ABSTRACT

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.

摘要

应力强度可靠性是比较两个系统寿命的一种度量。首先使用广义阶数统计推断双参数指数分布，首先不受位置和尺度参数的约束，其次是在尺度参数相等时。计算应力强度参数的广义置信区间、自举置信区间、贝叶斯区间和最高后验密度区间。蒙特卡罗模拟表明，广义置信区间提供了更准确的置信区间平均长度和包含参数真实值的更高概率。应用：在大多数广义统计模型中，20 名接受两种药物之一治疗的白血病患者达到缓解时间的置信区间大致相同。此外，