Bayesian Group Replacement Policies

Much research has been performed in finding optimal group replacement policies for production systems consisting of parallel components, where the failure times of the components are independent identically distributed exponential random variables with a common parameter λ. This paper introduces a class of decision rules that utilizes the statistical information obtained during operation of the components. Two forms of statistical input are allowed. We assume that a prior distribution over the possible values of λ is available. It is not required that this prior distribution be in conjugate form. Statistical information that is provided by the actual failure times of the components is incorporated into the decision rule via the sufficient statistics for the problem. This results in group replacement policies that are intuitively attractive, easy to implement, and mathematically tractable.