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.

Some bivariate life time models in discrete time"

The term reliability of an equipment or device is often meant to indicate the probability that it carries out the functions expected of it adequately or without failure and within specified performance limits at a given age for a desired mission time when put to use under the designated application and operating environmental stress. A broad classification of the approaches employed in relation to reliability studies can be made as probabilistic and deterministic, where the main interest in the former is to device tools and methods to identify the random mechanism governing the failure process through a proper statistical frame work, while the latter addresses the question of finding the causes of failure and steps to reduce individual failures thereby enhancing reliability. In the probabilistic attitude to which the present study subscribes to, the concept of life distribution, a mathematical idealisation that describes the failure times, is fundamental and a basic question a reliability analyst has to settle is the form of the life distribution. It is for no other reason that a major share of the literature on the mathematical theory of reliability is focussed on methods of arriving at reasonable models of failure times and in showing the failure patterns that induce such models. The application of the methodology of life time distributions is not confined to the assesment of endurance of equipments and systems only, but ranges over a wide variety of scientific investigations where the word life time may not refer to the length of life in the literal sense, but can be concieved in its most general form as a non-negative random variable. Thus the tools developed in connection with modelling life time data have found applications in other areas of research such as actuarial science, engineering, biomedical sciences, economics, extreme value theory etc.

Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Studies Using Computer Simulation Models to Solve Problems Related to Logistics Terminals

This thesis deals with the use of simulation as a problem-solving tool to solve a few logistic system related problems. More specifically it relates to studies on transport terminals. Transport terminals are key elements in the supply chains of industrial systems. One of the problems related to use of simulation is that of the multiplicity of models needed to study different problems. There is a need for development of methodologies related to conceptual modelling which will help reduce the number of models needed. Three different logistic terminal systems Viz. a railway yard, container terminal of apart and airport terminal were selected as cases for this study. The standard methodology for simulation development consisting of system study and data collection, conceptual model design, detailed model design and development, model verification and validation, experimentation, and analysis of results, reporting of finding were carried out. We found that models could be classified into tightly pre-scheduled, moderately pre-scheduled and unscheduled systems. Three types simulation models( called TYPE 1, TYPE 2 and TYPE 3) of various terminal operations were developed in the simulation package Extend. All models were of the type discrete-event simulation. Simulation models were successfully used to help solve strategic, tactical and operational problems related to three important logistic terminals as set in our objectives. From the point of contribution to conceptual modelling we have demonstrated that clubbing problems into operational, tactical and strategic and matching them with tightly pre-scheduled, moderately pre-scheduled and unscheduled systems is a good workable approach which reduces the number of models needed to study different terminal related problems.

Design and Development of data mining models for the predictions of manpower placement in the technical Domain

Data mining is one of the hottest research areas nowadays as it has got wide variety of applications in common man’s life to make the world a better place to live. It is all about finding interesting hidden patterns in a huge history data base. As an example, from a sales data base, one can find an interesting pattern like “people who buy magazines tend to buy news papers also” using data mining. Now in the sales point of view the advantage is that one can place these things together in the shop to increase sales. In this research work, data mining is effectively applied to a domain called placement chance prediction, since taking wise career decision is so crucial for anybody for sure. In India technical manpower analysis is carried out by an organization named National Technical Manpower Information System (NTMIS), established in 1983-84 by India's Ministry of Education & Culture. The NTMIS comprises of a lead centre in the IAMR, New Delhi, and 21 nodal centres located at different parts of the country. The Kerala State Nodal Centre is located at Cochin University of Science and Technology. In Nodal Centre, they collect placement information by sending postal questionnaire to passed out students on a regular basis. From this raw data available in the nodal centre, a history data base was prepared. Each record in this data base includes entrance rank ranges, reservation, Sector, Sex, and a particular engineering. From each such combination of attributes from the history data base of student records, corresponding placement chances is computed and stored in the history data base. From this data, various popular data mining models are built and tested. These models can be used to predict the most suitable branch for a particular new student with one of the above combination of criteria. Also a detailed performance comparison of the various data mining models is done.This research work proposes to use a combination of data mining models namely a hybrid stacking ensemble for better predictions. A strategy to predict the overall absorption rate for various branches as well as the time it takes for all the students of a particular branch to get placed etc are also proposed. Finally, this research work puts forward a new data mining algorithm namely C 4.5 * stat for numeric data sets which has been proved to have competent accuracy over standard benchmarking data sets called UCI data sets. It also proposes an optimization strategy called parameter tuning to improve the standard C 4.5 algorithm. As a summary this research work passes through all four dimensions for a typical data mining research work, namely application to a domain, development of classifier models, optimization and ensemble methods.

Discrete Time Inventory Models with/without Positive Service Time

In everyday life different flows of customers to avail some service facility or other at some service station are experienced. In some of these situations, congestion of items arriving for service, because an item cannot be serviced Immediately on arrival, is unavoidable. A queuing system can be described as customers arriving for service, waiting for service if it is not immediate, and if having waited for service, leaving the system after being served. Examples Include shoppers waiting in front of checkout stands in a supermarket, Programs waiting to be processed by a digital computer, ships in the harbor Waiting to be unloaded, persons waiting at railway booking office etc. A queuing system is specified completely by the following characteristics: input or arrival pattern, service pattern, number of service channels, System capacity, queue discipline and number of service stages. The ultimate objective of solving queuing models is to determine the characteristics that measure the performance of the system