Abstract
In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.
Highlights
This paper is concerned with reliability indicators for semi-Markov systems
We propose a new measure for analysing the performance of a system, called the sequential interval reliability (SIR)
We define the sequential interval reliability, SIR(N)(t, p), as the probability that the system is in the up-states U during the time intervals {[ti, ti + pi]}i=1,...,N, meaning that: SIR(N)(t, p) := P(Zl ∈ U, for all l ∈ [ti, ti + pi], i = 1, . . . , N); (8)
Summary
This paper is concerned with reliability indicators for semi-Markov systems As it is well known (see, e.g., [1,2,3,4,5,6]), semi-Markov processes represent an important modelling tool for practical problems in reliability, survival analysis, financial mathematics, and manpower planning, among other applied domains. We propose a new measure for analysing the performance of a system, called the sequential interval reliability (SIR). This generalises the notion of interval reliability, as it is introduced in [20] for discrete-time semi-Markov processes and further studied in [21,22]. A numerical example is provided in Section 4, illustrating some aspects of our theoretical work
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