Degree Type

Dissertation

Date of Award

2009

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

William Q. Meeker

Abstract

Accelerated life tests (ALTs) are often used to make timely assessments of the life time distribution of materials and components. The goal of many ALTs is estimation of a quantile of a log-location failure time distribution. Much of the previous work on planning accelerated life tests has focused on deriving test-planning methods under a specific log-location distribution. This thesis presents a new approach for computing approximate large-sample variances of maximum likelihood estimators of a quantile of general log-location distribution with censoring and time-varying stress based on a cumulative exposure model. This thesis also presents a strategy to develop useful test plans using a small number of test units.

We provide an approach to find optimum step-stress accelerated life test plans by using the large-sample approximate variance of the maximum likelihood estimator of a quantile of the failure time distribution at use conditions from a step-stress accelerated life test. In Chapter 2, we show this approach allows for multi-step stress changes and censoring for general log-location-scale distributions. As an application of this approach, the optimum variance is studied as a function of shape parameter for both Weibull and lognormal distributions. Graphical comparisons among test plans using step-up, step-down, and constant-stress patterns are also presented. The results show that, depending on the values of the model parameters and quantile of interest, each of the three test plans can be preferable in terms of optimum variance. In Chapter 3, using sample data from a published paper describing optimum ramp-stress test plans, we show that our approach and the one used in the previous work give the same variance-covariance matrix of the quantile estimator from the two different approaches. Then, as an application of this approach, we extend the previous work to a new optimum ramp-stress test plan obtained by simultaneously adjusting the ramp rate and the lower start level of stress. We find that the new optimum test plan can have smaller variances than that of the optimum ramp-stress test plan previously obtained by adjusting only the ramp rate. We also compare optimum ramp-stress test plans with the more commonly used constant-stress accelerated life test plans.

Previous work on planning accelerated life tests has been based on large-sample approximations to evaluate test plan properties. In Chapter 4, we use more accurate simulation methods to investigate the properties of accelerated life tests with small sample sizes where large-sample approximations might not be expected to be adequate. These properties include the simulated bias and variance for quantiles of the failure-time distribution at use conditions. We focus on using these methods to find practical compromise test plans that use three levels of stress. We also study the effects of not having any failures at test conditions and the effect of using incorrect planning values. We note that the large-sample approximate variance is far from adequate when the probability of zero failures at certain test conditions is not negligible. We suggest a strategy to develop useful test plans using a small number of test units while meeting constraints on the estimation precision and on the probability that there will be zero failures at one or more of the test stress levels.

Copyright Owner

Haiming Ma

Language

en

Date Available

2012-04-30

File Format

application/pdf

File Size

103 pages

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