Abstract
In the field of reliability, there are many indexes, such as reliability, point availability, interval availability, and others, which have been widely used to describe the properties of repairable systems. However, some situations of interest cannot be covered by the existing indexes. In this paper, we introduce the definitions of multipoint covering availability and multi-interval covering availability, and formulas are derived in matrix forms for aggregated Markov repairable systems especially when the covering working intervals can overlap. The formulas of binary-point and binary-interval covering availabilities are given by an enumeration method. For multipoint and multi-interval problems, a recursive method is employed. Numerical examples are shown to illustrate the results derived in this paper and finally some conclusions and discussions are presented.
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