指数分布场合系统应力强度模型可靠度的统计推断

Statistical inference for reliability of system stress-strength model under exponential distribution

利用最大似然估计和广义区间估计方法,研究了元件的强度和承受的应力均服从指数分布时系统应力强度模型可靠度的估计问题,导出了可靠度的最大似然估计和广义区间估计,同时也讨论了模型的拟合检验问题,利用模拟方法研究了提出的广义置信区间的覆盖率和拟合检验的功效,模拟结果表明提出的广义置信区间的覆盖率与名义置信系数是一致的,提出的拟合检验的功效是好的,最后用一个例子说明提出的方法。

The maximum likelihood estimation and generalized confidence interval of the system reliability of general multi-component stress-strength model are derived when the component strengths and the stress are independent exponential random variables. The goodness-of-fit test of the model is discussed. The coverage probability of the proposed generalized confidence interval and the power of the test are evaluated by Monte Carlo simulation. The simulation results show that the proposed generalized confidence interval and test are very satisfactory even for small and moderate samples. Finally, an example is shown to illustrate the proposed procedures.