Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units

A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model

Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields

This book covers a broad range of research results in the field of Markov and Semi-Markov chains, processes, systems and related emerging fields. The authors of the included research papers are well-known researchers in their field. The book presents the state-of-the-art and ideas for further research for theorists in the fields. Nonetheless, it also provides straightforwardly applicable results for diverse areas of practitioners

Findings about the two-state BMMPP for modeling point processes in reliability and queueing systems

The Batch Markov Modulated Poisson Process (BMMPP) is a subclass of the versatile Batch Markovian Arrival process (BMAP) which have been widely used for the modeling of dependent and correlated simultaneous events (as arrivals, failures or risk events, real-time multimedia communications). Both theoretical and applied aspects are examined in this paper. On one hand, the identifiability of the stationary BMMPP2(K) is proven, where K is the maximum batch size. This is a powerful result when inferential tasks related to real data sets are carried out. On the other hand, some findings concerning the correlation and autocorrelation structures are provided.The first and second authors acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, research project ECO2015-66593-P. The Third author acknowledge financial support from the Spanish Ministry of Economy and Competitiveness, research project MTM2015-65915-R; and also from Junta de Andalucía, and BBVA Fundation, research project P11- FQM-7603 and FQM-32