Innovative approaches to reliability and survival analysis

Date of Completion

January 2000






Analysis of life time data has been one of the major fields in the development of statistical theory in twentieth century. Many of the well-defined problems had been addressed in the literature providing an established theory towards their solution. Parallely, numerous other complicated issues have emerged seeking novel solutions. In the present research, some of these important issues are being addressed. Multivariate life time data are one of the major attractions that the statisticians are interested in. Methods towards modeling multivariate life time data in a more general set-up are proposed in the present research with a detailed description of necessary tools for implementation in practice. Also, in recent times, there has been a tremendous need for the thorough statistical analysis of the so-called Accelerated Life Tests (ALT) experiments. Engineers are often interested in investigation of the pattern of the technological lives of certain test equipment which are in general immune to normal circumstances and subject them to more stressed situation to assess their failure mechanism under higher stress. Useful tools have been provided in this research for modeling such data. Practical data set, in appropriate contexts, indicate the presence of the so-called surviving fractions, the fraction of the population, which is immune to failure. Modeling of such data set has been a major part of the present thesis. Situations of proper and improper distributions, more specifically, improper mixture distributions are handled with appropriate data analysis. Finally, the situations where one is more likely to observe a non-ignorable change in the pattern of the failure rate or hazard function have also been investigated. Such models are typically called as Change-point hazard models. In the present research, we address single and multiple change point models with appropriate data analysis. All the computations in the present research were performed using Bayesian methods. MCMC methods were used to draw samples from intractable posterior distributions of the parameters. ^