SPC Q Charts for a Binomial Parameter p: Short or Long Runs


Quesenberry, Charles   (1991, ASQC)   North Carolina State University

Journal of Quality Technology    Vol. 23    No. 3
QICID: 11316    July 1991    pp. 239-246
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Article Abstract

Approximately normalized control charts, called Q charts, are proposed for charting a binomial random variable. Transformations are given for the two cases when the parameter p is known before charting is begun and when it is not known before charting is begun. These charts permit real-time charting essentially from the beginning of sampling and are especially useful for the case when p is not known in advance. These charts are all plotted in a standard normal scale and permit a flexible chart management program. For the case when p is assumed known, we present a table to compare the closeness of the control probabilities for these Q charts with those of the approximating normal distribution, and with those achieved by either classical 3-sigma p charts or with charts based on a standardized arcsin transformation chart. These results show that Q charts give better approximations than the classical p charts to the nominal normal probabilities, and are comparable with, but differ from, the arcsin charts.


Control charts,Statistics,Short runs

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