Choosing parameter values for a geometric CUSUM chart for detecting an upward shift in a proportion

This article considers the task of providing practical advice to quality engineers and practitioners on the choice of values for the two parameters of a geometric CUSUM control chart. This CUSUM chart was developed to enable the detection of sudden shifts from an acceptable level for a proportion (<i>p</i>) such as fraction nonconforming. In the first part of the article, tables are presented listing recommended parameter-choices for each of 18 in-control levels for <i>p</i> in the range (0.04 to 0.001) for detection of each of five sizes of upward shift. In the second part of the article, some empirical relationships among the parameter values are identified. These relationships are used with interpolation to design geometric CUSUM schemes for any in-control level (<i>p_a</i>) of <i>p</i> within the range covered by the tables, and with extrapolation for levels of <i>p_a</i> as low as 0.0001. Because of the equivalence between a geometric CUSUM and a Bernoulli CUSUM, the tables and the proposed methods of interpolation and extrapolation also provide assistance in the design of a Bernoulli CUSUM chart.