Discrete-time dynamic signatures and associated properties

In this work, we consider used coherent systems in the case when the component lifetimes are independent and identically distributed (i.i.d.) with a discrete-time distribution instead of a continuous-time distribution. Then, discrete-time dynamic signature and discrete-time residual signature are proposed for single coherent systems, and discrete-time dynamic joint signature and discrete-time residual joint signature are proposed for two coherent systems with shared components. Associated properties of these proposed discrete-time dynamic signatures are discussed in detail. Some illustrative examples are also presented.