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

Xiaowen Zhang,Zaiyou Yang,Hao Lyu,Shuai Wang,Michael Pecht

doi:10.17531/ein.2021.4.5

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

Highlights

Many systems will fail due to various failure modes caused by degradation and random external shocks during operation [1]
It is assumed that the interarrival time between shocks follows the common phase-type distribution, the total number of shocks before the hard failure occurring follows the discrete phase-type distribution, and the survival function is employed to calculate the hard failure reliability
It can be seen from the soft failure reliability curve and the total reliability curve in Fig. 5 (a) that when t is around 0.8×105, the decline rate of the soft failure reliability curve and the total reliability curve becomes faster, which is because the number of shock arrivals reaches a certain threshold at this time

Summary

Introduction

Many systems will fail due to various failure modes caused by degradation and random external shocks (such as wear, corrosion, fatigue, fracture, and shock loads) during operation [1]. When the interarrival time between shocks follows the common continuous phase-type distribution, the survival function and mean residual lifetime of the multi-state system were derived. The survival function of the system was studied when the interarrival time and the shock magnitude are independent and dependent using the property of phase-type distribution. It is assumed that the interarrival time between shocks follows the common phase-type distribution, the total number of shocks before the hard failure occurring follows the discrete phase-type distribution, and the survival function is employed to calculate the hard failure reliability.

System description and preliminaries

Reliability analysis of DCFP considering time phasetype distribution

Soft failure model under degradation and random shocks

Hard failure model under extreme shock

Hard failure model under cumulative shock

Hard failure model under run shock

System reliability analysis

Numerical examples

GPa σW

Conclusions