Package 'ReliaGrowR'

Duane Analysis

Description

This function performs a Duane analysis (1962) https://doi.org/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, conf.level = NULL)

Arguments

times	Either: A numeric vector of exact failure times, or A data frame containing two columns: times and failures. The times column contains exact 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).
conf.level	Deprecated. Use conf_level instead.

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 exact 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(), plot.duane_predict(), predict_duane(), print.duane(), print.duane_predict()

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)

---

Exposure Analysis for Repairable Systems.

Description

Computes exposure (total operating time at risk) across one or more repairable systems as a function of time. Exposure is defined as the total accumulated observation time summed across all systems still under observation. The function also computes the number of systems at risk and the event rate (events per unit exposure) at each event time.

Usage

exposure(id = NULL, time = NULL, event = NULL, data = NULL)

Arguments

id	A vector of system/unit identifiers. Each unique value represents a distinct system.
time	A numeric vector of event or censoring times. Must be positive and finite.
event	An optional numeric vector of event indicators: 1 for an event, 0 for censoring (end of observation). If NULL (default), all observations are treated as events, and the maximum time per system is treated as the end of observation.
data	An optional data frame containing columns named id, time, and optionally event.

Details

Exposure is the total amount of operating time during which events can occur. For a fleet of $k$ systems observed up to times $T_1, T_2, \ldots, T_k$, the total exposure is $E = \sum_{i=1}^{k} T_i$.

The cumulative exposure at time $t$ is $E(t) = \sum_{i=1}^{k} \min(t, T_i)$, i.e., each system contributes time up to the lesser of $t$ or its observation end.

The event rate at time $t$ is the cumulative number of events divided by the cumulative exposure: $r(t) = N(t) / E(t)$.

Value

An object of class exposure containing:

time	Sorted unique event times (excluding censoring-only times).
n_at_risk	Number of systems under observation at each event time.
cum_exposure	Cumulative total exposure (system-time) up to each event time.
cum_events	Cumulative number of events up to each event time.
event_rate	Cumulative event rate (cum_events / cum_exposure) at each event time.
total_exposure	Total exposure across all systems and the full observation period.
total_events	Total number of events.
n_systems	Number of distinct systems.
end_times	Named numeric vector of end-of-observation times per system. Can be passed directly to mcf(end_time = ...) to ensure the MCF properly accounts for system exposure.

See Also

Other Repairable Systems Analysis: mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

id   <- c(1, 1, 1, 2, 2, 2, 3, 3, 3, 3)
time <- c(100, 350, 500, 80, 300, 600, 150, 250, 400, 700)
result <- exposure(id, time)
print(result)
plot(result)

# With censoring
id    <- c(1, 1, 1, 2, 2, 2, 3, 3, 3)
time  <- c(100, 350, 500, 80, 300, 400, 150, 250, 700)
event <- c(  1,   1,   0,  1,   1,   0,   1,   1,   1)
result2 <- exposure(id, time, event)
print(result2)

---

Goodness-of-Fit Statistics for RGA Objects

Description

Computes numerical goodness-of-fit statistics for a fitted Reliability Growth Analysis (RGA) model using the time-transformation approach. For a Crow-AMSAA (Power Law NHPP) model with parameters $\beta$ and $\lambda$, the transformed values $W_i = (t_i / t_n)^{\beta}$ should follow a Uniform(0, 1) distribution if the model fits. The Cramér-von Mises and Kolmogorov-Smirnov statistics are computed against this null distribution.

Usage

gof(x, ...)

## Default S3 method:
gof(x, ...)

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

Arguments

x	An object for which a goodness-of-fit method is defined.
...	Additional arguments passed to methods.

Value

An object of class gof.

See Also

Other goodness-of-fit: ppplot.rga(), print.gof(), qqplot.rga()

Examples

times <- c(5, 10, 15, 20, 25)
failures <- c(1, 2, 1, 3, 2)
fit <- rga(times, failures)
g <- gof(fit)
print(g)

---

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)

---

Mean Cumulative Function for Repairable Systems.

Description

Computes the non-parametric Mean Cumulative Function (MCF) for recurrent event data from one or more repairable systems, using the Nelson-Aalen estimator. The MCF estimates the expected cumulative number of events per system as a function of time, properly accounting for system exposure (observation windows).

