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Preventive Maintenance Models Based on the Generalized Geometric Process

机译：基于广义几何过程的预防性维修模型

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摘要

For a generalized geometric process (GGP), the geometric ratio changes with the number of repairs rather than a constant. The GGP is a more flexible maintenance model that can reflect the varying of the repair effect to the system. On the basis of the GGP, two imperfect preventive maintenance (PM) models are studied. First, we assume that the system is preventively maintained periodically after every T time unit, and is correctively repaired at failure. The corrective repair is a minimal repair that just restores the system to work, while the PM results in a GGP, i.e., the lifetime sequence of a system after PM constitute a decreasing GGP. The long-run average cost rate C(N, T ) of the system is derived, and the optimal bivariate policy (N*, T *) is determined by minimizing C(N, T ), where N is the number of PMs before replacement. Next, a sequential PM model is investigated for a system in which a sequential time interval to be determined for PM. An algorithm is given to seek the optimal replacement policy N* and the optimal time intervals T1*, T2*,..., TN* between PMs. By assuming that the lifetime of the system is Weibull distributed, the optimal policy is obtained explicitly. In both models, numerical examples are provided to verify the effectiveness of the approaches developed.
机译：对于广义几何过程（GGP），几何比率随修复次数而不是常数而变化。 GGP是一种更灵活的维护模型，可以反映系统修复效果的变化。在GGP的基础上，研究了两种不完善的预防性维护（PM）模型。首先，我们假设系统在每个T时间单位后定期进行预防性维护，并在故障时进行正确的维修。纠正性修复是一种最小的修复，仅能使系统恢复正常工作，而PM会导致GGP，即PM构成递减的GGP后系统的寿命序列。得出系统的长期平均成本率C（N，T），并通过最小化C（N，T）来确定最佳的双变量策略（N *，T *），其中N是之前的PM数替代。接下来，针对其中要确定PM的顺序时间间隔的系统研究顺序PM模型。给出了寻找最优替换策略N *和最优时间间隔T 1 *，T 2 *，...，T N *。通过假设系统的寿命是Weibull分布，可以明确获得最佳策略。在两个模型中，均提供了数字示例以验证所开发方法的有效性。

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