In many real-life scenarios, system failure depends on dynamic stress-strength interference, where strength degrades and stress accumulates concurrently over time. In this paper, we consider the problem of finding an optimal replacement strategy that balances the cost of replacement with the cost of failure and results in the minimum expected cost per unit time under cumulative damage model with strength degradation. In the most general setting, we propose to find optimal choices of three thresholds on operation time, number of arriving shocks and amount of cumulative damage such that replacement of the system due to failure or reaching any of the three thresholds, whichever occurs first, results in the minimum expected cost per unit time. The existing recommendations are applicable only under the assumption of Exponential damage distribution including Poisson arrival of shocks and/or with fixed strength. As theoretical evaluation of the expected cost per unit time turns out to be very complicated, a simulation-based algorithm is proposed to evaluate the expected cost rate and find the optimal replacement strategy. The proposed method is easy to implement having wider domain of application including non-Poisson arrival of shocks and non-Exponential damage distributions. For illustration, the proposed method is applied to real case studies on mailbox and cell-phone battery experiments.

在许多实际场景中，系统故障取决于动态应力-强度干扰，其中强度会随着时间的推移而降低，应力会同时累积。在本文中，我们考虑以下问题：找到一种最佳的更换策略，该策略可以在更换成本与故障成本之间取得平衡，并在具有强度退化的累积损坏模型下得出单位时间的最小预期成本。在最一般的情况下，我们建议找到三个阈值的最佳选择：运行时间，到达的冲击次数和累积损坏的数量，以使由于故障或达到三个阈值中的任何一个而导致的系统更换，以先发生者为准。以每单位时间的最低预期成本计算。现有建议仅在指数分布（包括泊松冲击波和/或固定强度）的假设下适用。由于理论上对单位时间预期成本的评估非常复杂，因此提出了一种基于仿真的算法来评估预期成本率并找到最佳替代策略。所提出的方法易于实现，具有更广泛的应用范围，包括非泊松冲击到达和非指数损伤分布。为了说明起见，将所提出的方法应用于邮箱和手机电池实验的真实案例研究。提出了一种基于仿真的算法来评估预期成本率并找到最佳的替换策略。所提出的方法易于实现，具有更广泛的应用范围，包括非泊松冲击到达和非指数损伤分布。为了说明起见，将所提出的方法应用于邮箱和手机电池实验的真实案例研究。提出了一种基于仿真的算法来评估预期成本率并找到最佳的替换策略。所提出的方法易于实现，具有更广泛的应用范围，包括非泊松冲击到达和非指数损伤分布。为了说明起见，将所提出的方法应用于邮箱和手机电池实验的真实案例研究。