Usage

mcf(
  id = NULL,
  time = NULL,
  event = NULL,
  end_time = NULL,
  data = NULL,
  conf_level = 0.95
)

Arguments

id	A vector of system/unit identifiers. Each unique value represents a distinct system. Ignored if data is provided.
time	A numeric vector of event or censoring times. Must be positive and finite. Ignored if data is provided.
event	An optional numeric vector of event indicators: 1 for an event, 0 for censoring (end of observation). If NULL (default), all observations are treated as events.
end_time	An optional named numeric vector of end-of-observation times per system, where names correspond to system identifiers. This defines the actual exposure window for each system. When provided, a system remains in the risk set until its end_time, even if its last event occurred earlier. If NULL (default), the end of observation is inferred as the maximum time recorded for each system (from both events and censoring records).
data	An optional data frame containing columns named id, time, and optionally event and end_time.
conf_level	Confidence level for bounds (default 0.95).

Details

The MCF at time $t$ is estimated as:

$\hat{M}(t) = \sum_{t_j \le t} \frac{d_j}{n_j}$

where $d_j$ is the number of events at time $t_j$ and $n_j$ is the number of systems still under observation at $t_j$. Variance is estimated as $\hat{V}(t) = \sum_{t_j \le t} d_j / n_j^2$.

The risk set $n_j$ is determined by each system's exposure window. A system is considered at risk at time $t_j$ if its end-of-observation time (from end_time, censoring records, or last event) is $\ge t_j$. Specifying end_time is important when systems were observed beyond their last event – without it, the MCF may overestimate the true recurrence rate because systems with no late events are assumed to have left observation at their last event time.

Value

An object of class mcf containing:

time	Unique event times.
mcf	MCF values at each event time.
variance	Variance estimates at each event time.
lower_bounds	Lower confidence bounds.
upper_bounds	Upper confidence bounds.
conf_level	Confidence level used.
n_systems	Number of distinct systems.
n_events	Total number of events.
end_times	Named vector of end-of-observation times per system.

See Also

Other Repairable Systems Analysis: exposure(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

# Basic usage (end of observation inferred from last event)
id <- c(1, 1, 1, 2, 2, 3, 3, 3, 3)
time <- c(100, 300, 500, 150, 400, 50, 200, 350, 600)
result <- mcf(id, time)
print(result)
plot(result, main = "Mean Cumulative Function")

# With explicit end-of-observation times (exposure-adjusted)
end_time <- c("1" = 800, "2" = 800, "3" = 800)
result2 <- mcf(id, time, end_time = end_time)
print(result2)

df <- data.frame(id = id, time = time)
result3 <- mcf(data = df)
print(result3)

---

Non-Homogeneous Poisson Process Model for Repairable Systems.

Description

Fits a parametric NHPP model to recurrent event data from repairable systems. Supported models include the Power Law process and the Log-Linear process. The Power Law model can also be fit as a piecewise (segmented) model with automatic change point detection or user-specified breakpoints.

Usage

nhpp(
  time,
  event = NULL,
  data = NULL,
  model_type = "Power Law",
  breaks = NULL,
  method = c("MLE", "LS"),
  conf_level = 0.95
)

Arguments

time	A numeric vector of cumulative event times, or a data frame containing columns time and optionally event. All values must be positive, finite, and strictly increasing.
event	An optional numeric vector of event counts at each time. If NULL (default), each time is treated as a single event.
data	An optional data frame containing columns time and optionally event.
model_type	Model type: "Power Law" (default) or "Log-Linear".
breaks	Optional vector of breakpoints for piecewise Power Law model.
method	Estimation method: "MLE" (default) or "LS". "LS" is not supported for "Log-Linear" models.
conf_level	Confidence level for bounds (default 0.95).

Details

The Power Law NHPP models the cumulative number of events as $N(t) = \lambda t^\beta$. The parameter $\beta > 1$ indicates a deteriorating system (increasing event rate), $\beta < 1$ an improving system, and $\beta = 1$ a constant rate (HPP).

The Log-Linear NHPP models the intensity as $\lambda(t) = \exp(a + bt)$ with cumulative function $\Lambda(t) = \frac{e^a}{b}(e^{bt} - 1)$.

