xmr chart farrokh alemi, ph.d.. purpose of control chart real or random. tell a story of changes...
TRANSCRIPT
XmR Chart
Farrokh Alemi, Ph.D.
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
Time period
Observed value
Difference of 2
consecutive values
1 1992 201 23 197 4 44 197 0 4 45 200 3 3 46 195 5 5 57 193 2 7 7
Farrokh Alemi, Ph.D.
Moving Range
Time period
Observed value
Difference of 2
consecutive values
Difference of 3
consecutive values
1 1992 201 23 197 4 44 197 0 4 45 200 3 3 46 195 5 5 57 193 2 7 7
Farrokh Alemi, Ph.D.
Moving Range
Time period
Observed value
Difference of 2
consecutive values
Difference of 3
consecutive values
Difference of 4
consecutive values
1 1992 201 23 197 4 44 197 0 4 45 200 3 3 46 195 5 5 57 193 2 7 7
Farrokh Alemi, Ph.D.
Moving Range
Time period
Observed value
Difference of 2
consecutive values
Difference of 3
consecutive values
Difference of 4
consecutive values
1 1992 201 23 197 4 44 197 0 4 45 200 3 3 46 195 5 5 57 193 2 7 7
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
175
180
185
190
195
200
205
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time
Ob
serv
atio
ns
Pre-intervention
Farrokh Alemi, Ph.D.
Selection of Time Period
175
180
185
190
195
200
205
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time
Ob
serv
atio
ns
Pre-intervention
Farrokh Alemi, Ph.D.
Calculate Average Moving Range for 2 Consecutive Values
Average range |Xt - Xt-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
Number of time
periods E values
Number of time
periods E values d2 values11 0.945
2 2.660 12 0.9213 1.772 13 0.8994 1.457 14 0.8815 1.290 15 0.8646 1.184 16 0.8497 1.109 17 0.8368 1.054 18 0.8249 1.010 19 0.81310 0.975 20 0.803
Based on Wheeler DJ. Advanced topics in statisical process control, 1995 SPC Press
Inc, Knoxville TN 37919
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
175
180
185
190
195
200
205
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time
Ob
serv
atio
ns
Pre-intervention
Farrokh Alemi, Ph.D.
Time periodWeight 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
10 196
11 193
12 190
13 194
14 189
15 185
16 188
Average 197.43 2.67
3. 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 = 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
Plot the x and y axis, plot the observations Plot the limits as line with no marker
– Plot solid line for pre-intervention period
175
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200
205
210
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time period
Po
un
ds Observations
UCL
LCL
Farrokh Alemi, Ph.D.
6. Interpret the Chart
Points outside the limits show real changes in outcomes of the process
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180
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205
210
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time period
Pou
nds
Observations
UCL
LCL
175
180
185
190
195
200
205
210
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time period
Pou
nds
Observations
UCL
LCL
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