Testing for sphericity in phase I control chart applications

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.