duane: Duane Analysis

In ReliaGrowR: Reliability Growth Analysis

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 documentation built on Nov. 7, 2025, 9:06 a.m.