Value

An object of class nhpp containing:

time	The input cumulative event times.
event	The event counts.
cum_events	Cumulative event counts.
n_obs	Number of observations.
model	Fitted model object (lm or segmented), or NULL for MLE.
model_type	"Power Law" or "Log-Linear".
method	"MLE" or "LS".
params	Named list of estimated parameters.
params_se	Named list of standard errors.
vcov	Variance-covariance matrix (MLE only).
fitted_values	Fitted cumulative events.
lower_bounds	Lower confidence bounds.
upper_bounds	Upper confidence bounds.
residuals	Model residuals.
logLik	Log-likelihood.
AIC	Akaike Information Criterion.
BIC	Bayesian Information Criterion.
breakpoints	Breakpoints (log scale) if piecewise model.
conf_level	Confidence level used.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

time <- c(200, 400, 600, 800, 1000)
event <- c(3, 5, 4, 7, 6)
result <- nhpp(time, event)
print(result)
plot(result, main = "Power Law NHPP")

result_ll <- nhpp(time, event, model_type = "Log-Linear")
print(result_ll)

---

Overlay Plot for Multiple NHPP Models

Description

Plots multiple fitted nhpp objects on a single set of axes, using distinct colors per model. Observed data points, fitted lines, and optional confidence bounds are drawn for every model. Models may have been fit to different datasets.

Usage

overlay_nhpp(
  models,
  conf_bounds = TRUE,
  legend = TRUE,
  legend_pos = "topleft",
  colors = NULL,
  ...
)

Arguments

models	A named or unnamed list of objects of class nhpp. At least one model must be provided. If the list is named, those names are used as legend labels; otherwise labels default to "Model 1", "Model 2", etc.
conf_bounds	Logical; draw confidence bounds for each model (default: TRUE).
legend	Logical; draw a legend (default: TRUE).
legend_pos	Legend position keyword (default: "topleft").
colors	Optional character vector of colors, one per model. If NULL (default), palette() colors are cycled.
...	Additional arguments passed to the initial plot() call (e.g., main, xlab, ylab). Not forwarded to subsequent lines() or points() calls.

Value

Invisibly returns NULL.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

t1 <- c(200, 400, 600, 800, 1000)
e1 <- c(3, 5, 4, 7, 6)
t2 <- c(300, 600, 900, 1200, 1500)
e2 <- c(4, 6, 5, 8, 7)
m1 <- nhpp(t1, e1)
m2 <- nhpp(t2, e2)
overlay_nhpp(list(System_A = m1, System_B = m2),
  main = "NHPP Overlay", xlab = "Time",
  ylab = "Cumulative Events"
)

---

Overlay Plot for Multiple RGA Models

Description

Plots multiple fitted rga objects on a single set of axes, using distinct colors per model. Observed data points, fitted lines, and optional confidence bounds are drawn for every model. Models may have been fit to different datasets.

Usage

overlay_rga(
  models,
  conf_bounds = TRUE,
  legend = TRUE,
  legend_pos = "bottomright",
  colors = NULL,
  log = FALSE,
  ...
)

Arguments

models	A named or unnamed list of objects of class rga. At least one model must be provided. If the list is named, those names are used as legend labels; otherwise labels default to "Model 1", "Model 2", etc.
conf_bounds	Logical; draw confidence bounds for each model (default: TRUE).
legend	Logical; draw a legend (default: TRUE).
legend_pos	Legend position keyword (default: "bottomright").
colors	Optional character vector of colors, one per model. If NULL (default), palette() colors are cycled.
log	Logical; use log-log axes (default: FALSE).
...	Additional arguments passed to the initial plot() call (e.g., main, xlab, ylab). Not forwarded to subsequent lines() or points() calls.

Value

Invisibly returns NULL.

See Also

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

Examples

t1 <- c(100, 200, 300, 400, 500)
f1 <- c(1, 2, 1, 3, 2)
t2 <- c(150, 300, 450, 600, 750)
f2 <- c(2, 1, 3, 2, 4)
m1 <- rga(t1, f1)
m2 <- rga(t2, f2)
overlay_rga(list(System_A = m1, System_B = m2),
  main = "RGA Overlay", xlab = "Cumulative Time",
  ylab = "Cumulative Failures"
)

---

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_bounds = TRUE,
  legend = TRUE,
  legend_pos = "topleft",
  conf.int = NULL,
  legend.pos = NULL,
  ...
)

Arguments

x	An object of class "duane".
log	Logical; whether to use logarithmic scales for axes (default: TRUE).
conf_bounds	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").
conf.int	Deprecated. Use conf_bounds instead.
legend.pos	Deprecated. Use legend_pos instead.
...	Further arguments passed to plot().

Value

Invisibly returns NULL.

See Also

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

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 duane_predict Objects

Description

Plots observed MTBF, fitted Duane curve, and forecast with optional confidence bounds for a duane_predict object.

