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.

Abstract not provided.

Abstract not provided.

Abstract not provided.

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.