关于定数截尾失效率参数比的最优置信区间(Ⅰ)——存在性、算法及应用

设X,Y独立且分别服从指数分布f1(x,λ1),f2(x,λ2),在可靠性工程中,X,Y常用来描述系统(元件)的寿命,λ表示系统的失效率。失效率参数比的置信区间可用来判定两种产品平均失效率的差异,因此,对参数比做出尽可能可靠和精确的区间估计是非常重要的。这必须考虑其可靠度和精度,衡量精度的指标是其长度,置信区间的长度愈小愈好。引入了“具有一致最小平均长度性质的置信区间”(最优置信区间)的概念,从直观上刻画了最优置信区间的精度,研究了定数截尾失效率参数比具有一致最小平均长度的区间估计,最优置信区间存在性及其计算方法,并给出了应用实例。

The Best Confidence Interval of Failure Rate Parameters Proportion on Censored Data (Ⅰ): Existing, Algorithm And Application

Let two independent random variables X and Y obey exponential distribution f1 ( x , λ1 ), f2 ( x, λ 2 ), respectively. Random variables X and Y usually describe the life of system, and the parameter A indicates the failure rate of system in the reliable project. The confidence interval of failure rate parameters proportion can judge the difference of two different product average failure rate, so, it is very important to obtain a reliable and accurate interval estimation of parameters proportion. Therefore, the reliability and precision must be thought. The common index describing precision is interval length, the shorter the length of confidence interval, the better it is. The conception of possessing uniformly minimum mean length confidence interval (the best confidence interval) was introduced, which directly described precision of the best confidence interval. The interval estimation about the failure rate parameters proportion based on censored data, possessing the uniformly minimum mean length interval and exiting of the best confidence interval and method of numerical calculation were studied, then an example was given.