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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 (PHc). 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.

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