Discrete complex redundant systems with loss of units and an indeterminate number of repairpersons

Resumen

Summary DISCRETE COMPLEX REDUNDANT SYSTEMS WITH LOSS OF UNITS AND AN INDETERMINATE NUMBER OF REPAIRPERSONS Mohammed A S Dawabsha The overall aim of this project is to model complex systems that evolve in discrete time through Markovian Arrival Processes with marked arrivals (D-MMAP) in an algorithmic and computational form. These systems are subject to several types of failure, repairable and/or non-repairable, as a consequence of internal wear or external shocks. Random inspections are included in the models and preventive maintenance is carried out as a consequence of this. Loss of units is introduced; i.e. each time that a non-repairable occurs, it is removed and no replaced. Variable numbers of repairpersons are considered; i.e. each time that a non-repairable occurs, (the number of repairpersons changes and depends on the number of units in the system). The system will be optimised by considering two different standpoints: the profitability of preventive maintenance and the number of repairpersons present according to the number of units in the system. The main objective is to develop complex multi-state systems; complex unit-system, complex cold standby systems, complex warm standby systems and k-out-of-n: G system, in a well-structured and algorithmic form. The following aspects are analyzed for each system proposed. • The system is subject to multiple failure factors (internal and accidental external failures, repairable or non-repairable). • Preventive maintenance is included as a consequence of random inspections. • We build new models with loss of units and with a non-fixed number of repairpersons. The number of repairpersons will vary according to the number of units in the system. • Phase type distributions and D-MMAPs are considered in the modelling. Thus, the results are given in an algorithmic and computational way. • A transient analysis is carried out and the stationary distribution is worked out by considering matrix analytic methods. • For both cases, transient and stationary regime, several reliability measures of interest such as the availability, reliability, conditional probability of different types of failures, etcetera are calculated in a well-structured way. • Rewards and costs are included in the models to optimize the behavior of the system according to preventive maintenance and number of repairpersons. • All results are expressed in algorithmic and computational form and they have been implemented computationally with Matlab. This work has been performed in a sequential form, from a multi-state complex one-unit system to complex redundant systems.  Chapter 1 presents the basic theory that is going to play an important role throughout this work. Phase type distributions, Markovian Arrival Processes, BMAP, MMAP, Costs, etc will be introduced in this chapter.  Chapter 2 analyzes the behavior of one unit multi-state dynamic system subject to multiple events through a Markovian arrival process with marked arrivals (MMAP). This study considers if preventive maintenance is profitable or not, and also shows how the system can be optimised according to its internal performance and the external cumulative damage states revealed by inspection. A numerical example, optimising the system by determining the optimum states from an economic standpoint, illustrates the versatility of the model proposed.  Chapter 3 describes cold standby systems with multiple variable repairpersons, evolving in discrete time. The online unit works as the one of chapter 2. This complex system is modelled by a MMAP in an algorithmic and computational form. Two interesting contributions are made in the present study. The number of repairpersons is indeterminate and variable depending on the number of units in the system.  Chapter 4 shows complex multi-state warm standby systems subject to different types of failures with loss of units. In this study we extend chapter 3 to the warms standby case. We model general reliability systems and associated measures to analyse the behaviour and effectiveness of preventive maintenance depending on the number of repairpersons and net rewards.  Chapter 5 describes a multi-state complex k-out-of-n: G system with loss of units. It is modelled in an algorithmic and computational form. Several interesting reliability measures are obtained, for both transient and stationary regimes. A numerical example is given to show the versatility of the model. The main references used in this work are the following. [1] Alfa A.S. (2016) Applied discrete-time queues. Springer Science+Business Media New York. [2] Artalejo, J. R.: Gómez-Corral, A. and He, Q.M. 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