Maintenance helps to extend equipment life by improving its condition and avoiding catastrophic failures. Appropriate model or mechanism is, thus, needed to quantify system availability vis-a-vis a given maintenance strategy, which will assist in decision-making for optimal utilization of maintenance resources. This paper deals with semi-Markov process (SMP) modeling for steady state availabili...

Time dependent availability is an important index used for evaluation of operational performance of repairable industrial systems. Traditionally, Markov analysis procedures are carried out for such studies. This becomes mathematically intensive when applied for larger systems. Moreover, this method does not indicate at what time a system reaches its steady state. However, in practice it is impo...

This paper introduces a Markov model for a multi-state repairable system in which some states are changeable in the sense that whether those physical states are up or down depends on the immediately preceding state of the system evolution process. Several reliability indexes, such as availability, mean up time, steady-state reliability, are calculated using the matrix method. A sufficient condi...

This paper introduces a Markov model for a multi-state repairable system in which some states are changeable in the sense that whether those states are up or down depends on the recent system evolution history. Several reliability indexes, such as availability, mean up time, steady-state reliability, are calculated using the matrix method. A sufficient condition under which the availabilities o...

Repairable standby system’s study and analysis is an important topic in reliability. Analytical techniques become very complicated and unrealistic especially for modern complex systems. There have been attempts in the literature to evolve more realistic techniques using simulation approach for reliability analysis of systems. This paper proposes a hybrid approach called as Markov system ...

We consider semi-Markov reliability models of multi-component systems with a discrete state space, general enough to include systems with maintenance or repair. We assume that for all system states the functioning or failure of each component is specified. In this setup we propose a component importance measure which is close in spirit to the classical steady state Barlow–Proschan importance me...

Liying Wang, Xujie Jia and Jie Zhang Department of Mathematics & Physics, Shijiazhuang Tiedao University, Shijiazhuang, China School of Science, Minzu University of China, Beijing, China The 54 Research Institute of China Electronics Technology Group Corporation, Shijiazhuang, China (Received March 2012, accepted November 2012) ___________________________________________________________________...

Systems often operate over a set of time periods, known as phases, in which their reliability structure varies and many include both repairable and nonrepairable components. Success for such systems is defined as the completion of all phases, known as a phased mission, without failure. An example of such a system is an aircraft landing gear system during a flight. The Binary Decision Diagram (B...

In this lecture we will discuss Markov Chains in continuous time. Continuous time Markov Chains are used to represent population growth, epidemics, queueing models, reliability of mechanical systems, etc. In Continuous time Markov Process, the time is perturbed by exponentially distributed holding times in each state while the succession of states visited still follows a discrete time Markov ch...