We consider a hybrid preventive maintenance policy. As in the classic model of age-replacement, a system is replaced either on failure or on reaching a predetermined age T. Additionally, it can be replaced on reaching a predetermined level of deterioration at some intermediate time in [0,T). We use a transformed gamma process with dependent increments to model the deterioration. A failure of an item occurs when this process reaches a predetermined deterministic level. We show that the proposed policy outperforms the classical one, that is, it achieves a lower value of the long-run cost rate. A detailed numerical illustration is presented and sensitivity analysis for the main parameters of the model is performed. The work in the paper makes an important contribution to maintenance modelling because dependent increments can better represent deterioration of a real system.

中文翻译：

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由具有依赖增量的随机退化描述的项目的年龄替换策略

我们考虑混合预防性维护策略。与经典的老化替换模型一样，系统在发生故障或达到预定老化 T 时被替换。此外，它可以在 [0,T) 中的某个中间时间达到预定劣化水平时被替换。我们使用具有相关增量的变换伽马过程来模拟恶化。当此过程达到预定的确定性级别时，就会发生项目故障。我们表明，所提出的政策优于经典政策，也就是说，它实现了较低的长期成本率值。给出了详细的数值说明，并对模型的主要参数进行了敏感性分析。