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XmR Chart. Farrokh Alemi, Ph.D. Purpose of Control Chart. Real or random. Tell a story of changes in outcomes of the process. Moving Range. Moving Range. Moving Range. Moving Range. Most common approach. Which Chart is Right?. Assumptions of XmR chart. Assumptions.

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Xmr chart

XmR Chart

Farrokh Alemi, Ph.D.


Purpose of control chart
Purpose of Control Chart

  • Real or random.

  • Tell a story of changes in outcomes of the process.

Farrokh Alemi, Ph.D.


Moving range
Moving Range

Farrokh Alemi, Ph.D.


Moving range1
Moving Range

Farrokh Alemi, Ph.D.


Moving range2
Moving Range

Farrokh Alemi, Ph.D.


Moving range3
Moving Range

Most common

approach

Farrokh Alemi, Ph.D.


Which chart is right
Which Chart is Right?

Assumptions of XmR chart


Assumptions
Assumptions

  • There is one observation per time period

  • Observations are measured in an “interval” scale

  • Observations are independent of each other

Farrokh Alemi, Ph.D.


Selection of time period
Selection of Time Period

Pre-intervention

Farrokh Alemi, Ph.D.


Selection of time period1

Pre-intervention

Selection of Time Period

Farrokh Alemi, Ph.D.


Calculate average moving range for 2 consecutive values

Number of observations

Observation at time “t”

Absolute value of difference of two consecutive observations

Calculate Average Moving Range for 2 Consecutive Values

Farrokh Alemi, Ph.D.


Formula for calculating upper and lower control limits
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

E Depends on Number of Time Periods in the Range

Farrokh Alemi, Ph.D.


Example
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
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

2. Select Pre- Or Post-Intervention Period

Farrokh Alemi, Ph.D.


3 calculation of moving range
3. Calculation of Moving Range

Farrokh Alemi, Ph.D.


Xmr chart

=abs(B3-B2)

Farrokh Alemi, Ph.D.


Xmr chart

=Average(C3:C8)

Farrokh Alemi, Ph.D.


Xmr chart

=Average(B2:B8)

Farrokh Alemi, Ph.D.


4 calculation of control limits
4. Calculation of Control Limits

  • UCL = 197.43 + 2.66 * 2.67 = 204.52

  • LCL = 197.43  - 2.66 * 2.67 = 190.33

Farrokh Alemi, Ph.D.


5 plot the control chart
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
6. Interpret the Chart

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

Farrokh Alemi, Ph.D.


7 distribute the chart
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

Farrokh Alemi, Ph.D.


Take home lesson

Take Home Lesson

How and When to Construct an XmR chart