Abstract

We propose optimal preventive maintenance strategies for n-component coherent systems. We assume that in the early time of the system operation all failed components are repaired, such that the state of a failed component gets back to a working state, worse than that of prior to failure. To model this repair action, we utilize a counting process on the interval $(0,\tau ],$ known as the generalized Pólya process (which subsumes the non-homogeneous Poisson process as a special case). Two generalized Pólya process-based repair strategies are proposed. The criteria to be optimized are the cost function formulated based on the repair costs of the components/system, and the system availability, to obtain the optimal time of preventive maintenance of the system. To illustrate the theoretical results, two coherent systems are studied for which the optimal preventive maintenance times are explored under different conditions.

摘要

我们为n分量相干系统提出了最佳的预防性维护策略。我们假设在系统运行的早期，所有故障组件都被修复，使得故障组件的状态恢复到工作状态，比故障前的状态更差。为了模拟这个修复动作，我们在间隔上使用了一个计数过程$(0,\tau ],$称为广义 Pólya 过程（将非齐次 Poisson 过程包含为一个特例）。提出了两种基于 Pólya 过程的通用修复策略。要优化的标准是基于组件/系统的维修成本和系统可用性制定的成本函数，以获得系统预防性维护的最佳时间。为了说明理论结果，研究了两个相干系统，探索了不同条件下的最佳预防性维护时间。