Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
808019 | Reliability Engineering & System Safety | 2010 | 8 Pages |
Failure data are often modeled using continuous distributions. However, a discrete distribution can be appropriate for modeling interval or grouped data. When failure data come from a complex system, a simple discrete model can be inappropriate for modeling such data. This paper presents two types of discrete distributions. One is formed by exponentiating an underlying distribution, and the other is a two-fold competing risk model. The paper focuses on two special distributions: (a) exponentiated Poisson distribution and (b) competing risk model involving a geometric distribution and an exponentiated Poisson distribution. The competing risk model has a decreasing-followed-by-unimodal mass function and a bathtub-shaped failure rate. Five classical data sets on bus-motor failures can be simultaneously and appropriately fitted by a general 5-parameter competing risk model with the parameters being functions of the number of successive failures. The lifetime and aging characteristics of the fitted distribution are analyzed.