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A study on stochastic degradation process models under different types of failure Thresholds

机译：不同类型故障阈值下的随机退化过程模型研究

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摘要

Stochastic degradation process models are developed in terms of cumulative degradation signals of systems under three types of thresholds including alarm line and two different failure thresholds. One of the failure thresholds corresponds to the degradation amount, and the other corresponds to the duration. We assume that the degradation process can be separated into two distinctive stages by a change-point which is the first passage time of the degradation process with respect to the alarm line. For simplicity, the first stage is regarded as an age-dependent (or non-stationary) Wiener process or an age-dependent (or non-stationary) Gamma process, and the second stage is regarded as an age-dependent (or non-stationary) Gamma process; thus, two special degradation models, Wiener-Gamma and Gamma-Gamma, are constructed. Specially, two-stage stationary Wiener-Gamma and Gamma-Gamma models can be viewed as special cases. The system reliability is defined as the probability that the degradation signals do not exceed a failure threshold and the duration of exceeding the alarm line is less than the duration threshold. Some reliability results including two cases in terms of duration thresholds (constants and random variables) are derived. The moments of lifetime are also given based on the results. In addition, simulation is carried out to verify the given results. And some numerical examples are presented to illustrate the results obtained in the paper.
机译：随机退化过程模型是根据系统在三种阈值（包括警报线和两个不同的故障阈值）下的累积退化信号开发的。故障阈值之一对应于劣化量，另一个阈值对应于持续时间。我们假设可以通过一个变化点将退化过程分为两个不同的阶段，变化点是退化过程相对于警报线的第一次通过时间。为简单起见，第一阶段被视为与年龄有关（或非平稳）的维纳过程或与年龄有关（或非平稳）的伽玛过程，第二阶段被视为与年龄有关（或非平稳）的维纳过程固定的）伽玛过程；因此，构造了两个特殊的退化模型，即维纳伽玛和伽玛伽玛。特别地，可以将两阶段固定式Wiener-Gamma和Gamma-Gamma模型视为特殊情况。系统可靠性定义为降级信号不超过故障阈值且超过警报线的持续时间小于持续时间阈值的概率。从持续时间阈值（常数和随机变量）两个方面得出了一些可靠性结果。寿命的时刻也基于结果给出。另外，进行仿真以验证给定的结果。并给出了一些数值例子来说明本文获得的结果。

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