A Markov regenerative process with recurrence time and its application

This study proposes a non-homogeneous continuous-time Markov regenerative process with recurrence times, in particular, forward and backward recurrence processes. We obtain the transient solution of the process in the form of a generalized Markov renewal equation. A distinguishing feature is that Markov and semi-Markov processes result as special cases of the proposed model. To model the credit rating dynamics to demonstrate its applicability, we apply the proposed stochastic process to Standard and Poor’s rating agency’s data. Further, statistical tests confirm that the proposed model captures the rating dynamics better than the existing models, and the inclusion of recurrence times significantly impacts the transition probabilities.

ESTIMATING DISCRETE-TIME PERIODIC SOFTWARE REJUVENATION SCHEDULES UNDER COST EFFECTIVENESS CRITERION

Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this article, we consider the similar periodic software rejuvenation model to Garg et al.13 under the different operation circumstance. That is, we model the stochastic behavior of telecommunication billing applications by using a discrete-time Markov regenerative process, and determine the optimal periodic software rejuvenation schedule maximizing the so-called cost effectiveness, in discrete-time setting. Also, we provide a statistically non-parametric method to estimate the optimal software rejuvenation schedule, based on the discrete total time on test concept. Numerical examples are devoted to illustrate the determination/estimation of the optimal software rejuvenation schedule and to examine the asymptotic behavior of the estimator developed here.

Preventive Maintenance of Multi-State System with Phase-Type Failure Time Distribution and Non-Zero Inspection Time

Preventive maintenance is applied to improve the system availability or decrease the operational cost. This paper addresses the optimal preventive maintenance problem for multi-state deteriorating systems, where the system experiences multiple stages of performance degradation before it fails. We consider a general case where the inspection and repair time are generally distributed. The threshold type maintenance policy is employed for preventive minor maintenance and preventive major maintenance, where minor or major maintenance is carried out when the system deterioration stage is found to be larger than certain thresholds. The mathematical model of the system is set up by means of a Markov regenerative process (MRGP). With this formulation, the system steady-state probabilities under consideration are computed.