In order to balance the deviation time between replacement and failure, a new notion of cost named as deviation cost is taken into account for planning replacement policies. We firstly take up a standard parallel system with n identical units and model replacement policies that are done at planned time and at periodic times. Next, we model again the above replacement policies when the number of units is a random variable that has a Poisson distribution. Thirdly, replacement policies are planned preventively at the completion of random working times. Optimum number of units is scheduled for a total working interval that is constantly and randomly given. Finally, we give reliability functions of k-out-of-n systems for extensions of parallel systems. We give analytical discussions for the above replacement policies and illustrate numerical examples when the failure time of each unit has an exponential distribution.

中文翻译：

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并行系统的预防性更换策略，更换和故障之间的偏差成本

为了平衡更换和故障之间的偏差时间，在规划更换策略时考虑了称为偏差成本的新成本概念。我们首先采用具有 n 个相同单元和模型替换策略的标准并行系统，这些策略在计划时间和周期性时间完成。接下来，当单元数是具有泊松分布的随机变量时，我们再次对上述替换策略进行建模。第三，在随机工作时间结束时预防性地计划更换政策。为持续随机给出的总工作间隔安排了最佳单元数。最后，我们给出了k-out-of-n系统的可靠性函数，用于并行系统的扩展。