Publications

We develop a method for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which parsimoniously characterizes variability in the baseline data. Based on the proposed model, we define two different types of tolerance bounds that are able to measure both types of variability, and as a result, identify when the data has gone beyond the bounds of amplitude and/or phase. The first functional tolerance bounds are computed via a bootstrap procedure on the geometric space of amplitude and phase functions. The second functional tolerance bounds utilize functional Principal Component Analysis to construct a tolerance factor. This work is motivated by two main applications: process control and disease monitoring. The problem of statistical analysis and modeling of functional data in process control is important in determining when a production has moved beyond a baseline. Similarly, in biomedical applications, doctors use long, approximately periodic signals (such as the electrocardiogram) to diagnose and monitor diseases. In this context, it is desirable to identify abnormalities in these signals. We additionally consider a simulated example to assess our approach and compare it to two existing methods.

Accelerated testing is a form of testing commonly employed in industry, especially at Sandia National Laboratories, in order to extract information about product lifetime behavior that cannot be acquired under normal operating conditions due to the extensive durations of the intended life- times. As of the writing of this report, there is no known guideline for the design of accelerated tests at the laboratories and yet there is an entire field in the statistical literature on the optimal design of accelerated tests covering a wide range of limitations and constraints available for reference. A potential roadblock to incorporating this knowledge is the common difficulty at Sandia of having severely limited data available for such testing. Nearly all of the methodology presented in the statistical literature is based on asymptotic or large-sample theory and so may not be appropriate for the testing conditions present at Sandia. This report investigates optimal accelerated test plans derived based on small-sample or exact methodology for both a basic test setting as well as a more realistic setting and compares the resulting test plans to those derived based on the large- sample methodology from the literature. It is shown that the large-sample test plans are actually quite robust to the presence of limited data and are generally more flexible than the small-sample test plans.

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Many industrial products consist of multiple components that are necessary for system operation. There is an abundance of literature on modeling the lifetime of such components through competing risks models. During the life-cycle of a product, it is common for there to be incremental design changes to improve reliability, to reduce costs, or due to changes in availability of certain part numbers. These changes can affect product reliability but are often ignored in system lifetime modeling. By incorporating this information about changes in part numbers over time (information that is readily available in most production databases), better accuracy can be achieved in predicting time to failure, thus yielding more accurate field-failure predictions. This paper presents methods for estimating parameters and predictions for this generational model and a comparison with existing methods through the use of simulation. Our results indicate that the generational model has important practical advantages and outperforms the existing methods in predicting field failures. Copyright © 2016 John Wiley & Sons, Ltd.

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The purpose of this research is to describe and illustrate practical methods that can be used to construct tolerance bounds for a multivariate measurement associated with a covariate. These methods rely on principal components analysis and the parametric bootstap. The methods are illustrated with an example in which the vibration environment experienced by a test object being carried by an aircraft (known as captive carry) is characterized.