Continuity Adjustment for Control Charts for Attributes
Abstract
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.,
$$
n\hat{p}_{i}
$$
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.