Usage

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

Arguments

x	An object of class duane_predict.
conf_bounds	Logical; include confidence bounds (default: TRUE).
legend	Logical; show the legend (default: TRUE).
legend_pos	Position of the legend (default: "topleft").
...	Additional arguments passed to plot().

Value

Invisibly returns NULL.

See Also

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

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit <- duane(times, failures)
fc <- predict_duane(fit, times = c(1000, 2000))
plot(fc, main = "Duane Forecast", xlab = "Cumulative Time", ylab = "MTBF")

---

Plot Method for exposure Objects.

Description

Produces a multi-panel plot of exposure analysis results. The default layout shows cumulative exposure and cumulative events versus time (top panel), the number of systems at risk over time (middle panel), and the event rate over time (bottom panel). Alternatively, a single which panel can be selected.

Usage

## S3 method for class 'exposure'
plot(
  x,
  which = c("all", "exposure", "at_risk", "event_rate"),
  legend = TRUE,
  legend_pos = "topleft",
  ...
)

Arguments

x	An object of class exposure.
which	Character string selecting which panel(s) to plot. One of "all" (default), "exposure", "at_risk", or "event_rate".
legend	Logical; show the legend (default: TRUE).
legend_pos	Position of the legend (default: "topleft").
...	Additional arguments passed to the underlying plot().

Value

Invisibly returns NULL.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

id   <- c(1, 1, 1, 2, 2, 2, 3, 3, 3, 3)
time <- c(100, 350, 500, 80, 300, 600, 150, 250, 400, 700)
result <- exposure(id, time)
plot(result)
plot(result, which = "exposure")

---

Plot Method for mcf Objects.

Description

Plots the Mean Cumulative Function with optional confidence bounds.

Usage

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

Arguments

x	An object of class mcf.
conf_bounds	Logical; include confidence bounds (default: TRUE).
legend	Logical; show the legend (default: TRUE).
legend_pos	Position of the legend (default: "topleft").
...	Additional arguments passed to plot().

Value

Invisibly returns NULL.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

id <- c(1, 1, 1, 2, 2, 3, 3, 3, 3)
time <- c(100, 300, 500, 150, 400, 50, 200, 350, 600)
result <- mcf(id, time)
plot(result, main = "Mean Cumulative Function")

---

Plot Method for nhpp Objects.

Description

Plots observed cumulative events with the fitted NHPP model and optional confidence bounds.

Usage

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

Arguments

x	An object of class nhpp.
conf_bounds	Logical; include confidence bounds (default: TRUE).
legend	Logical; show the legend (default: TRUE).
legend_pos	Position of the legend (default: "topleft").
...	Additional arguments passed to plot().

Value

Invisibly returns NULL.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

time <- c(200, 400, 600, 800, 1000)
event <- c(3, 5, 4, 7, 6)
result <- nhpp(time, event)
plot(result, main = "Power Law NHPP", xlab = "Time", ylab = "Cumulative Events")

---

Plot Method for nhpp_predict Objects.

Description

Plots observed data, fitted model, and forecast with optional confidence bounds.

Usage

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

Arguments

x	An object of class nhpp_predict.
conf_bounds	Logical; include confidence bounds (default: TRUE).
legend	Logical; show the legend (default: TRUE).
legend_pos	Position of the legend (default: "topleft").
...	Additional arguments passed to plot().

Value

Invisibly returns NULL.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

time <- c(200, 400, 600, 800, 1000)
event <- c(3, 5, 4, 7, 6)
fit <- nhpp(time, event)
fc <- predict_nhpp(fit, time = c(1500, 2000))
plot(fc, main = "NHPP Forecast", xlab = "Time", ylab = "Cumulative Events")

---

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: overlay_rga(), 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

x	An object of class rga_predict.
conf_bounds	Logical; include confidence bounds (default: TRUE).
legend	Logical; show the legend (default: TRUE).
legend_pos	Position of the legend (default: "bottomright").
...	Additional arguments passed to plot().

Value

Invisibly returns NULL.

See Also

Other Reliability Growth Analysis: overlay_rga(), 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

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: gof(), print.gof(), 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 MTBF from a Duane Model

Description

Takes a fitted duane object and a vector of cumulative times, returning predicted MTBF with confidence bounds as a duane_predict S3 object.

Usage

predict_duane(object, times, conf_level = 0.95)

Arguments

object	An object of class duane returned by duane().
times	A numeric vector of cumulative times at which to forecast MTBF. All values must be finite and > 0. A warning is issued if any value is at or below the maximum observed cumulative time (hindcasting).
conf_level	The desired confidence level (default 0.95). Must be a single finite numeric in (0, 1).

