Multivariate reliability modelling with empirical Bayes inference

Recent developments in technology permit detailed descriptions of system performance to be collected and stored. Consequently, more data are available about the occurrence, or non-occurrence, of events across a range of classes through time. Typically this implies that reliability analysis has more information about the exposure history of a system within different classes of events. For highly reliable systems, there may be relatively few failure events. Thus there is a need to develop statistical inference to support reliability estimation when there is a low ratio of failures relative to event classes. In this paper we show how Empirical Bayes methods can be used to estimate a multivariate reliability function for a system by modelling the vector of times to realise each failure root cause.