Sample size determination for p-charts

Abstract

Two types of decision errors can be made when using a quality control chart for non-conforming units (p-chart). A Type I error occurs when the process is not out of control but a search for an assignable cause is performed unnecessarily. A Type II error occurs when the process is out of control but a search for an assignable cause is not performed. The probability of a Type I error is under direct control of the decision-maker while the probability of a Type II error depends, in part, on the sample size. A simple sample size formula is presented for determining the required sample size for a p-chart with specified probabilities of Type I and Type II errors.