基于三阶段故障过程的多重点检策略优化模型

针对工程系统检测中常采用小检和大检相结合的方式，在基于三阶段故障延迟时间的概念上提出了多重点检策略.三阶段故障延迟 时间的概念将系统的寿命分为三阶段，即，正常，初始缺陷和严重缺陷阶段.通过考虑故障更新，小检更新和大检更新，采用更新收益 理论对单部件系统建立了一个多重点检策略模型.该模型以小检和大检间隔期为决策变量，单位时间内的期望费用最小为决策目标. 为了分析多重点检策略的有效性，本文也建立了一个对应的仅含有大检的单一点检策略模型，并通过将这两种策略模型进行比较得 出了多重点检优于单一点检的小检成本的临界阈值表达式，最后通过算例进行了分析.结果证明：在其他参数不变的情况下，当小检成本小于阈值时多重点检策略是最优的.

Modeling of the optimal multiple inspection policy based on a three-stage failure process

In line with the fact that major inspections and minor inspections are usually adopted together for system inspection in engineering practice, this paper proposes a multiple inspection policy model based on a three-stage failure process. The concept of the three-stage failure process divides the system lifetime into three stages, that is, normal stage, minor defective stage and severe defective stage. With the consideration of all the possible scenarios for failure renewal, minor inspection renewal and major inspection renewal, a multiple inspection policy model is presented for single-unit systems using the renewal reward theory. The objective of the model is to minimize the long-run expected cost per unit time, with the minor and major inspection intervals as the decision variables. In order to illustrate the applicability of the multiple inspection policy, a single inspection policy counterpart which includes only major inspections is also developed for the purpose of comparison. The threshold value for the minor inspection cost which makes the multiple inspection more favorable than the single inspection policy is studied. Numerical examples are presented and the results show that the multiple inspection policy is better than the single inspection policy when the cost of minor inspection is smaller than the threshold level and other parameters are fixed.