On the monotonic properties of discrete failure rates

As is well known, the monotonicity of failure rate of a life distribution plays an important role in modeling failure time data. In this paper, we develop techniques for the determination of increasing failure rate (IFR) and decreasing failure rate (DFR) property for a wide class of discrete distributions. Instead of using the failure rate, we make use of the ratio of two consecutive probabilities. The method developed is applied to various well known families of discrete distributions which include the binomial, negative binomial and Poisson distributions as special cases. Finally, a formula is presented to determine explicitly the failure rate of the families considered. This formula is used to determine the failure rate of various classes of discrete distributions. These formulas are explicit but complicated and cannot normally be used to determine the monotonicity of the failure rates. (C) 1997 Elsevier Science B.V.