Reliability modeling for dependent competing failure processes with changing degradation rate

This article proposes reliability models for devices subject to dependent competing failure processes of degradation and random shocks with a changing degradation rate according to particular random shock patterns. The two dependent failure processes are soft failure due to continuous degradation, in addition to sudden degradation increases caused by random shocks, and hard failure due to the same shock process. In complex devices such as Micro-Electro-Mechanical Systems the degradation rate can change when the system becomes more susceptible to fatigue and deteriorates faster, as a result of withstanding shocks. This article considers four different shock patterns that can increase the degradation rate: (i) generalized extreme shock model: when the first shock above a critical value is recorded; (ii) generalized -shock model: when the inter-arrival time of two sequential shocks is less than a threshold ; (iii) generalized m-shock model: when m shocks greater than a critical level are recorded; and (iv) generalized run shock model: when there is a run of n consecutive shocks that are greater than a critical value. Numerical examples are presented to illustrate the developed reliability models, along with sensitivity analysis.