Date of Award

Fall 2012

Degree Type

Thesis

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics and Statistics

Supervisor

N. Balakrishnan

Language

English

Abstract

In this thesis, inferential methods for one-shot device testing data from accelerated life-test are developed. Due to constraints on time and budget, accelerated life-tests are commonly used to induce more failures within a reasonable amount of test-time for obtaining more lifetime information that will be especially useful in reliability analysis. One-shot devices, which can be used only once as they get destroyed immediately after testing, yield observations only on their condition and not on their real lifetimes. So, only binary response data are observed from an one-shot device testing experiment. Since no failure times of units are observed, we use the EM algorithm for determining the maximum likelihood estimates of the model parameters. Also, inference for the reliability at a mission time and the mean lifetime at normal operating conditions are also developed.

The thesis proceeds as follows. Chapter 2 considers the exponential distribution with single-stress relationship and develops inferential methods for the model parameters, the reliability and the mean lifetime. The results obtained by the EM algorithm are compared with those obtained from the Bayesian approach. A one-shot device testing data is analyzed by the proposed method and presented as an illustrative example. Next, in Chapter 3, the exponential distribution with multiple-stress relationship is considered and corresponding inferential results are developed. Jackknife technique is described for the bias reduction in the developed estimates. Interval estimation for the reliability and the mean lifetime are also discussed based on observed information matrix, jackknife technique, parametric bootstrap method, and transformation technique. Again, we present an example to illustrate all the inferential methods developed in this chapter. Chapter 4 considers the point and interval estimation for the one-shot device testing data under the Weibull distribution with multiple-stress relationship and illustrates the application of the proposed methods in a study involving the development of tumors in mice with respect to risk factors such as sex, strain of offspring, and dose effects of benzidine dihydrochloride. A Monte Carlo simulation study is also carried out to evaluate the performance of the EM estimates for different levels of reliability and different sample sizes. Chapter 5 describes a general algorithm for the determination of the optimal design of an accelerated life-test plan for one-shot device testing experiment. It is based on the asymptotic variance of the estimated reliability at a specific mission time. A numerical example is presented to illustrate the application of the algorithm. Finally, Chapter 6 presents some concluding remarks and some additional research problems that would be of interest for further study.

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