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A Compound Measure of Dependability for Continuous-Time Markov Models of Repairable Systems

  • Attila Csenki
Part of the Lecture Notes in Statistics book series (LNS, volume 90)

Abstract

In the previous chapter, we were looking at the distribution of \({M_{{A_1}}}({t_0})\) the number of visits during [0, t0], t0> 0, to a subset A1 of the state space S by an irreducible finite Markov process Y. In the reliability context, \({M_{{A_1}}}({t_0})\) will become the number of repair periods MB (t0) if we put A1= B, the set of system ‘down’ states. The cumulative distribution function of MB(t0) is of course available from Theorem 5.1. For reliability assessment it is desirable to consider several system characteristics simultaneously; in this chapter, MB(t0) will be supplemented by TG(t0), the total time spent by Y during [0, t0] in the set of ‘good’ states G = A2 = S\A1. More precisely, we shall consider here Pr{ TG(t0) > t, MB(t0) ≤ m } for t ∈ (0, t0) and m ∈ {0, 1, … }, i.e., the probability that during [0, t0] the system is ‘up’ for more than t units of time and that the number of ‘down’ periods does not exceed m.

Keywords

Markov Chain Cumulative Distribution Function Closed Form Expression Sojourn Time Transition Probability Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag NewYork, Inc. 1994

Authors and Affiliations

  • Attila Csenki
    • 1
  1. 1.Department of Computer Science and Applied MathematicsAston UniversityBirminghamGreat Britain

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