Box-chart: Combining x and S charts

Among the techniques that form the core of statistical process control (SPC), control charts are perhaps the most important and widely used tools. First developed by Shewhart (1925), the use of control charts has become standard practice in industrial applications. Although over the years other control charts have been developed, the variables control charts, xÅ and R (or xÅ and S), remain the most popular. These charts are used to monitor simultaneously both the process mean and process variability. The xÅ chart monitors changes in location, while the R (or S) chart monitors changes in spread or dispersion. The xÅ and R chart can identify special causes of variation while using relatively small sample sizes. Though the xÅ and R charts are easy to construct and easy to interpret, at times they `over react’ to variations. The xÅ and S charts, on the other hand, work well for larger sample sizes and estimate the variation more eYciently (Gitlow, 1995). Recent developments deviate from early ones, most notably on the emphasis placed on target values on simultaneously monitoring the process mean and process variability (Yeh & Lin, 1999). Control charts based on these target values help determine whether the existing process is capable of meeting the desirable standards. Furthermore, they also help management set realistic goals for the existing process. One must be cautious when interpreting control charts based on target values. Sample observations can still fall outside the control limits even though no special causes are present in the process, since the desirable standards may not be consistent with the process conditions. Time and resources might be wasted looking for special causes that actually do not exist. The focus of this paper is to develop new variable control charts which will maintain the ability to monitor simultaneously, on a single chart, the process mean and the process variability. First, the Shewhart xÅ and S charts are constructed using target values for a univariate process (Mitra, 1993). Next, the same data are used to construct the proposed chartÐ the box-chart. Then the performance of the box-chart is compared with the Shewhart xÅ and S charts.