Some concepts and models usefulninthe analysis of discrete life time data

This thesis entitled Reliability Modelling and Analysis in Discrete time Some Concepts and Models Useful in the Analysis of discrete life time data.The present study consists of five chapters. In Chapter II we take up the derivation of some general results useful in reliability modelling that involves two component mixtures. Expression for the failure rate, mean residual life and second moment of residual life of the mixture distributions in terms of the corresponding quantities in the component distributions are investigated. Some applications of these results are also pointed out. The role of the geometric,Waring and negative hypergeometric distributions as models of life lengths in the discrete time domain has been discussed already. While describing various reliability characteristics, it was found that they can be often considered as a class. The applicability of these models in single populations naturally extends to the case of populations composed of sub-populations making mixtures of these distributions worth investigating. Accordingly the general properties, various reliability characteristics and characterizations of these models are discussed in chapter III. Inference of parameters in mixture distribution is usually a difficult problem because the mass function of the mixture is a linear function of the component masses that makes manipulation of the likelihood equations, leastsquare function etc and the resulting computations.very difficult. We show that one of our characterizations help in inferring the parameters of the geometric mixture without involving computational hazards. As mentioned in the review of results in the previous sections, partial moments were not studied extensively in literature especially in the case of discrete distributions. Chapters IV and V deal with descending and ascending partial factorial moments. Apart from studying their properties, we prove characterizations of distributions by functional forms of partial moments and establish recurrence relations between successive moments for some well known families. It is further demonstrated that partial moments are equally efficient and convenient compared to many of the conventional tools to resolve practical problems in reliability modelling and analysis. The study concludes by indicating some new problems that surfaced during the course of the present investigation which could be the subject for a future work in this area.

Reliability Estimation of Open Source Software based Computational Systems

Software systems are progressively being deployed in many facets of human life. The implication of the failure of such systems, has an assorted impact on its customers. The fundamental aspect that supports a software system, is focus on quality. Reliability describes the ability of the system to function under specified environment for a specified period of time and is used to objectively measure the quality. Evaluation of reliability of a computing system involves computation of hardware and software reliability. Most of the earlier works were given focus on software reliability with no consideration for hardware parts or vice versa. However, a complete estimation of reliability of a computing system requires these two elements to be considered together, and thus demands a combined approach. The present work focuses on this and presents a model for evaluating the reliability of a computing system. The method involves identifying the failure data for hardware components, software components and building a model based on it, to predict the reliability. To develop such a model, focus is given to the systems based on Open Source Software, since there is an increasing trend towards its use and only a few studies were reported on the modeling and measurement of the reliability of such products. The present work includes a thorough study on the role of Free and Open Source Software, evaluation of reliability growth models, and is trying to present an integrated model for the prediction of reliability of a computational system. The developed model has been compared with existing models and its usefulness of is being discussed.