Abstract
In this paper, we computed general interval indicators of availability and reliability for systems modelled by time non-homogeneous semi-Markov chains. First, we considered duration-dependent extensions of the Interval Reliability and then, we determined an explicit formula for the availability with a given window and containing a given point. To make the computation of the window availability, an explicit formula was derived involving duration-dependent transition probabilities and the interval reliability function. Both interval reliability and availability functions were evaluated considering the local behavior of the system through the recurrence time processes. The results are illustrated through a numerical example. They show that the considered indicators can describe the duration effects and the age of the multi-state system and be useful in real-life problems.
Highlights
Reliability measures of repairable systems have been extensively investigated
It is common to come across reliability, availability, and maintainability functions when dealing with general mechanical systems or to single-use reliability function for software performance assessment
Time semi-Markov processes in [31,32]. We extended this indicator to the more general non-homogeneous discrete-time semi-Markov framework and we derived formulas that consider the influence of recurrence time processes in different ways
Summary
Reliability measures of repairable systems have been extensively investigated. Specific indicators are used according to the characteristics of the system that the user wishes to understand and to the nature of the system. The reason for the existence of this duration dependence resides in the fact that the conditional waiting time distribution functions in the states of the system, i.e., the length of time in a state before making a transition, can be of any type, no memoryless distributions can be used In this case, the time length spent in the starting state (backward value) changes the transition probabilities as well as the information concerning how long the process will stay in the current state (forward value). The solution gives the probability of the system to be operational in a given time interval originating at some time s and length x This measure contains, as special cases, the availability function and the reliability function and has been evaluated concerning discrete-time systems, see [31,32].
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