To monitor the nonconforming fraction of a production process, usually np or p control charts are used for this purpose. However, in many practical situations, the binary variables are correlated but not easily perceived by practitioners. The aim of this article is to present the maximum likelihood and method of moment estimators of the correlation parameter ρ of an overdispersed binomial distribution. Inferential procedure is also introduced to test the null hypothesis H0: ρ = 0 x H1: ρ > 0. A Shewhart‐type control chart np ρ and an Exponentiated Weighted Moving Average (EWMA)‐type control chart (EWMA np ρ ) are proposed to evaluate the nonconforming fraction when the binary variables are correlated. The traditional np chart is a particular case of the np ρ control chart when ρ = 0. The misuse of control limits of np control in case of correlated binary variables will result a large number of false alarms. To have the same performance (in terms of average run length) of the traditional np control chart, the np ρ control chart needs at least to double the sample size. Numerical example illustrates the proposal. Copyright © 2012 John Wiley & Sons, Ltd.