In this work, we consider two coherent systems with shared components in the case when the component lifetimes are independent and identically distributed with a discrete-time distribution instead of a continuous-time distribution. Then, a discrete-time joint signature is proposed for the two systems by generalizing the traditional joint signature for systems with continuous lifetimes. Some stochastic properties of the proposed joint signature are studied in detail, including joint distribution, stochastic ordering, and transformation formula for comparison of pairs of systems of different sizes. Some illustrative examples are also presented.

In this work, by considering coherent systems comprising independent components with discrete lifetimes, we introduce the notion of discrete-time signature and then discuss some of its properties. With the use of the introduced signature, a stochastic ordering result is also established. We then introduce transformation formulas for the discrete-time signature to facilitate the comparison of systems of different sizes. Some examples are also presented to illustrate all the results developed here.

In this paper, we give a transformation formula of Dwork’s p-adic hypergeometric function between t and $t^{-1}$. As an appendix, we introduce a finite analogue of this transformation formula, which implies a special case of the transformation formula for Dwork’s p-adic hypergeometric function.