Optimization of maintenance policy under parameter uncertainty using portfolio theory

In reliability mathematics, the optimization of a maintenance policy is derived based on reliability indexes, such as the reliability or its derivatives (e.g., the cumulative failure intensity or the renewal function) and the associated cost information. The reliability indexes, also referred to as models in this article, are normally estimated based on either failure data collected from the field or lab data. The uncertainty associated with them is sensitive to several factors, including the sparsity of data. For a company that maintains a number of different systems, developing maintenance policies for each individual system separately and then allocating the maintenance budget may not lead to optimal management of the model uncertainty and may lead to cost-ineffective decisions. To overcome this limitation, this article uses the concept of risk aggregation. It integrates the uncertainty of model parameters in the optimization of maintenance policies and then collectively optimizes maintenance policies for a set of different systems, using methods from portfolio theory. Numerical examples are given to illustrate the application of the proposed methods.