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Title: The effect of replacement and repair on the reliability of systems
Author: Fawzi, B. B.
Awarding Body: University College of Swansea
Current Institution: Swansea University
Date of Award: 1991
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In this thesis we consider the reliability, availability, uptime distribution and downtime distribution of R-out-of-N systems of identical components with components which have exponential operating times before break down. In particular, we are interested in systems where a finite number, M, of spares is available and a finite number of service facilities is available to install the spares into the system and to repair the failed items to a good-as-new state, and then to join the stock of spares which can be re-installed into the system at a later time. In chapter two we assume that repair times and installation times both have exponential distributions so that our system can be represented as a finite-state continuous-time Markov process. Two models are considered (a) with distinct repair and installation facilities and (b) with service facilities which carry out both repair and installation, with priority given to the installation activity. In chapter three we study a series system with 3 spares and a single service facility with arbitrary distributions for repair times and installation times. Installation takes pre-emptive priority over repairs, and we consider both 'resume' and 'restart' assumptions for interrupted repairs. We consider an approach based on Laplace transforms and the use of supplementary variables to make the process, Markovian. Chapter four generalises the results of chapter three to an arbitrary number, M, of spares. Here only the equilibrium results are obtained by probabilistic arguments. Chapter five deals with the uptime and downtime for both models of chapter four. We consider various distributions of repair times and of installation times. In chapter six we generalise the pre-emptive restart model with a single server and M spares for the series system, discussed in chapter four, to general R-out-of-N system (with single server). The pre-emptive resume case is rather more difficult, and is not dealt with in this thesis. Chapter seven dealt with the downtime distribution for this model. In chapter eight we study a standby system where installation and repair times are both constant. Although this is a special case of the models studied in chapter four, it can be approached differently with some interesting mathematics. Also some extra results about the number of failures over an interval are obtained. Throughout there are numerical examples which have been calculated using APL. We found that this was in some cases, particularly suitable for representing the mathematics of the problem, quite apart from actually computing answers. A large set of APL functions is included in the appendix.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available