This paper presents a comprehensive survey of discrete probability distributions used in reliability for modeling discrete lifetimes of nonrepairable systems. The basic properties of each model are given. A classification into two families is proposed, highlighting the interest of using a Pólya urn scheme. The quality of the estimation of models parameters is numerically assessed. Some criteria are given in order to select among the presented distributions the most useful for applications.
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Bracquemond et al. (2003) studied this question.
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