Reliability modeling for dependent competing failure processes with phase-type distribution considering changing degradation rate

Abstract

In this paper, a system reliability model subject to Dependent Competing Failure Processes (DCFP) with phase-type (PH) distribution considering changing degradation rate is proposed. When the sum of continuous degradation and sudden degradation exceeds the soft failure threshold, soft failure occurs. The interarrival time between two successive shocks and total number of shocks before hard failure occurring follow the continuous PH distribution and discrete PH distribution, respectively. The hard failure reliability is calculated using the PH distribution survival function. Due to the shock on soft failure process, the degradation rate of soft failure will increase. When the number of shocks reaches a specific value, degradation rate changes. The hard failure is calculated by the extreme shock model, cumulative shock model, and run shock model, respectively. The closed-form reliability function is derived combining with the hard and soft failure reliability model. Finally, a Micro-Electro-Mechanical System (MEMS) demonstrates the effectiveness of the proposed model.

Reliability modeling of dependent competing failure processes based on time‐dependent threshold level δ and degradation rate changes

“…24 When no shock occurs, that is, 𝑁(𝑡) = 0, compound random variable 𝑆(𝑡) = 0. ii) When the shock count reaches a certain level, the degradation rate changes. 31 It is assumed that the jth shock will trigger a transition of degradation rate from 𝛽 1 to 𝛽 2 , where 𝛽 1 , 𝛽 2 are constant, and 𝛽 1 < 𝛽 2 .…”

“…Then the cumulative degradation caused by shock at time t is $$S(t) = \sum_{i = 1}^{N(t)} {{Y}_i} $$ 24 . When no shock occurs, that is, $$N( t ) = 0$$, compound random variable $$S( t ) = 0$$. ii) When the shock count reaches a certain level, the degradation rate changes 31 . It is assumed that the j th shock will trigger a transition of degradation rate from β 1 to β 2 , where $${\beta }_1,{\beta }_2$$ are constant, and $${\beta }_1 &lt; {\beta }_2$$.…”

Reliability modeling for dependent competing failure processes considering random cycle times

“…Hao and Yang 19 proposed a practical reliability model for the sea-bridge system and considered the effect of random shocks on the degradation rate according to a new mixed shock pattern. Lyu et al 20 studied three different shock models and considered the effect of the number of shocks reaching a specific value on the degradation rate. Gao et al 21 derived the reliability indexes of the system according to the general path model and the Wiener process model.…”

Reliability assessment of a system with multi‐shock sources subject to dependent competing failure processes under phase‐type distribution

“…Although Eryilmaz et al have developed a deep insight into reliability models based on phase-type distribution, they may not integrate the phase-type distribution to reliability modeling subject to DCFPs. Lyu et al 36 evaluated the reliability for a micro-engine subject to DCFPs considering shifting the degradation rate where the phase-type distribution calculated the reliability function of hard failure. Phase-type distribution has many advantages.…”