Discrete hazard rate functions

Discrete hazard rate functions are a useful tool for modeling joint distributions of discrete lifetimes. In this paper the authors study a dynamic approach to discrete reliability theory based on discrete hazard rate functions. The hazard rate functions are first defined and studied in the univariate case. Then the general multivariate case is considered. Necessary and sufficient conditions are given for a set of functions to be discrete multivariate conditional hazard rate functions. An application of the harzard rate functions, to characterizations of ageing properties of discrete lifetimes distributions, is described. Further applications of these functions to modelings of univariate and multivariate discrete imperfect repair are also included. Some examples illustrate the theory.