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Sampling inspection for the evaluation of time-dependent reliability of deteriorating systems under imperfect defect detection

机译：不完善缺陷检测下评估劣化系统随时间变化的可靠性的抽样检查

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The paper presents a sampling-inspection strategy for the evaluation of time-dependent reliability of deteriorating systems, where the deterioration is assumed to initiate at random times and at random locations. After initiation, defects are weakening the system's resistance. The system becomes unacceptable when at least one defect reaches a critical depth. The defects are assumed to initiate at random times modeled as event times of a non-homogeneous Poisson process (NHPP) and to develop according to a non-decreasing time-dependent gamma process. The intensity rate of the NHPP is assumed to be a combination of a known time-dependent shape function and an unknown proportionality constant. When sampling inspection (i.e. inspection of a selected subregion of the system) results in a number of defect initiations, Bayes' theorem can be used to update prior beliefs about the proportionality constant of the NHPP intensity rate to the posterior distribution. On the basis of a time- and space-dependent Poisson process for the defect initiation, an adaptive Bayesian model for sampling inspection is developed to determine the predictive probability distribution of the time to failure. A potential application is, for instance, the inspection of a large vessel or pipeline suffering pitting/localized corrosion in the oil industry. The possibility of imperfect defect detection is also incorporated in the model.
机译：本文提出了一种抽样检查策略，用于评估恶化系统的时间依赖性可靠性，其中假定恶化是在随机时间和随机位置开始的。启动后，缺陷会削弱系统的抵抗力。当至少一个缺陷达到临界深度时，该系统变得不可接受。假定缺陷在建模为非均匀泊松过程（NHPP）的事件时间的随机时间开始，并根据不依赖时间的伽马过程逐渐发展。假设NHPP的强度比率是已知的随时间变化的形状函数和未知的比例常数的组合。当抽样检查（即对系统选定子区域的检查）导致许多缺陷引发时，贝叶斯定理可用于更新关于NHPP强度比率与后验分布的比例常数的先验信念。基于时间和空间相关的泊松过程来引发缺陷，开发了用于抽样检查的自适应贝叶斯模型，以确定失效时间的预测概率分布。潜在的应用是，例如，对石油工业中遭受点蚀/局部腐蚀的大型容器或管道进行检查。不完善的缺陷检测的可能性也包含在模型中。

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