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Testing for sphericity in phase I control chart applications
Author(s) -
Windfeldt Gitte B.,
Bisgaard Søren
Publication year - 2009
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.1000
Subject(s) - sphericity , statistics , control chart , mathematics , statistical hypothesis testing , graph , chart , computer science , combinatorics , geometry , process (computing) , operating system
When using x̄–R charts it is a crucial assumption that the observations within samples are independent and have common variance. However, this assumption is almost never checked. We propose to use the samples gathered during the phase I study and the test for distributional sphericity, to check this assumption. We supply a graph of the exact percentage points for the distribution of the test statistics. The test statistics can be computed with standard statistical software. Together with the graph of the exact percentage points, the test can easily be performed during a phase I study. We illustrate the method with examples. Copyright © 2009 John Wiley & Sons, Ltd.