A Study on Joint Availability for k out of n and Consecutive k out of n Points and Intervals

The performance of maintenance systems can be described by many indexes such as availability, mean up-time and mean down-time and so forth. The availability is the most important measure among them. Availability has many types, including instantaneous, steady-state and average availability, etc. In this paper, the joint availabilities for k out of n intervals and consecutive k out of n intervals under the Markov assumption are presented in recursive equations. When n = k, the k out of n and consecutive k out of n systems reduce to a series system, and in this situation, the corresponding results have been given by Csenki [9] and Cui et al. [17] using different methods. In contrast, the major contributions of the paper are the extensions of the known results for series systems; that is, the situations when k < n have not been covered in the previous studies and will be presented in the present paper. Some numerical examples and discussions are given to illustrate the results obtained in the paper. Finally, the conclusions are summarized