Inference on stress-strength reliability for the two-parameter exponential distribution based on generalized order statistics

Stress-strength reliability is a measure to compare the lifetimes of two systems. It is inferred for the two-parameter exponential distribution using generalized order statistics first without constraint on the location and scale parameters, second when the scale parameters are equal. A generalized confidence interval, bootstrap confidence intervals, a Bayesian interval, and a highest posterior density interval are computed for the stress-strength parameter. A Monte Carlo simulation shows that generalized confidence intervals provide more accurate average lengths of confidence intervals and higher probabilities to contain the true value of the parameter. Application: Confidence intervals for the time to remission of 20 leukemic patients treated with one of two drugs are approximately the same in most generalized statistical models. In addition, the time to remission for patients with the first drug is tested to be shorter than for patients with the second drug.