounds as an rga_predict S3 object.

Usage

predict_rga(object, times, conf_level = 0.95)

Arguments

Value

An object of class rga_predict containing:

See Also

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

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit <- rga(times, failures)
fc <- predict_rga(fit, times = c(1500, 2000))
print(fc)

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

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

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

Value

Invisibly returns the input object.

See Also

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

Examples

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

Print Method for rga_predict Objects

Description

Prints a formatted table of forecast cumulative failures with confidence bounds for an rga_predict object.

Usage

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

Arguments

Value

Invisibly returns the input object.

See Also

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

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit <- rga(times, failures)
fc <- predict_rga(fit, times = c(1500, 2000))
print(fc)

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

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,
  f = 0,
  n = NULL,
  test_time = NULL
)

Arguments

Value

The function returns an object of class rdt that contains:

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) (AMSAATR138) 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,
  times_type = c("failure_times", "cumulative_failure_times"),
  model_type = "Crow-AMSAA",
  breaks = NULL,
  conf_level = 0.95,
  method = c("LS", "MLE")
)

Arguments

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:

See Also

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

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)

cum_times <- cumsum(times)
result2b <- rga(cum_times, failures, times_type = "cumulative_failure_times")
print(result2b)

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

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

Simulate Failures from a Conditional Weibull Model

Description

Simulates which units in a non-failed population fail next by using a Weibull life model conditional on each unit's current runtime. When a positive window is supplied, the function calibrates a Weibull scale parameter (unless provided directly) so that the expected number of failures within the window matches n. Units are then sampled with probability proportional to their conditional Weibull failure probability over the window, and failure times are drawn from the truncated conditional Weibull distribution. The full fleet is returned: selected units are labelled "Failure" and the remaining units are labelled "Suspension".

Usage

sim_failures(n, runtimes, replace = FALSE, window = NULL, beta = 1, eta = NULL)

Arguments

Details

When window = NULL, the function returns the current fleet state at the supplied runtimes. In this case, failing units are selected using relative Weibull hazard weights implied by beta.

Value

A data frame with length(runtimes) rows sorted ascending by runtime, containing:

The returned object also carries attributes weibull_beta and weibull_eta describing the Weibull parameters used for the simulation.

See Also

Other data preparation: weibull_to_rga()

Examples

set.seed(42)
runtimes <- c(100, 500, 200, 800, 300)
result <- sim_failures(2, runtimes, beta = 1.5)
print(result)

# With an observation window
set.seed(42)
result_w <- sim_failures(2, runtimes, window = 50, beta = 1.5)
print(result_w)

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)

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

Value

The data frame contains two columns:

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

See Also

Other data preparation: sim_failures()

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)