The development of integrated modelling for maintenance policies of multi-component repairable system and production scheduling is challenging for two reasons. First, capturing dependency of this multi-component repairable system is difficult because different failure types associated with different components are under competing risks and their complicated relationships may lead to overall system dependency. Second, the integrated model is difficult to optimize because it is an NP-hard problem that exact optimization methods are intractable. For coping with these two difficulties, we propose a parametric statistical model using copula function to capture the overall system dependency. Under partially perfect maintenance policy at component-level, the likelihood functions for observed failures are derived and maximum likelihood method is used to estimate unknown parameters. Then relying on this parametric statistical model, the system hazard function is derived to depict the reliability-based imperfect preventive maintenance policy at system-level. Finally, to obtain the optimal solution(s) of the integrated model, we design an adaptive immune clone selection–culture algorithm, which is inspired from immune clone selection algorithm and culture algorithm. Results of the case study validate that our proposed maintenance policies and methodology have great advantages over the component-level or system-level maintenance policy and immune clone selection algorithm.

对于多组件可修复系统的维护策略和生产计划的集成建模的开发具有挑战性，这有两个原因。首先，很难捕获此多组件可修复系统的依赖关系，因为与不同组件关联的不同故障类型处于竞争风险之下，并且它们之间的复杂关系可能会导致整个系统的依赖关系。其次，集成模型难以优化，因为精确的优化方法难以解决是NP难题。为了解决这两个困难，我们提出了一种使用copula函数的参数统计模型来捕获整个系统依赖性。根据组件级的部分完善维护政策，推导了观察到的故障的似然函数，并使用最大似然法估计未知参数。然后依靠此参数统计模型，得出系统危害函数，以在系统级描述基于可靠性的不完善的预防性维护策略。最后，为了获得集成模型的最优解，我们设计了一种自适应免疫克隆选择-培养算法，该算法受免疫克隆选择算法和培养算法的启发。案例研究结果证明，我们提出的维护策略和方法论比组件级或系统级维护策略和免疫克隆选择算法具有更大的优势。推导了系统危害函数，以在系统级别描述基于可靠性的不完善的预防性维护策略。最后，为了获得集成模型的最优解，我们设计了一种自适应免疫克隆选择-培养算法，该算法受免疫克隆选择算法和培养算法的启发。案例研究结果证明，我们提出的维护策略和方法论比组件级或系统级维护策略和免疫克隆选择算法具有更大的优势。推导了系统危害函数，以在系统级别描述基于可靠性的不完善的预防性维护策略。最后，为了获得集成模型的最优解，我们设计了一种自适应免疫克隆选择-培养算法，该算法受免疫克隆选择算法和培养算法的启发。案例研究的结果证明，我们提出的维护策略和方法论比组件级或系统级维护策略和免疫克隆选择算法具有更大的优势。