Abstract: Usually, preventive maintenance policy decisions are made without taking into account the system’s work cycle, resulting in a fixed-time preventive maintenance policy that may affect the normal use of the system. In addition, in actual production life, the price and labor cost of spare parts that need to be replaced are not always optimal due to economic and objective operating environment factors, so this paper proposes an age replacement policy that considers opportunities and contains time windows in order to be able to enhance the applicability of the model and reduce the cost of the system in use. The advantages and disadvantages of the policy can be compared in two dimensions: efficiency and flexibility. The policy is to relax the replacement of the system to be performed in a certain time window period. The policy is proposed to facilitate maintenance, or to enable low-cost maintenance.
By building the expected cost rate function, the range of window time start point S and prevention time point T are discussed using image method and differentiation method, etc., and the relationship between the magnitude of the cost rate under different conditions is compared with numerical visualization. In the study of this paper, completion of the task is shown to provide an opportunity for substitution. The analysis shows that replacement first, replacement last, age replacement and random replacement are the special cases of the model proposed in this paper. The results of the final numerical validation show that there is no optimal time window in the strict sense, and the optimal age replacement policy is a simplified optimal time window with the highest efficiency but the narrowest applicability; the replacement first policy and the replacement last policy have the lowest efficiency, but have a semi-open time window for preventive replacement, which is the most flexible replacement policy; and the time window replacement policy balances the efficiency and flexibility of replacement. In practical application, the optimal age replacement policy is preferred if the conditions permit; when the time window replacement policy is used, the policy with the left end of the time window S less than the optimal replacement age or the right end of the time window T greater than the optimal replacement age is preferred, and the closer to the optimal replacement age, the higher its efficiency. However, the use of the corresponding time window policy close to the age of replacement enhances the applicability of the model.
In this paper, the same preventive replacement cost is used for non-repairable parts. In a more in-depth study, we can also discuss the study of economically efficient strategies, e.g., giving a corresponding discount to the replacement cost considering the currency variation factor; the replacement cost can also vary dynamically at different time points. In addition, the model can also be extended to repairable parts to study the policy study under the cumulative shock process, etc.

Key words: time window, opportunity-based age replacement, expected cost rate, optimal strategy

摘要： 为了能增强模型的适用性、降低系统在使用过程中的成本,本文提出了一种考虑机会且含有时间窗口的不可修部件年龄替换策略。通过构建期望成本率目标函数,采用随机过程分析工具讨论窗口时间始点S和预防时间点T的范围,并用数值直观地分析比较了不同条件下的费用率的大小关系。分析表明,最先替换、最迟替换、年龄替换和随机替换是本文提出模型的特殊情况。最终结果表明,不存在严格意义上的最优时间窗口,最优年龄替换策略是退化的最优时间窗口,但采用接近年龄替换的对应时间窗策略增强了模型的适用性。本文针对不可修部件采用了相同的预防替换成本,实际过程中任务完成或预防替换机会的到达可能有更加节省的预防替换,对于可修部件也有待进行详细分析。

关键词: 时间窗, 基于机会的年龄替换, 期望成本率, 最优策略