Reliability model of series systems with multiple shock sources subject to dependent competing failure processes using phase-type distribution

ABSTRACT In this paper, we introduce the concept of a series system with two components and three shock sources considering degradation to build a reliability model. Sources 1 and 2 affect components 1 and 2, respectively. Source 3 covers both components. Both components are subject to dependent competing failure processes (DCFPs). A general reliability model of the n-component series system with m-shock sources subject to DCFPs is derived. The phase-type distribution method is applied to calculate the reliability of the hard failure process. The time lag among shocks follows the continuous phase-type distribution (PH c ). The lifetime and system reliability properties are discussed based on the phase-type distribution. The dependence of shock sources is also considered according to the proposition of phase-type distribution (PH). Finally, an application example and sensitivity analysis of micro-electro-mechanical systems (MEMS) oscillators subject to various shock models are presented to illustrate the developed reliability models.