Continuity Adjustment for Control Charts for Attributes

A unified approach is proposed for making a continuity adjustment on some control charts for attributes, e.g., np-chart and c-chart, through adding a uniform (0, 1) random observation to the conventional sample statistic (e.g., and c _i ). The adjusted sample statistic then has a continuous distribution. Consequently, given any Type I risk α (the probability that the sample statistic is on or beyond the control limits), control charts achieving the exact value of α can be readily constructed. Guidelines are given for when to use the continuity adjustment control chart, the conventional Shewhart control chart (with ±3 standard deviations control limits), and the control chart based on the exact distribution of the sample statistic before adjustment. Partially supported by the Natural Science and Engineering Research Council of Canada and Research Grant Council of Hong Kong grants.