A study on the analysis of two-unit redundant repairable complex systems

Abstract

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.