|
Abstract:
|
The purpose of this paper is to describe and illustrate practical methods that can be used to construct tolerance bounds for a multivariate measurement. These methods rely on a version of principal components analysis and the bootstrap. 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. In this example, the dominant dimension extracted by principal components analysis is related to a measureable covariate (dynamic pressure). Utilizing this relationship, tolerance bounds are constructed that are specific to a target value of the covariate. The multivariate measurement (vibration amplitude) relates to an ordered index (frequency). However, the ordering of the multivariate response is not useful for constructing tolerance bounds due to the discontinuous nature of the vibration amplitude across the range of frequencies. Thus, the methods that are described here are simple and do not assume an underlying functional relationship of the response across the ordered index.
|
