Monitoring the process mean with an ATTRIVAR chart

Abstract

In this article, we propose an ATTRIVAR chart to control the process mean. With the ATTRIVAR chart, the sampling is performed in two stages, collecting attribute and variable sample data from the same sample (attribute plus variable data – ATTRIVAR). That is, if the first m items of the sample fail to pass the go gauge test, or they pass the no-go gauge test, the sampling moves on to stage two, where the quality characteristic X of the first m and the remaining n-m items of the sample is measured. Otherwise, the sampling is interrupted and the process is declared to be in control. The number of tested items, if one, or two, or as many as m, is only known after the completion of the first stage. At the second stage, the $\overline{X}$ value is computed and used to decide the state of the process. It is worthwhile to stress that the go/no-go gauge test truncates the X distribution and, because of that, the mathematical development to obtain the $\overline{X}$ distribution is not trivial. The ATTRIVAR chart signals faster than the Double Sampling $\overline{X}$ chart and, more important than that, it is simpler to use because the go/no-go gauge test reduces the frequency with which the quality characteristic X of the sample items is measured. The ATTRIVAR chart is also faster and simpler than the mixed chart. With the mixed chart, the sampling is also performed in two stages; the difference is that all items of the sample are always submitted to the go/no-go gauge test before deciding to go to stage two, where the $\overline{X}$ value is computed.

Keywords:

• ATTRIVAR chart
• mixed chart
• attribute/variable-type inspections
• process mean