Abstract Control charts for variables are a reference tool for the statistical monitoring of a quantitative variable. However, there are processes in which the exact measurement of the variable is highly complex or costly. In these cases, one option is to base the monitoring on the number of units that are classified by a gauge as being above, below, or between a pair of reference limits. With this approach, the process control achieves the economy and agility of control by attributes. In the literature, one can find different alternatives to such schemes. In this paper, a more general formulation is introduced that subsumes many of the previously proposed schemes into a new control scheme by means of an additional parameter. Through a specially designed optimization procedure, it is possible to obtain the parameters that maximize the scheme's performance against a specified process shift.