On Discrete Failure Models

In some situations, discrete failure ``time'' distributions are appropriate to model ``lifetimes''. For example, a discrete distribution is appropriate when a piece of equipment operates in cycles and the number of cycles prior to failure is observed. This paper provides three families of discrete parametric distributions which are versatile in fitting increasing, decreasing, and constant failure rate models to either uncensored or right-censored discrete life-test data. The maximum likelihood estimation of parameters, survival probabilities, and mean lifetime is investigated. The MLEs can be computed by simple numerical methods.