Date of Award

Fall 1999

Project Type

Dissertation

Program or Major

Mathematics

Degree Name

Doctor of Philosophy

First Advisor

Debajyoti Sinha

Abstract

An accelerated life test (ALT) is often used to obtain timely information for highly reliable items. The increased use of ALTs has resulted in nontraditional reliability data which can not be analyzed with standard statistical methodologies. I propose new methods for analyzing ALT data for studies with (1) two independent populations, (2) paired samples and (3) limited failure populations (LFP). Here, the Weibull distribution, which can accommodate a variety of failure rates, is assumed for the models I develop. For case (1), a parametric hypothesis test, a Bayesian analysis and a test using partial likelihood are proposed and discussed. For paired samples, I show that there is no exact test for the equality of the survival distributions. Thus, several tests are investigated using a simulation study of their Type I errors. A Bayesian approach that allows for the comparison and estimation of the failure rates is also considered. For computation, Markov Chain Monte Carlo (MCMC) methods are implemented using BUGS.

Certain types of devices (such as integrated circuits) that are operated at normal use conditions are at risk of failure because of inherent manufacturing faults (latent risk factors). A small proportion of defective units, p, may fail over time under normal operating conditions. For the non-defective units, the probability of failing under normal conditions during their "technological lifetime" is zero. Meeker ([29], [31]) called a population of such units a limited failure population (LFP). I propose a new model for LFP in which the number of latent risk factors and the times at which they become fatal depend on the stress level. This model allows for a fraction of the population to be latent risk free. For analyzing this model, I propose a classical as well as a Bayesian approach, which can be very useful when an engineer has expert knowledge of the manufacturing process. In all cases, a real data set is analyzed to demonstrate my procedures.

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