Control Limits for p Control Charts With Small Subgroup Sizes

The p chart is widely used in health care and other service organizations as well as in manufacturing to monitor the proportion of observations with some particular characteristic for comparing several sources of data or for tracking a single source of data over time. The conventional approach is to use 3sigma limits found by using the normal approximation to the binomial distribution. This article reviews a method for taking into account the fact that 3sigma limits are not always appropriate, and suggests the use of the exact binomial distribution instead of the normal approximation to eliminate the problems associated with small subgroups. An example with only 4 small subgroups shows that the use of probability control limits and of modified control limits avoids the above problems.