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This paper intends to investigate the reliability model for competing failure systems under the influence of random failure thresholds. The random threshold distribution function of hard failure is developed incorporating parameter estimation and goodness-of-fit analysis while the soft failure threshold is assumed to be normally distributed. Specifically, the competing failure result is composed of a degradation process and a shock process, in which the former is simultaneously affected by random shocks and the latter is concurrently influenced by cumulative degradation. For the degradation process, a normal distribution is adopted for soft failure threshold to reflect the randomness of threshold level, and the soft failure survival function is developed subsequently. While for the shock process, the initial random hard failure threshold is regarded as the intensity distribution and a time-varying hard failure threshold function is developed, which describes the dependent strength between the hard failure process and the soft failure process. System reliability function is finally constructed based on the competing and dependent result of these two processes. An illustrative example of a micro-electro-mechanical system (MEMS) is analyzed to examine the developed reliability model, demonstrating that the dependence between degradation and shocks has a greater impact on reliability and overestimation may be caused without considering random characteristics of failure thresholds.

Reliability analysis for systems subject to dependent and competing failure processes with random failure thresholds