Two models for a repairable two-system with phase-type sojourn time distributions

A cold standby repairable system with working vacations and vacation interruption following Markovian arrival process

“…From then on, the PH distribution have been frequently applied in queuing theory, statistics signal analysis and inventory theory and so on. In recent years, the PH distribution has also been used in reliability field by several Spanish scholars (see references [20][21][22][23][24][25][26][27][28][29][30], and references contained therein). Repairable systems are usually studied in the continuous time case; nevertheless, not all systems can be continuously monitored, and they must be observed at certain epochs.…”

Probabilistic analysis of two reliability models of a single-unit system with preventive maintenance beyond warranty and degradation

“…By using regenerating point and semi-Markov technique, various researchers including Kadyan et al [3], Yang and Dhillon [6], Perez Ocon and Ruiz Castro [8], Philip and Cristiano [9] and Yuan and Meng [11] have studied reliability models of one or more unit systems under different sets of assumptions on failure and repair policies. When the failure rate or repair rate or both are timedependent, the system loses its Markov character and becomes nonMarkovian.…”

Non-Markovian Modeling of a BladeCenter Chassis Midplane

“…By contrast, such dependencies and multiple failure modes can be easily captured by state-space models such as Markov chains, semi-Markov processes, and Markov regenerative processes [6,7]. However, the computational requirements for building, storing, and solving state space models for real systems can lead to a state space explosion, and could be mitigated by using symbolic techniques and Kronecker algebra [8,9,10]. But a more practical alternative is to use a hierarchical approach where a judicious combination of state space and nonstate-space methods is utilized.…”