Multi-State Joint Survival Signature for Multi-State Systems with Shared Multi-State Components

In this paper, the multi-state joint survival signature is proposed for two multi-state semi-coherent or mixed systems with shared independent and identically distributed (i.i.d.) multi-state components, and then its properties are studied along with the related multi-state joint signature. By using the idea of equivalent systems, generalized triangle rule for order statistics and the independence assumption of component lifetimes at different states, transformation formulas of multi-state joint survival signatures of different sizes are presented so that stochastic comparisons of multi-state semi-coherent or mixed system pairs that share different numbers of multi-state components can be carried out. For illustrating the theoretical results established here, some examples are presented. Finally, some concluding remarks are made.