Reliability measures for dynamic multistate nonrepairable systems and their applications to system performance evaluation

The main focus of this paper is on the development of reliability measures for dynamic multistate systems which have M + I discrete states of working efficiency. In traditional reliability models for binary systems, one measure that is commonly used is the probability of success at some time t. For multistate systems, we can extend this definition and define the reliability of a multistate system to be the probability that the system still functions at some intermediate state k, 0 <= k <= M or higher at time t. To develop the reliability measures for multistate systems, we assume that the degradation of the multistate systems follows a Markov process and that the system can directly degrade into any lower state. The other focus of this paper is on the evaluation of multistate systems for system design. For traditional binary reliability evaluation, the better system at time t is the one that has a greater value of the area created by the integration over time of the expected value of the state of the system from time 0 to time t. This integration is also related to a customer's experience with the system over the period under consideration. For binary systems, the expected value of the state of the system at any time is equal to the probability of success at the time under consideration. Similarly, one way to evaluate multistate systems is to calculate some accumulated value which is the integration of the expected value of the state of the system from time 0 to time t. Another way to evaluate multistate systems is to estimate how much benefit the customer can receive through using the system. To obtain this measure, we include a customer's utility function over time, and develop a model that can calculate a customer's expected total utility for their experience with the system. A better system should give the customer a high total utility over time and then these measures can be used in system design and evaluation.