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

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 and sudden exceeds soft failure threshold, occurs. The interarrival time between two successive shocks total number before hard occurring follow PH discrete distribution, respectively. calculated using survival function. Due shock on process, will increase. reaches specific value, changes. by extreme model, cumulative run closed-form function derived combining model. Finally, Micro-Electro-Mechanical System (MEMS) demonstrates effectiveness proposed