An Extended Pearson System Useful In Reliability Analysis

In the present environment, industry should provide the products of high quality. Quality of products is judged by the period of time they can successfully perform their intended functions without failure. The cause of the failures can be ascertained through life testing experiments and the times to failure due to different cause are likely to follow different distributions. Knowledge of this distribution is essential to eliminate causes of failures and thereby to improve the quality and the reliability of products. The main accomplishment expected to the study is to develop statistical tools that could facilitate solution to lifetime data arising in such and similar contexts

Fish habitats and species assemblage in the selected rivers of Kerala and investigation on life history traits of Puntius carnaticus(Jerdon,1849)

This thesis entitled Fish habitats and species assemblage in the selected rivers of kerala and investigation on life history traits of puntius carnaticus (JERDON,1849). Ecology is a new and exceedingly complex field of study, even though its concept was recognized by the Apostles in their use of the phrase ‘all flesh is grass.central role to play both in order to understand better the biodiversity phenomenon and to be able to draw up clear guidelines for careful resource management. In a review by WWF, IUCN and UNEP on the ways of conserving genetic diversity of freshwater fish it was recommended that the best way to conserve species diversity is to conserve habitat.The habitat studies in freshwater ecosystems are very essential for the proper understanding and management of human impact on fish diversity, to study the relationship between habitat variables and fish species assemblage structure, quantification of ecosystem degradation, habitat quality and biotic integrity of the ecosystems, development of habitat suitability index (I-ISI) models and classification of river reaches based on their physico-chemical properties. Therefore in the present study an attempt was made to assess the biodiversity potential and the relationship between habitat variables and fish species assemblage structure in six major river systems of Kerala which would be very useful in impressing upon the seriousness of habitat degradIn the present study, in Kabbini river system 15 locations encompassing between 721 946m above MSL were surveyed.ation and biotic devastation undergone in the major river systems of Kerala.During the present study the Habitat Quality Score (HQ) developed by the Ohio EPA was applied for the first time in India.The result of the present study revealed that, among various variables analysed, altitude has a very significant influence in deciding the fish diversity in six major river systems of Kerala. The fish diversity studied on the basis of Shanon-Weiner and Simpson diversity indices revealed that even though some minor variations occur with the suitability and complexity of habitats, the altitude showed inverse relationship with fish diversity.The present study revealed that the National Policy on the interlinking of rivers would permanently alter the HSI indices of the above mentioned fish species, which are now solely protected by the individuality of the rivers where their limited occurrence was notice.

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.