Duane Analysis

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).

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).

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.

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)
#> Duane Analysis Result
#> ----------------------
#> Linear model (log-log scale): log(MTBF) ~ log(Time)
#> 
#> Number of observations (failures): 5
#> 
#> Coefficients:
#>                Estimate Std. Error
#> (Intercept)   3.6144974 0.35199619
#> log_cum_times 0.2013244 0.05624037
#> 
#> Log-likelihood: 4.78
#> AIC: -3.55, BIC: -4.72
#> Confidence level: 90.0%

df <- data.frame(times = times, failures = failures)
fit2 <- duane(df, conf.level = 0.95)
print(fit2)
#> Duane Analysis Result
#> ----------------------
#> Linear model (log-log scale): log(MTBF) ~ log(Time)
#> 
#> Number of observations (failures): 5
#> 
#> Coefficients:
#>                Estimate Std. Error
#> (Intercept)   3.6144974 0.35199619
#> log_cum_times 0.2013244 0.05624037
#> 
#> Log-likelihood: 4.78
#> AIC: -3.55, BIC: -4.72
#> Confidence level: 95.0%