The second limit that we will create is called the lower control limit (LCL).

The formula for the lower control limit is:

LCL = X-avg - 2.66 x mR-Avg

From Table 12.2, we see that the running record average (X-Avg) is equal to 9.22. Therefore the UCL = 9.22 + 2.66 x 42.70 = 122.80. And the LCL = 9.22 - 2.66 x 42.70 = -104.36.

Because the UCL, LCL and X-Avg add meaningful information to any running record, we call the resulting chart an “X-Chart.” We display the X-chart in Figure 12.4.

Figure 12.4

On Figure 12.4, the top green line is the UCL, the bottom violet line is the LCL and the red line is X-Avg .

We can clearly see that there are no values outside the X-chart limits. We don’t have to guess. It is very visible. And it is to be expected because we are dealing with computer-perfect play.

In other words, under the controlled conditions, there is no abnormal variation.

The limits let us know that under the specified conditions, we should never have a win exceeding 122.80 units.

If we do have an win that exceeds 122.80 units over an 8-shoe Trial, then there is definite reason to suspect a “special cause.”

 © 2009 Norman Wattenberger