XmR Chart

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XmR Chart

• Farrokh Alemi, Ph.D.

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Purpose of Control Chart

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

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Moving Range
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Moving Range
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Moving Range
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Moving Range
Most common approach
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Which Chart is Right?
Assumptions of XmR chart
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Assumptions

• There is one observation per time period
• Observations are measured in an interval scale
• Observations are independent of each other

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Selection of Time Period
Pre-intervention
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Selection of Time Period
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Calculate Average Moving Range for 2 Consecutive
Values
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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

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E Depends on Number of Time Periods in the Range
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Example

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

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1. Check Assumptions

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

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2. Select Pre- Or Post-Intervention Period
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3. Calculation of Moving Range
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abs(B3-B2)
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Average(C3C8)
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Average(B2B8)
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4. Calculation of Control Limits

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

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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

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6. Interpret the Chart

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

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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

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Take Home Lesson

• How and When to Construct an XmR chart