Value

An object of class duane_predict containing:

times	The forecast cumulative times.
mtbf	Predicted MTBF values.
lower_bounds	Lower confidence bounds on MTBF.
upper_bounds	Upper confidence bounds on MTBF.
conf_level	The confidence level used.
duane_object	The original duane object (used by the plot method).

See Also

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

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit <- duane(times, failures)
fc <- predict_duane(fit, times = c(1000, 2000))
print(fc)

---

Forecast Cumulative Events from an NHPP Model.

Description

Takes a fitted nhpp object and a vector of future cumulative times, returning predicted cumulative events with confidence bounds.

Usage

predict_nhpp(object, time, conf_level = 0.95)

Arguments

object	An object of class nhpp returned by nhpp().
time	A numeric vector of cumulative times at which to forecast. All values must be finite and > 0.
conf_level	Confidence level (default 0.95).

Value

An object of class nhpp_predict containing:

time	Forecast times.
cum_events	Predicted cumulative events.
lower_bounds	Lower confidence bounds.
upper_bounds	Upper confidence bounds.
conf_level	Confidence level used.
model_type	Model type.
nhpp_object	The original nhpp object.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), print.exposure(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

time <- c(200, 400, 600, 800, 1000)
event <- c(3, 5, 4, 7, 6)
fit <- nhpp(time, event)
fc <- predict_nhpp(fit, time = c(1500, 2000))
print(fc)
plot(fc, main = "NHPP Forecast", xlab = "Time", ylab = "Cumulative Events")

---

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

object	An object of class rga returned by rga().
times	A numeric vector of cumulative times at which to forecast. All values must be finite and > 0. A warning is issued if any value is at or below the maximum observed cumulative time (hindcasting).
conf_level	The desired confidence level (default 0.95). Must be a single finite numeric in (0, 1).

Value

An object of class rga_predict containing:

times	The forecast cumulative times.
cum_failures	Predicted cumulative failures.
lower_bounds	Lower confidence bounds.
upper_bounds	Upper confidence bounds.
conf_level	The confidence level used.
model_type	Either "Crow-AMSAA" or "Piecewise NHPP".
rga_object	The original rga object (used by the plot method).

See Also

Other Reliability Growth Analysis: overlay_rga(), 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

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(), plot.duane_predict(), predict_duane(), print.duane_predict()

Examples

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

---

Print Method for duane_predict Objects

Description

Prints a formatted table of forecast MTBF with confidence bounds.

Usage

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

Arguments

x	An object of class duane_predict.
...	Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

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

Examples

times <- c(100, 200, 300, 400, 500)
failures <- c(1, 2, 1, 3, 2)
fit <- duane(times, failures)
fc <- predict_duane(fit, times = c(1000, 2000))
print(fc)

---

Print Method for exposure Objects.

Description

Prints a summary of the exposure analysis results.

Usage

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

Arguments

x	An object of class exposure.
...	Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.mcf(), print.nhpp(), print.nhpp_predict()

Examples

id   <- c(1, 1, 2, 2)
time <- c(100, 200, 150, 300)
result <- exposure(id, time)
print(result)

---

Print Method for gof Objects

Description

Prints a summary of goodness-of-fit statistics.

Usage

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

Arguments

x	An object of class gof.
...	Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

Other goodness-of-fit: gof(), ppplot.rga(), qqplot.rga()

Examples

times <- c(5, 10, 15, 20, 25)
failures <- c(1, 2, 1, 3, 2)
fit <- rga(times, failures)
g <- gof(fit)
print(g)

---

Print Method for mcf Objects.

Description

Prints a summary of the Mean Cumulative Function results.

Usage

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

Arguments

x	An object of class mcf.
...	Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.nhpp(), print.nhpp_predict()

Examples

id <- c(1, 1, 1, 2, 2, 3, 3, 3, 3)
time <- c(100, 300, 500, 150, 400, 50, 200, 350, 600)
result <- mcf(id, time)
print(result)

---

Print Method for nhpp Objects.

Description

Prints a summary of the NHPP model results.

Usage

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

Arguments

x	An object of class nhpp.
...	Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp_predict()

Examples

time <- c(200, 400, 600, 800, 1000)
event <- c(3, 5, 4, 7, 6)
result <- nhpp(time, event)
print(result)

---

Print Method for nhpp_predict Objects.

