Step-stress Accelerated life tests - Design and inference
Abstract
Accelerated Life Testing (ALT) is commonly used in industry to obtain reliability information in a timely manner. Various stress loading designs have been proposed and recent research interests have emerged concerning the development of statistical equivalent ALT plans. ALT plans are statistically equivalent if they have the same performance in some statistics. Depending on the statistics, there are several types of definition of statistical equivalency. Step-Stress ALT (SSALT) is a commonly used stress loadings because it usually shortens the test duration and reduces the number of required test units. This dissertation considers the design and statistical inference of SSALT. Questions that I try to answer include: (1) Can a SSALT be designed so that it is equivalent to other stress loadings? (2) When optimizing a multi-level SSALT, does the resulting plan degenerate to a simple SSALT using two most extreme stress levels? (3) The proof that two equivalent ALT plans must be equivalent in terms of the strongest version of equivalency for many objective functions. We address these questions in Chapters 2 and 3 assuming some commonly accepted model assumptions and provide formal proofs in our answer to each of the questions. Numerical examples are presented to apply the results for finding equivalent SSALT plans given in the literature. In addition, we use the minimax regret approach to obtain SSALT plans that are robust against lifetime distribution misspecification. Two possible lifetime distributions are considered, namely, the Weibull and lognormal distributions. Under the assumptions of cumulative exposure and Type-I censoring, the optimal simple SSALT plans are designed to minimize either the maximum of the asymptotic average bias or the maximum of the mean square error of estimated p-th percentile when the fitted distribution might not be the correct one. Such plans, although conservative, provide protection in the accuracy/precision of the resulting estimates from distribution misspecification. In Chapter 5, using data from a simple SSALT, a nonparametric proportional hazard rate model is proposed for obtaining upper confidence bounds for the cumulative failure probability of a product under normal use conditions. The approach is nonparametric in the sense that most of the functions involved in the model do not assume any specific forms, except for certain verifiable conditions. Test statistics are introduced to verify assumptions about the model and to test the goodness of fit of the proposed model to the data. A numerical example, using data simulated from the lifetime distribution of an existing parametric study on metal-oxide-semiconductor capacitors, is used to illustrate the proposed methodology.
Degree
Ph.D.
Advisors
Tang, Purdue University.
Subject Area
Industrial engineering
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