Reliability and maintenance modeling for competing risk processes with Weibull inter-arrival shocks

In this paper, a new Weibull inter-arrival shock process is proposed for modeling the competing risk process. The dependent competing failure/risk processes exists in many systems and the reliability modeling for those processes has attracted much attention in the recent years. However, the arrivals of random shocks are usually modeled as Poisson process which indicates the constant hazard rate of shock inter-arrival time. Our proposed Weibull inter-arrival shock process generalized the Poisson shock process and can deal with the cases when the shock count data are over-dispersion or under-dispersion. On the other hand, the dependency between the soft failure process and hard failure process is emphasized by assuming the linear dependent damage size. In four different hard failure models, analytic forms of the reliability functions are derived by using the polynomial expansion. The maintenance optimization for the developed model is discussed under different shock failure mechanisms. Numerical examples based on a micro-engine are also presented to illustrate the proposed model.