Multi-Point and Multi-Interval Bounded-Covering Availability Measures for Aggregated Markovian Repairable Systems

In reliability theory, there are many measures for describing the characteristics of repairable systems, such as reliability, point availability and interval availability. However, these reliability measures do not cover some situations that one may be interested in. In this work, two new reliability measures, multi-point bounded-covering availability and multi-interval bounded-covering availability, are introduced, and derived in matrix form for aggregated Markovian repairable systems. The formulas for single-point, single-interval, binary-point and binary-interval bounded-covering availabilities are all obtained by an enumeration method. The formulas for multi-point and multi-interval bounded-covering availabilities are given in a recursive computational form. Some properties of these two new measures are then discussed briefly, and a few numerical examples are provided to illustrate the results presented here. Finally, some conclusions and discussions are given.