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- W34192733 abstract "In this chapter, we deal with absorbing Markov reliability models whose state space S is partitioned as S = G ∪ B ∪{ω}, where G and B are transient sets and ω is an absorbing state. Let Y = { Yt : t ≥ 0 } be such a Markov process and let ({T_G} = T{S_{G,infty }}) and NB stand respectively for the total time spent by Y in G, and the number of visits by Y to B, until absorption. We know TG from Chapter 4; it can be interpreted as the total amount of work delivered by the system until system breakdown if G is the set of ‘up’ states and B is the set of repairable system ‘down’ states. Then, NB is the number of repair periods until failure. With this interpretation then, it seems reasonable to specify a required simultaneous lower, and upper bound for TG and NB respectively. (Notice that NB is an appropriate cost measure if every repair instance carries the same cost.) Individually, we know the distributions of NB and TG from Corollary 2.6 and Theorem 4.12 respectively. For the required probability, Pr{ TG > t, NB ≤ n }, however, the joint distribution of TG and NB needs examining. This will be accomplished in Section 7.1. The result is a closed-form expression in terms of exponentials of certain submatrices of the transition rate matrix of Y. Section 7.2 contains the proofs. In Section 7.3, we report on the MATLAB implementation of our dependability measure for Model 3 from Section 1.2.1. This chapter is based on material first reported in [CSE9]." @default.
- W34192733 created "2016-06-24" @default.
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- W34192733 date "1994-01-01" @default.
- W34192733 modified "2023-09-28" @default.
- W34192733 title "A Compound Measure of Dependability For Continuous- Time Absorbing Markov Systems" @default.
- W34192733 doi "https://doi.org/10.1007/978-1-4612-2674-1_7" @default.
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