This paper deals with degradation processes whose onset is triggered at a random time and which stay hidden until they are discovered through inspection or when they begin to show symptoms. This is applicable in many healthcare and industrial scenarios, for example, in the modeling of breast cancer or termite infestation. In our model, we assume that symptoms appear after hitting a random critical threshold and that inspections may have a sensitivity less than one as well as a nonzero false positive rate. The expected cost of repair is derived, and the inspection rate is optimized for a cycle (which lasts from degradation‐free to repaired state). This gives results for three cases: the first is for a finite observation period with no degradation recurrence, the second for infinite time horizon allowing recurrence. In the third case, we derive an upper bound for the expected cost in a given constant time period. Finally, the model is applied to determine the optimal strategy for breast cancer screening with regard to the effects of different parametrizations.

中文翻译：

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随机触发的隐藏恶化过程的最佳检查

本文讨论了降解过程，这些过程的发作是在随机时间触发的，直到通过检查发现它们或开始表现出症状之前，它们一直隐藏。这适用于许多医疗保健和工业场景，例如乳腺癌或白蚁侵扰的建模。在我们的模型中，我们假设在达到随机临界阈值后出现症状，并且检查的灵敏度可能低于1，而且假阳性率也非零。得出了预期的维修成本，并针对一个周期优化了检查率（从无降解状态持续到维修状态）。这给出了三种情况的结果：第一种情况是在有限的观察期内没有退化的复发，第二种情况是在无限的时间范围内允许复发。在第三种情况下 我们得出给定恒定时间段内预期成本的上限。最后，该模型可用于确定关于不同参数化效应的乳腺癌筛查的最佳策略。