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Stochastic modeling for systems with delayed failures

机译：延迟故障的系统随机造型

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摘要

We present stochastic description for repairable systems with delayed failures. Initial defects in a system result in its failure only after some delay. Specifically, it happens in repairable systems when the defects are not repaired within some period of time that can be either deterministic or random. Therefore, operation of a system is described by the corresponding terminating renewal process. We derive and analyze relationships for the survival probability and the mean time to failure for these systems. The results are derived in the form of the corresponding Laplace transforms that are numerically inverted for illustrative examples. Simple fast repair approximations are considered and their accuracy is also discussed.
机译：我们提出了具有延迟故障的可修复系统的随机描述。系统中的初始缺陷仅在某些延迟后才导致其故障。具体地，当在可以是确定性或随机的一段时间内没有修复缺陷时，它发生在可修复系统中。因此，通过相应的终止续展过程描述了系统的操作。我们派生并分析了这些系统的生存概率和平均故障的关系。结果以相应的拉普拉斯变换的形式衍生，其用于说明性示例。考虑简单的快速修复近似，还讨论了它们的准确性。

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