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A series of bounds for the availability and unavailability in a fixed time interval, I, for a system of maintained, interdependent components are given in Natvig (1980) in the traditional binary case, and in Funnemark and Natvig (1985) in the multistate case. For the special case of independent components the only assumption needed to arrive at these bounds is that the marginal performance process of each component is associated in I. When these processes are Markovian and binary, a sufficient condition for this to hold is given by Esary and Proschan (1970). In the present paper we generalize this condition to the multistate case, and give an equivalent and much more convenient condition in terms of the transition intensities.

The association in time of a Markov process with application to multistate reliability theory