Accelerated life tests (ALT) are appealing to practitioners seeking to maximize information gleaned from reliability studies, while navigating resource constraints due to time and specimen costs. A popular approach to accelerated life testing is to design test regimes such that experimental specimens are exposed to variable stress levels across time. Such ALT experiments allow the practitioner to observe lifetime behavior across various stress levels and infer product life at use conditions using a greater number of failures than would otherwise be observed with a constant stress experiment. The downside to accelerated life tests, however, particularly for those that utilize non-constant stress levels across time on test, is that the corresponding lifetime models are largely dependent upon assumptions pertaining to variant stress. Although these assumptions drive inference at product use conditions, little to no statistical methods exist for assessing their validity. One popular assumption that is prevalent in both literature and practice is the cumulative exposure model which assumes that, at a given time on test, specimen life is solely driven by the integrated stress history and that current lifetime behavior is path independent of the stress trajectory. This dissertation challenges such black box ALT modeling procedures and focuses on the cumulative exposure model in particular. For a simple strep-stress accelerated life test, using two constant stress levels across time on test, we propose a four-parameter Weibull lifetime model that utilizes a threshold parameter to account for the stress transition. To circumvent regularity conditions imposed by maximum likelihood procedures, we use median rank regression to fit and assess our lifetime model. We improve the model fit using a novel incorporation of desirability functions and ultimately evaluate our proposed methods using an extensive simulation study. Finally, we provide an illustrative example to highlight the implementation of our method, comparing it to a corresponding Bayesian analysis. / Ph. D. / Have you ever wondered how manufacturers determine the guaranteed lifetime warranty for the products they produce? From automotive showrooms to store shelves, consumer goods often have a unique story to tell, one involving meticulous research, engineered design, and statistically driven testing. This is the realm of accelerated life testing (ALT) where reliability engineers, in their e↵orts to estimate overall product life, subject test specimens to harsher conditions than what are expected under normal operating conditions. Ideally, ALT experiments will induce multiple failures in a short amount of time and provide a basis for statistical modeling to predict failure in the field. The problem with this, however, is that such experiments require many mathematical assumptions which describe the physics of failure. This dissertation challenges one of the most common assumptions used for ALT experiments when specimens are exposed to multiple stress levels. We develop an alternative approach to the analysis of ALT data which drops this assumption (referred to as cumulative exposure) and explore the statistical properties of our method. We find that our approach has many features which will appeal to practitioners who may wish to use our procedures as they seek to understand the data gleaned from ALT experiments. Overall, this work represents an important addition to the reliability practitioner’s toolbox and will allow researchers to avoid potentially dubious assumptions concerning real world behavior.
| Identifer | oai:union.ndltd.org:VTETD/oai:vtechworks.lib.vt.edu:10919/73362 |
| Date | 01 November 2016 |
| Creators | Rhodes, Austin James |
| Contributors | Statistics, Vining, Gordon G., Parker, Peter A., Driscoll, Anne R., Hong, Yili |
| Publisher | Virginia Tech |
| Source Sets | Virginia Tech Theses and Dissertation |
| Detected Language | English |
| Type | Dissertation |
| Format | ETD, application/pdf |
| Rights | In Copyright, http://rightsstatements.org/vocab/InC/1.0/ |
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