In this study, the variance of mean fraction nonconformance under the exact lot quality distribution with first order dependence is examined. The extent of the validity of binomial assumption with respect to the exact distribution in constructing the p-charts for dependent production processes is investigated and it is shown that neglect of dependence for small lot sizes may cause bias in the width of the area between the control limits. An approximate lot quality distribution with great versatility is proposed and is used for correcting the bias due to dependence in p-charts.