一个失效概率与时间相依的广义预烧模型

A Generalized Burn-in Model with Time-Dependent Probability of Failure

目的将文献[1]中考虑的广义预烧与替换模型推广到失效概率与时间相依的情况。方法考虑了2种预烧过程,并且在这2种策略均可行的条件下进行了比较。在某些特定的失效率函数r(t)以及失效概率函数p(t)条件下,研究了最佳预烧时间以及最优的替换策略问题。结果 2种预烧过程与可行的情况下,预烧过程Ⅱ永远(即对于所有的p(·)∈P)是优于预烧过程Ⅰ的,并且最佳预烧时间b~*一定发生在函数r(t)和p(t)的第一个变点t_1之前,最优替换策略T~*与最佳预烧时间b~*之和一定发生在函数r(t)和p(t)的第二个变点t_2之后。结论得到了最佳预烧时间b~*以及最优替换策略T~*。

Objective To further extend the generalized burn-in and replacement model from literature[1] to the case in which the probalility of failure is time dependent.Mehtods Two burn-in procedure were considered and they were compared in cases when both the procedures are applicable.Under the given failure rate function r(t) and the failure probability function p(t),the problems of determining optimal burn-in time and optimal replacement policy were considered.Results The burn-in Procedure Ⅱ was always(i.e.for all p(·)∈P)preferable to the burn-in Procedure Ⅰ when both procedures are applicable.And in this case,the optimal burn-in time b* must occur before the first change point t1 of the function r(t)p(t) and the sum of the optimal burn-in time b* and the replacement policy T* must occur after the second change point t2 of the function r(t)p(t).Conclusion The optimal burn-in time b* and replacement policy T* are obtained.