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. Farrokh Alemi, Ph.D. Moving Range

4. Farrokh Alemi, Ph.D. Moving Range

5. Farrokh Alemi, Ph.D. Moving Range

6. Farrokh Alemi, Ph.D. Moving Range Most common approach

7. Which Chart is Right? Assumptions of XmR chart

8. Farrokh Alemi, Ph.D. 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. Farrokh Alemi, Ph.D. Selection of Time Period Pre-intervention

10. Farrokh Alemi, Ph.D. Selection of Time Period Pre-intervention

11. Farrokh Alemi, Ph.D. Calculate Average Moving Range for 2 Consecutive Values Average range   |X t - X t-1 | / (n-1) Absolute value of difference of two consecutive observations Number of observations Observation at time “t”

12. Farrokh Alemi, Ph.D. 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. Farrokh Alemi, Ph.D. E Depends on Number of Time Periods in the Range Typically we look at two consecutive periods

14. Farrokh Alemi, Ph.D. Example  Diabetes patient measured weight for 16 weeks  First 7 weeks were pre-intervention  Has the patient’s weight changed?

15. Farrokh Alemi, Ph.D. 1. Check Assumptions One observation per time period Interval scale Independent observations

16. Farrokh Alemi, Ph.D. 2. Select Pre- Or Post-Intervention Period Pre-intervention

17. Farrokh Alemi, Ph.D. Time period Weight in PoundsRange of 2 consecutive values 1199Not available 22012 31974 4 0 52003 61955 71932 8198 Not relevant to control limits from pre- intervention period 9196 10196 11193 12190 13194 14189 15185 16188 Average197.432.67 3. Calculation of Moving Range

18. Farrokh Alemi, Ph.D. =abs(B3-B2)

19. Farrokh Alemi, Ph.D. =Average(C3:C8)

20. Farrokh Alemi, Ph.D. =Average(B2:B8)

21. Farrokh Alemi, Ph.D. 4. Calculation of Control Limits  UCL = 197.43 + 2.66 * 2.67 = 204.52  LCL = 197.43 - 2.66 * 2.67 = 190.33

22. Farrokh Alemi, Ph.D. 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. Farrokh Alemi, Ph.D. 6. Interpret the Chart  Points outside the limits show real changes in outcomes of the process

24. Farrokh Alemi, Ph.D. 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