Table of Contents
International Journal of Quality, Statistics, and Reliability
Volume 2009, Article ID 126283, 8 pages
Research Article

Tolerance Intervals in a Heteroscedastic Linear Regression Context with Applications to Aerospace Equipment Surveillance

1Reed Institute for Applied Statistics, Claremont McKenna College, Claremont, CA 91711, USA
2Department of Statistics, University of California, Riverside, CA 92521, USA
3Mathematical Research and Analysis Corporation, Claremont, CA 91711, USA

Received 1 June 2009; Revised 12 October 2009; Accepted 18 December 2009

Academic Editor: Satish Bukkapatnam

Copyright © 2009 Janet Myhre et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A heteroscedastic linear regression model is developed from plausible assumptions that describe the time evolution of performance metrics for equipment. The inherited motivation for the related weighted least squares analysis of the model is an essential and attractive selling point to engineers with interest in equipment surveillance methodologies. A simple test for the significance of the heteroscedasticity suggested by a data set is derived and a simulation study is used to evaluate the power of the test and compare it with several other applicable tests that were designed under different contexts. Tolerance intervals within the context of the model are derived, thus generalizing well-known tolerance intervals for ordinary least squares regression. Use of the model and its associated analyses is illustrated with an aerospace application where hundreds of electronic components are continuously monitored by an automated system that flags components that are suspected of unusual degradation patterns.