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IMA Journal of Management Mathematics Advance Access published online on June 27, 2008
IMA Journal of Management Mathematics, doi:10.1093/imaman/dpn013
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© The authors 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Risk aversion in maintenance: a utility-based approach

Rose Baker{dagger}

Centre for Operational Research and Applied Statistics, University of Salford, The Crescent, Salford, M5 4WT, UK

{dagger} Email: r.d.baker{at}salford.ac.uk

Received on 25 September 2007. Accepted on 3 June 2008.

In the author's concept of risk-averse maintenance, introduced in a previous paper, we seek to minimize the disutility of cost per unit time rather than to minimize cost per unit time itself. This gives a maintenance policy that is optimal under risk aversion. This paper extends the earlier work by providing a solution to the problem of combining risk aversion with the cost discounting that arises from the time value of money. The effect of parameter uncertainty, which was touched on in the earlier work, is here shown to lead to a minimax solution when operation for a long period with model uncertainty is planned. The possible use of non-exponential utility functions is discussed. In an attempt to make risk-averse maintenance more meaningful for practitioners, a fresh example of its use, the maintenance of a standby system, is given. A graphical aid to decision support is given, and some useful financial measures of risk, value at risk and expected shortfall, are introduced. These can be used to characterize planned maintenance policies.

Keywords: maintenance; inspection; utility function; risk aversion; standby system; Wald identity; VaR; expected shortfall; discounting; minimax policy


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