XmR Chart Farrokh Alemi, Ph.D.

Purpose of Control Chart  Real or random.  Tell a story of changes in outcomes of the process.

Farrokh Alemi, Ph.D. Moving Range

Farrokh Alemi, Ph.D. Moving Range

Farrokh Alemi, Ph.D. Moving Range

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

Which Chart is Right? Assumptions of XmR chart

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

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

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

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”

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

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

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

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

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

Farrokh Alemi, Ph.D. Time period Weight in PoundsRange of 2 consecutive values 1199Not available Not relevant to control limits from pre- intervention period Average Calculation of Moving Range

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

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

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

Farrokh Alemi, Ph.D. 4. Calculation of Control Limits  UCL = * 2.67 =  LCL = * 2.67 =

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

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

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

Take Home Lesson How and When to Construct an XmR chart