标题： 复杂可靠性系统在预防性维护策略和伯努利休假策略下受到多个事件影响的算法分析通过MMAPs 显示英文标题

标题： Algorithmic analysis of a complex reliability system subject to multiple events with a preventive maintenance strategy and a Bernoulli vacation policy through MMAPs

摘要： 在本工作中，考虑了一个单单元多状态系统。 该系统会受到内部故障以及具有多种后果的外部冲击的影响。 它还结合了预防性维护策略和维修人员的伯努利休假政策。 该系统使用标记马尔可夫到达过程（MMAP）在连续时间和离散时间中进行算法建模。 系统的运行/退化级别被划分为不确定数量的级别。 在休假期结束后，维修技术人员可能会启动纠正性维修、执行预防性维护、更换单元、在工作场所闲置，或开始新的休假期。 后两种情况的决策是基于系统运行级别的概率做出的。 这种方法允许在瞬态和稳态条件下以矩阵算法形式算法地推导模型及其相关度量。 使用解析矩阵方法获得系统的稳态行为以及各种性能度量。 引入成本和收益以分析系统何时变得有利可图。 定义并考虑了随时间变化的成本和稳态条件下的成本度量，用于优化研究。 一个数值示例通过使用多目标帕累托分析方法求解概率优化问题，并对多个模型进行比较评估，展示了该模型的通用性。 遗传算法被应用于减少的解空间中找到优化结果。 所有建模和相关度量已在Matlab中进行了计算实现。 显示英文摘要

摘要： In this work, a single-unit multi-state system is considered. The system is subject to internal failures, as well as external shocks with multiple consequences. It also incorporates a preventive maintenance strategy and a Bernoulli vacation policy for the repairperson. It is algorithmically modeled in both continuous and discrete time using Marked Markovian Arrival Processes (MMAP). The system's operation/degradation level is divided into an indeterminate number of levels. Upon returning from a vacation period, the repair technician may initiate corrective repair, perform preventive maintenance, replace the unit, remain idle at the workplace, or begin a new vacation period. The decision in the latter two cases is made probabilistically based on the system's operational level. This methodology allows the model and its associated measures to be algorithmically derived in both transient and stationary regimes, presented in a matrix-algorithmic form. Analytical-matrix methods are used to obtain the system's steady-state behaviour as well as various performance measures. Costs and rewards are introduced to analyze when the system becomes profitable. Measures associated with costs over time and in the stationary regime are defined and considered for optimization studies. A numerical example demonstrates the versatility of the model by solving a probabilistic optimization problem using a multi-objective Pareto analysis approach and performing a comparative evaluation of multiple models. Genetic algorithm is applied to find the optimization results in the reduced solution space. All modeling and associated measures have been computationally implemented in Matlab.