The probability of an out of control signal from Nelson's supplementary zig-zag test

Authors

David Griffiths, University of WollongongFollow
Martin Bunder, University of WollongongFollow
Chandra Gulati, University of WollongongFollow
Takeo Onizawa, University of Wollongong

RIS ID

34720

Publication Details

Griffiths, D., Bunder, M. W., Gulati, C. M. & Onizawa, T. (2010). The probability of an out of control signal from Nelson's supplementary zig-zag test. Journal of Statistical Theory and Practice, 4 (4), 609-615.

Abstract

Nelson's ‘supplementary runs’ tests are widely used to augment the standard ‘out of control’ test for an [xbar] 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 the process has negative autocorrelation. Using a recursive formula, die exact probability of a zig-zag sequence of length 14 is calculated for an in control process. This value does not appear in the SQC literature, but can be simply determined from results of André (1879, 1881, 1883). rediscovered by Entringer (1966), which long precede the development of SQC. Two curious properties, relating die probabilities of zig-zag sequences of successive lengths, are also demonstrated.