A customer's utility measure based on the reliability of multi-state systems

The main focus of this paper is on the development of utility measures for dynamic multi-state systems that have M + 1 discrete states of working efficiency. To develop the utility measures for multi-state systems, we assume that the degradation of the multi-state systems follows a non-homogeneous semi-Markov process together with a backward recurrence time process and that the system can directly degrade into any lower state. The measure considers the immediate utility derived from the state of the system occupancy and the utility due to the system survival expectations derived from its reliability. Moreover, in order to measure the customer's cumulative utility, the discounted non-homogeneous continuous time semi-Markov process with rewards is implemented. In such a way, the higher order moments of the reward process can be evaluated and then, in particular, the expectation and the standard deviation of the consumer's accumulated discounted utility. These statistic indices are useful both to the industry in order to compare different system designs offered by the market and to the market itself, in order to know the customer's utility deriving from the goods she/he consumes. Finally, a numerical example shows the possibility of implementing the model in real-life problems. © 2010 Springer-Verlag.