A complex multi-state system subject to different types of failures, repairable and/or non-repairable, external shocks and preventive maintenance is modelled by considering a discrete Markovian arrival process with marked arrivals (D-MMAP). The internal performance of the system is composed of several degradation states partitioned into minor and major damage states according to the risk of failure. Random external events can produce failures throughout the system. If an external shock occurs, there may be an aggravation of the internal degradation, cumulative external damage or extreme external failure. The internal performance and the cumulative external damage are observed by random inspection. If major degradation is observed, the unit goes to the repair facility for preventive maintenance. If a repairable failure occurs then the system goes to corrective repair with different time distributions depending on the failure state. Time distributions for corrective repair and preventive maintenance depend on the failure state. Rewards and costs depending on the state at which the device failed or was inspected are introduced. The system is modelled and several measures of interest are built into transient and stationary regimes. A preventive maintenance policy is shown to determine the effectiveness of preventive maintenance and the optimum state of internal and cumulative external damage at which preventive maintenance should be taken into account. A numerical example is presented, revealing the efficacy of the model. Correlations between the numbers of different events over time and in non-overlapping intervals are calculated. The results are expressed in algorithmic-matrix form and are implemented computationally with Matlab.

中文翻译：

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用于分析受多个事件影响的多状态复杂动态系统的行为的离散 MMAP

通过考虑具有标记到达的离散马尔可夫到达过程 (D-MMAP)，对遭受不同类型故障、可修复和/或不可修复、外部冲击和预防性维护的复杂多状态系统进行建模。系统的内部性能由几个退化状态组成，根据故障风险分为轻微和重大损坏状态。随机的外部事件可能会导致整个系统出现故障。如果发生外部冲击，可能会出现内部退化加剧、外部累积损坏或极端外部故障。通过随机检查观察内部性能和累积外部损坏。如果观察到严重退化，设备将前往维修设施进行预防性维护。如果发生可修复的故障，则系统会根据故障状态以不同的时间分布进行纠正性修复。纠正性维修和预防性维护的时间分布取决于故障状态。介绍了取决于设备出现故障或被检查的状态的奖励和成本。对系统进行建模，并将几个感兴趣的度量构建到瞬态和静止状态中。显示了预防性维护策略，以确定预防性维护的有效性以及应考虑预防性维护的内部和累积外部损坏的最佳状态。给出了一个数值例子，揭示了模型的有效性。计算随时间和非重叠间隔中不同事件的数量之间的相关性。