Description

Prints a formatted table of forecast cumulative events with confidence bounds.

Usage

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

Arguments

x	An object of class nhpp_predict.
...	Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

Other Repairable Systems Analysis: exposure(), mcf(), nhpp(), overlay_nhpp(), plot.exposure(), plot.mcf(), plot.nhpp(), plot.nhpp_predict(), predict_nhpp(), print.exposure(), print.mcf(), print.nhpp()

Examples

time <- c(200, 400, 600, 800, 1000)
event <- c(3, 5, 4, 7, 6)
fit <- nhpp(time, event)
fc <- predict_nhpp(fit, time = c(1500, 2000))
print(fc)

---

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: overlay_rga(), 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

x	An object of class rga_predict.
...	Additional arguments (not used).

Value

Invisibly returns the input object.

See Also

Other Reliability Growth Analysis: overlay_rga(), 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

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: gof(), ppplot.rga(), print.gof()

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

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.
f	Number of allowable failures during the test (non-negative integer). Default is 0 (zero-failure test plan). Increasing f reduces the required test time or sample size at the cost of accepting more observed failures.
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.
Allowed_Failures	Number of allowable failures during the test.
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) (AMSAATR138) or piecewise NHPP model by Guo et al. (2010) https://doi.org/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

times	Either a numeric vector of failure-time inputs or a data frame containing both time inputs and failure counts. If times_type = "failure_times" (default), times is treated exactly as in previous versions of the function and is cumulatively summed inside rga(). If times_type = "cumulative_failure_times", times is treated as already cumulative and is used directly without applying cumsum(). If a data frame is provided, it must contain two columns: times and failures.
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.
times_type	Character scalar indicating how to interpret times. "failure_times" (default) preserves the current behavior and cumulatively sums times inside rga(). "cumulative_failure_times" treats times as already cumulative and skips that internal cumsum().
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.
method	Estimation method: "LS" (default) for least-squares log-log regression, or "MLE" for maximum likelihood estimation of the Crow-AMSAA model. "MLE" is not supported for model_type = "Piecewise NHPP".

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 time vector, stored exactly as supplied.
cum_times	The cumulative time vector used for fitting.
times_type	How times was interpreted: "failure_times" or "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: overlay_rga(), 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)

---

Start the ReliaGrowR MCP Server

Description

Starts a Model Context Protocol (MCP) server that exposes the core ReliaGrowR analysis functions as tools for AI assistants such as Claude.

Usage

rga_mcp_server(...)

Arguments

...	Additional arguments passed to mcptools::mcp_server(), e.g., type = "stdio" (default) or type = "http".

Details

Requires the mcptools and ellmer packages to be installed.

Value

Called for its side effect of starting the MCP server.

Available tools

rga

Fit Crow-AMSAA reliability growth model

nhpp

Fit NHPP model for repairable systems

duane

Fit Duane log-log reliability growth model

mcf

Compute Mean Cumulative Function

predict_rga

Forecast from RGA model

predict_duane

Forecast MTBF from Duane model

rdt

Plan a Reliability Demonstration Test

gof_rga

Goodness-of-fit statistics for RGA model

Claude Code setup

claude mcp add -s user reliagrowR -- Rscript -e "ReliaGrowR::rga_mcp_server()"

Claude Desktop setup (claude_desktop_config.json)

{
  "mcpServers": {
    "reliagrowR": {
      "command": "Rscript",
      "args": ["-e", "ReliaGrowR::rga_mcp_server()"]
    }
  }
}

---

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

n	Positive integer. Number of failures to simulate.
runtimes	Numeric vector of positive values. The current operating runtime of each unit in the non-failed population.
replace	Logical scalar. If TRUE, sampling is done with replacement (a unit may be selected more than once). Default is FALSE.
window	NULL or a single positive numeric. The width of the observation window. When NULL (default), event times equal current runtimes. When provided, failure times are sampled from the conditional Weibull distribution over ⁠(runtime, runtime + window]⁠, and suspension times are runtime + window.
beta	Positive numeric scalar. Weibull shape parameter used to model the age-dependent hazard. Defaults to 1, corresponding to an exponential-process assumption.
eta	NULL or a single positive numeric. Weibull scale parameter. When NULL and window is supplied, the scale is calibrated so that the expected number of failures across the fleet during the window matches n.

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:

index	Integer index of the unit in runtimes.
runtime	Simulated event time.
type	Character; "Failure" for selected units, "Suspension" for the rest.

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

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.

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)

---