Two well-known methods of improving the reliability of a system are
(i) provision of redundant units, and
(ii) repair maintenance.
In a redundant system more units made available for performing the system function
when fewer are required actually. There are two major types of redundancy -
parallel and standby. In this dissertation we are concerned with both these types.
Some of the typical assumptions made in the analysis of redundant systems are
(i) the repair facility can take up a failed unit for repair at any time, if no other
unit is undergoing repair
(ii) the system under consideration is needed all the time
However, we frequently come accross systems where one or more assumptions have
to be relaxed. This is the motivation for the detailed study of the models presented
in this dissertation.
In this dissertation we present models of redundant systems relaxing one or more of
these assumptions simultaneously. More specifically it is a study of stochastic
models of redundant systems with 'vacation period' for the repair facility (both
standby and parallel systems), and intermittently used systems.
The dissertation contains five chapters. Chapter 1 is introductory in nature and
contains a brief description of the mathematical techniques used in the analysis of
redundant systems.
In Chapter 2 assumption (i) is relaxed while studying a model of cold standby
redundant system with 'vacation period' for the repair facility. In this model the
repair facility is not available for a random time immediately after each repair
completion. Integral equations for the reliability and availability functions of the
system are derived under suitable assumptions.
In Chapter 3, once again assumption (i) is relaxed while studying a model of parallel
redundant systems with the same 'vacation period' for the repair facility, explained
in the above paragraph.
In Chapter 4, the detailed review of intermittently used systems have been studied.
In Chapter 5, assumption (ii) is relaxed. This chapter is devoted to the study of an
intermittently used 2-unit cold standby system with a single repair facility. This
study was carried out using the 'correlated alternating renewal process' and the joint
forward recurrence times.
All the above models have been studied, when some of the underlying distributions have
a non-Markovian nature. They have been analysed using a regeneration point technique. / Mathematical Sciences / M. Sc. (Statistics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/17477 |
| Date | 06 1900 |
| Creators | Mohoto, Seth Themba |
| Contributors | Yadavalli, V. S. S. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
| Format | 1 online resource (vi, 76 leaves) |
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