Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Research and Training School (RTS)


Sethuraman, Jayaram (RTS-Kolkata; ISI)

Abstract (Summary of the Work)

The work presented in this thesis was carried out under the supervision of Dr. J. Sethuraman, Research & Training School, Indian Statistical Institute, Calcutta, and is devoted to the study of some stochastic models of standby and parallel redundant systems. Some of the reliability characteristics studied are the expected time to system failure, the long-run availability, expected number of system failures in a given interval of time, interval reliability etc. These reliability characteristics will be useful in the better design of systems and making management decisions in improving system reliability.The investigations carried out in this thesis are presented in four chapters which are preceded by an introductory chapter in which a brief history of the development of Reliability Theory and a review of the literature pertaining to the work presented in this thesis have been made.In chapter 1 is discussed the reliability of a single unit system with (N - 1) units as standby and the units on failure are repaired by a single repairlon, OGR, web mization uing a w copy of CVIBION PDP facility. Sections 1 and 2 of this chapter deal respectively with cases of continuous or intermittent usage of the active unit, while section 3 deals with the same system when the spares deteriorate in storage. The phase method. the supplementary variable method and the results of pure birth and death process are used in studying the various models.The case of N unit standby redundant system with multiple repair facilities with exponential failure time and exponential repair time distributions has been studied in chapter 2. The analysis is carried out by using the compensation function technique, In the first two chapters, the Laplace transform of the distribution of time to system failure and the associated probabilities have been derived first. These are then used to generate the general process probabilities using renewal theoretic arguments by observing that the time to system failure period and the system down-time period that follows it form a renewal process. The general process has been used to discuss the various reliability characteristics.Chapter 3 deals with the reliability of a standby redundant system with two types of units assigning preemptive resume and head-of-the-line priority repair policies for repair of the failed units. The system consists of two types of units, one type having only one unit POF y of VBio the other type having two units - an active unit backed by a standby unit. The two types of units are either series connected or parallel connected. The analysis of this system has been made through the semi-Markov process obtaining the Laplace transform of the distribution of time to system failure etc.The reliability of parallel redundant systems with two types of units assigning priority repair policies for the repair of the failed units is investigated in chapter 4 using supplementary variable method. In section 1 has been evaluated the Laplace transform of the distribution of the time-to-system failure of a (2,2) - parallel redundant system while in section 2, the long-run availability of a (N1 , N2) - system.Analytical inter-model and intra-model comparisons have been effected at suitable places in the thesis. Apart from this in all the chapters, the behaviour of the system has been studied by giving numerical values to the parameters involved and effecting comparisons between the reliability characteristics of standby and parallel redundant systems in chapters 1 and 2 and studying the effect of different priority allocation for repair in chapters 3 and 4.


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