Allocation of tasks for reliability growth using multi-attribute utility

• We model the decision problem of reliability growth task allocation.
• We utilise multiattribute utility theory to provide an optimal solution.
• The attributes in the decision problem are reliability, cost and time on test.
• Risk averse and loss averse conditional utility functions are investigated.
• General results are given for when these lead to multivariate risk aversion.

In reliability growth models in particular, and project risk management more generally, improving the reliability of a system or product is limited by constraints on cost and time. There are many possible tasks which can be carried out to identify and design out weaknesses in the system under development. This paper considers the allocation problem: which subset of tasks to undertake. While the method is applicable to project risk management generally, the work has been motivated by reliability growth programmes. We utilise a model for reliability growth, based on an efficacy matrix, developed with engineering experts in the aerospace industry. We develop a general multi-attribute utility function based on targets for cost, time on test and system reliability. The optimal subset is identified by maximising the prior expected utility. We derive conditions on the model parameters for risk aversion and loss aversion based on observed properties of preference. We give conditions for multivariate risk aversion under the general form of the utility function. The method is illustrated using an example informed by work with aerospace organisations.