Chart Preparation Exercise (9)

Next we can move on to the control limits themselves. The second section of your calculation sheet contains boxes to calculate 3 standard deviations (3s) for the process, and also the upper control limit for the moving range chart (UCL R). Note that you don't need to calculate a lower control limit for the moving range graph, because it will always be 0.

The first value (3s) is used in calculating both the upper and lower control limits for the X graph. We can calculate this value by using the constant d2 and the mean range. The actual calculation is 3/d2 × R-bar.

The value of control chart constants, like d2 changes depending on the size of the subgroups you are using. However in the case of XmR charts, the size of the subgroups is always 2, which means that the value of d2 is always going to be 1.128. This means that the result of 3/d2 will always be 2.66. This figure has already been entered in the first box in the section. The second box contains the value of R-bar which you calculated earlier.

Complete the calculation for 3s and enter your answer in the box outlined in red below. Since this is an intermediate result, for use in later calculations, it should not be rounded here. When you have done this, click the button to check your answer.

SUM X No. of Samples X-bar
÷ =
 
SUM R No. of Samples
(Minus one)
R-bar
÷ =
3/d2 R-bar 3s
× =
 
D4 R-bar UCL R
× =