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Abstract: 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. [Copyright &y& Elsevier]

Abstract: This paper uses mixture priors for Bayesian assessment of performance. In any Bayesian performance assessment, a prior distribution for performance parameter(s) is updated based on current performance information. The performance assessment is then based on the posterior distribution for the parameter(s). This paper uses a mixture prior, a mixture of conjugate distributions, which is itself conjugate and which is useful when performance may have changed recently. The present paper illustrates the process using simple models for reliability, involving parameters such as failure rates and demand failure probabilities. When few failures are observed the resulting posterior distributions tend to resemble the priors. However, when more failures are observed, the posteriors tend to change character in a rapid nonlinear way. This behavior is arguably appropriate for many applications. Choosing realistic parameters for the mixture prior is not simple, but even the crude methods given here lead to estimators that show qualitatively good behavior in examples. [Copyright &y& Elsevier]