A Bayesian logistic regression model for binomial failure data

The reliability assessment of systems which are relevant to security is an extremely important task in managing public health risk. We want to consider the failure probability p of such a critical system and find out whether there is a trend in this failure probability p over time. There are data available about unplanned demands for maintenance because of hazardous incidents in terms of incident times. Furthermore it has been recorded, whether or not a failure occurred shortly after the demand. As the failure probability obviously depends on these data it seems reasonable to find a statistical model covering these dependencies. Since we have binary outcomes, we use the logistic regression model. Here the logit function is used, which maps the odds ratio p/(1-p) of p via log(p/(1-p)) onto the real line. This logit function will be related to the times t , where the hazardous incidents occurred via log it( p ) = ß0 +ß1t . If there really exists a bias for the failure probability p, the parameter ß1 should be nonzero