XmR Chart

1
XmR Chart

• Farrokh Alemi, Ph.D.

2
Purpose of Control Chart

• Real or random.
• Tell a story of changes in outcomes of the
  process.

3
Moving Range
4
Moving Range
5
Moving Range
6
Moving Range
Most common approach
7
Which Chart is Right?
Assumptions of XmR chart
8
Assumptions

1. There is one observation per time period
2. Observations are measured in an interval scale
3. Observations are independent of each other

9
Selection of Time Period
Pre-intervention
10
Selection of Time Period
11
Calculate Average Moving Range for 2 Consecutive
Values
Average range å Xt - Xt-1 / (n-1)
12
Formula for Calculating Upper and Lower Control
Limits

• Upper Control Limit Average of observations
  E Average of moving range
• Lower Control Limit Average of observations -
  E Average of moving range

13
E Depends on Number of Time Periods in the Range
14
Example

• Diabetes patient measured weight for 16 weeks
• First 7 weeks were pre-intervention
• Has the patients weight changed?

15
1. Check Assumptions

• One observation per time period
• Interval scale
• Independent observations

16
2. Select Pre- Or Post-Intervention Period
17
3. Calculation of Moving Range
Time period Weight in Pounds Range of 2 consecutive values
1 199 Not available
2 201 2
3 197 4
4 197 0
5 200 3
6 195 5
7 193 2
8 198 Not relevant to control limits from pre-intervention period
9 196 Not relevant to control limits from pre-intervention period
10 196 Not relevant to control limits from pre-intervention period
11 193 Not relevant to control limits from pre-intervention period
12 190 Not relevant to control limits from pre-intervention period
13 194 Not relevant to control limits from pre-intervention period
14 189 Not relevant to control limits from pre-intervention period
15 185 Not relevant to control limits from pre-intervention period
16 188 Not relevant to control limits from pre-intervention period
Average 197.43 2.67
18
abs(B3-B2)
19
Average(C3C8)
20
Average(B2B8)
21
4. Calculation of Control Limits

• UCL 197.43 2.66 2.67 204.52
• LCL 197.43  - 2.66 2.67 190.33

22
5. Plot the Control Chart

• Plot the x and y axis, plot the observations
• Plot the limits as line with no marker
• Plot solid line for pre-intervention period

23
6. Interpret the Chart

• Points outside the limits show real changes in
  outcomes of the process

24
7. Distribute the Chart

• Distribute the chart by electronic media, as part
  of company newsletter, or as an element of a
  story board display
• Keep following in mind
• Show that you have verified assumptions
• Check that your chart is accurately labeled
• Include your interpretation of the finding

25
Take Home Lesson

• How and When to Construct an XmR chart