Mixture priors for Bayesian performance monitoring 1: fixed-constituent model

This paper addresses the problem of assessing the current performance of a system, given that performance can change over time. In many problems of interest, although a significant body of historical evidence is available, current performance information is too sparse to be the sole basis for an assessment of how well the system is currently performing. Therefore, it is desirable to apply current data within a Bayesian framework, making use of a broader body of evidence. However, both noninformative priors and simple informative priors have drawbacks for this application. The present work shows that 'mixture' priors have relatively desirable properties for performance assessment. These properties are illustrated using a simple example in assessment of reliability performance. It is also shown that one implementation of the mixture prior (the 'fixed-constituent model') is formally equivalent to methods used in signal detection, statistical decision rules in medical diagnosis, and many other applications. Building on the medical analogy, the potential benefits of an integrated treatment of reliability data and inspection results are illustrated. A companion paper develops a more sophisticated implementation of the mixture prior (the 'variable-constituent model'), and extends the treatment to more complex examples.