A Bayesian reliability model for failure count data

In reliability analyses recording the lifetimes of a sample of test units is not always possible, for example when a data capture system only keeps track of the number of malfunctions over a specified time interval. For the resulting so called failure count data the appropriate model is the Poisson distribution with parameter "lambda", which represents the mean number of failures in a time interval of given length. In this paper we present a Bayesian approach estimating this parameter, which allows for incorporating prior knowledge into the analyses. This prior knowledge can be obtained through experts' experience such as knowledge from previous development projects with similar products. Secondly, we will introduce a hierarchical Poisson model and show its use in handling more complex situations. Instead assuming a common failure rate "lambda", we allow different "lambda"j due to various operational conditions for the respective test units and demonstrate the advantages of this approach.