ATTRIVAR: Optimized control charts to monitor process mean with lower operational cost

Usually attribute control charts present lower costs (operational and implementation) than variable control charts, although they are less efficient at detecting process shifts. This paper's aim is to propose two new control charts that are a mixture of attribute and variable charts, namely, ATTRIVAR 1 and 2 (ATTRIbutes+VARiables), to monitor the process mean. These ATTRIVAR charts have a performance similar to the X̅ chart with the benefits of an attribute control chart. The process control begins by employing an attribute chart. Each sampled unit is classified as approved or rejected, normally using a go-no go gauge. However, the gauge's classification of a unit as rejected does not mean that the unit is non-conforming. If the number of items classified as rejected is equal to or greater than the control limit, then an out-of-control signal is triggered. Alternatively, if the number of rejected items is lower than the control limit but equal to or greater than a warning limit, then the units of the current sample (ATTRIVAR-1 version) or the units of the next sample (ATTRIVAR-2 version) are measured (numeric information is taken) and their average value, X̅, is calculated. If X̅ is not in the control limit region, then the process is considered out of control. The parameters of these new control charts are optimized using genetic algorithms both to match a required in-control average run length(ARL) and to minimize the out-of-control ARL for a given mean shift, also optimizing the gauge dimensions. The optimized ATTRIVAR-1 control chart performs in a manner similar to Shewhart's control chart, although the percentage of times that the variables are measured to compute X̅ is relatively low. Therefore, performance in terms of ARL is equivalent, but with a much lower operational cost. A numerical example illustrates the current proposal.