Warranty analysis of a two-component system with failure interaction

In recent decades, more attention has been given to warranty cost models of multi-component systems. This is mainly because the warranty cost could be a high expense to the manufacturer and should be rationally estimated. Moreover, since the dependence among components can affect the product availability, reliability, mean time to failure etc. the maintenance model concerning the multi-component systems should take this latter in consideration. The failure dependence of two-component systems was proposed by Murthy & Nguyen (1985) in which they introduced three types of failure interaction. Type I failure interaction supposes that a failed component can induce the simultaneous failure of the remaining (Scarf & Deara 1998, Scarf & Deara 2003, Jhang & Sheu 2000, Liu, Wu, & Xie 2015). Instead of inducing simultaneous failure, Type II failure interaction assumes that whenever a component fails, it causes an increase of the survival component’s failure rate because of extra shocks, stress or loads and so forth (Zequeira & Bérenguer 2005). Type III failure interaction is also called shock damage interaction which assumes that whenever a component fails, a random damage is induced to the other one which accelerate its degeneration (Sheu, Liu, Zhang, & Ke 2015).