The Probability of an Out of Control Signal from Nelson’s Supplementary Zig-Zag Test
by
David Griffiths
University of Wollongong
Coauthors: Martin Bunder, Chandra Gulati, Takeo Onizawa

Nelson’s ‘supplementary runs’ tests are widely used to augment the standard ‘out of control’ test for an x-bar control chart, or a chart with individual values, to determine if any special causes exist. The fourth of Nelson’s tests gives an out of control signal when fourteen points in a row follow a zig-zag pattern (alternating up and down); it is thus a signal that a process has a negative autocorrelation. Using a recursive formula, the exact probability of a zig-zag sequence of length 14 is calculated for an in control process. This also allows the calculation of the exact probability for a zig-zag sequence of any length. Two curious properties, relating the probabilities of zig-zag sequences of successive lengths, are demonstrated, and also illustrate the inherent beauty of mathematics and the ubiquity of pi.

Date received: November 20, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caim-02.