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

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 SciencesM. Sc. (Statistics

A k-out-of-n reliability system with an unreliable server and phase type repairs and services: the (N, T) policy

In this paper we study a k-out-of-n reliability system in which a single unreliable server maintains n identical components. The reliability system is studied under the (N,T) policy. An idle server takes a vacation for a random amount of time T and then attends to any failed component waiting in line upon completion of the vacation. The vacationing server is recalled instantaneously upon the failure of the Nth component. The failure times of the components are assumed to follow an exponential distribution. The server is subject to failure with failure times exponentially distributed. Repair times of the component, fixing times of the server, and vacationing times of the server are assumed to be of phase type. Using matrix-analytic methods we perform steady state analysis of this model. Time spent by a failed component in service, total time in the repair facility, vacation time of the server, non-vacation time of the server, and time until failure of the system are all shown to be of phase type. Several performance measures are evaluated. Illustrative numerical examples are presented

Maintenance and marginal cost analysis of a two-unit cold standby system

Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1997.Thesis (Master's) -- Bilkent University, 1997.Includes bibliographical references leaves 97-102.The Marginal Cost Analysis (MCA) of maintenance policies is a concept gaining interest in the recent years. This approach, due to Berg, has been categorized as an Economics Oriented Approach, as different from the classical probability centered approach. The MCA has been successfully applied to the Age Replacement and the Block Replacement policies, and was shown to be flexible enough to permit extensions and generalizations. In this thesis, we apply the MCA approach to a more complex model. We consider a two-unit cold standby system. Upon failure of the working unit in the time interval [0,T) the unit is replaced by the standby unit if available. If the standby unit is in repair, the system is down, and a downtime cost is incurred. The item inspected at time T is in one of two states: “good” , or “critical” . The good unit continues operation, whereas a unit in critical state is sent to repair. The switchover is immediate. We derive and compare the marginal cost function as well as the long-run cost per unit time function.Hamdaoui, ChokriM.S

Advanced flight control system study

The architecture, requirements, and system elements of an ultrareliable, advanced flight control system are described. The basic criteria are functional reliability of 10 to the minus 10 power/hour of flight and only 6 month scheduled maintenance. A distributed system architecture is described, including a multiplexed communication system, reliable bus controller, the use of skewed sensor arrays, and actuator interfaces. Test bed and flight evaluation program are proposed