Start of excerpt from Dynamic Blackjack
Steps required to determine abnormal variation
The following step-by-step procedure is used to detect abnormal variation from amongst all the normal variation.
|
Trial |
Payoff |
|
1 |
- |
|
2 |
30.08 |
|
3 |
64.97 |
|
4 |
54.94 |
|
5 |
7.82 |
|
6 |
48.30 |
|
7 |
20.56 |
|
8 |
38.41 |
|
9 |
53.13 |
|
10 |
76.70 |
|
11 |
42.19 |
|
12 |
37.89 |
|
13 |
51.56 |
|
14 |
55.07 |
|
15 |
16.15 |
|
mR_avg |
42.70 |
|
Table 12.3 |
|
Ø 1. Determine the moving range (mR)
Ø 2. Create an mR chart
Ø 3. Determine the average moving range (mR-Avg) and plot it on the mR chart
Ø 4. Determine the upper range limit (URL) and plot it on the mR chart
Ø 5. Plot the data points on an X-chart
Ø 6. Determine the upper control limit (UCL) and plot it on the X-chart
Ø 7. Determine the lower control limit (LCL) and plot it on the X-chart
Ø 8. Determine the sigma one and sigma two lines and plot them on the X-chart
Ø 9. Call the combination of X-chart and mR chart an XmR chart
Ø 10. Check the XmR chart for each of the eleven signals that will warn you of abnormal variation
Determining the moving range
One begins the procedure by determining a moving range. To determine the moving range, we first measure the “trial to trial” variation, and calculate the difference between the successive values.
For example, the moving range of 30.08 in Trial 2 of Table 12.3 is determined by finding the absolute value of the difference between the Trial 1 and Trial 2 payoffs from table 12.2.
In like manner, the moving range of 64.97 in Trial 3 of Table 12.3 is determined by finding the absolute value of the difference between the Trial 2 and Trial 3 payoffs from Table 12.2.
And so it goes. For all 15 values from Table 12.2, I show the moving ranges in Table 12.3 and their average (mR-Avg).
© 2009 Norman Wattenberger
