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Duncan Miller MBChB FRCA
Anaesthesia Registrar
Former QI fellow
Variation and Basic Queue Theory
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Topics
• Variation
• Basics of queue theory
• Practical examples
• Gantt Charts
• Other Variation Concepts
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Variation
Duncan Miller
Duncstable
Dunc
‘Intended Variation’
Daniel
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Intended
and
Unintended Variation
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Sir Ronald
Fisher
(1890 - 1962)
William Sealy
Gosset
(1876 - 1937)
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Walter
Shewhart
(1891 – 1967)
W. Edwards
Deming
(1900 - 1993)
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Common Cause Variation
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Shewhart’s Theory of Variation
• Common Causes—those causes inherent in the system over time, affect everyone working in the system, and affect all outcomes of the system
•Chance cause
•Stable process
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Common Cause Variation
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Shewhart’s Theory of Variation
• Special Causes—those causes not part of the system all the time or do not affect everyone, but arise because of specific circumstances
• Assignable cause
• Unstable process
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0
20
40
60
80
100
120
Consecutive trips
Min.
Special Cause - My trip to work
Mean
Upper process limit
Lower process limit
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RULE 1 – THE OUTLIER
Point above Upper Control Limit (UCL)
MEAN
LCL
UCL
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Or point below Lower Control Limit (LCL)
RULE 1 – THE OUTLIER
MEAN
LCL
UCL
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MEAN
Eight points above centre line
RULE 2 – THE SHIFT
LCL
UCL
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MEAN
RULE 2 – THE SHIFT
LCL
UCL Or eight points below centre line
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MEAN
Six points in a downward direction
RULE 3 – THE TREND
LCL
UCL
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MEAN
RULE 3 – THE TREND
LCL
Or six points in an upward direction
UCL
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Considerably less than 2/3 of all the points fall in this zone
LCL
UCL
RULE 4 – ALL ON THE EDGE
MEAN
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RULE 4 – ALL IN THE MIDDLE
Or considerably more than 2/3 of all the points fall in this zone
MEAN
UCL
LCL
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Variation – what to do?
21
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Common Cause
Variation
Reduce variation: Increase precision -
make the process even more reliable.
Not satisfied with performance
(average): Redesign process to get a better result.
Special Cause
Variation
Root cause analysis: If Desirable: Maximise, optimise, replicate,
standardise.
If Undesirable: Minimise, eliminate.
22
Responding to Variation
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Variation and Queues
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“If I had to reduce my message for management to just a few words, I’d say it all had to do with reducing variation.” W. Edwards Deming
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Variation & Queues
Consecutive Patients
Pro
cedure
Tim
e (
Min
ute
s)
50%
100% 80%
80% rule is the most efficient balancing waiting and waste
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Erlangs rule of thumb
Jan 1878 - Feb 1929
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Calculating the 80% rule
80% Rule = Variation x 0.8 + Lowest Value
(Variation = High Value – Low Value)
•Variation = 23 – 7 = 16
•16 x 0.8 = 12.8
•12.8 + 7 (Low value) = 19.8
•19.8 (approx. 20min)
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Plan Cycle Time = 20m
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Role Cycle Time at
80%
Lung Function 15m
Weight & Nurse 10m
Dietician 20m
Dr 20m
Others 15m
Cycle time at 80% - PDSA 1 M
ore
Variable
More
Relia
ble
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1.15 1.30 2.00 2.30 3.00 3.30 4.00 4.30 5.00
Patient 1L L L W N D D D D Dr Dr Dr Dr O O O
Patient 2L L L W N D D D D Dr Dr Dr Dr O O O
Patient 3L L L W N D D D D Dr Dr Dr Dr O O O
Patient 4L L L W N D D D D Dr Dr Dr Dr O O O
Patient 5L L L W N D D D D Dr Dr Dr Dr O O O
Patient 6L L L W N D D D D Dr Dr Dr Dr O O O
Patient 7L L L W N D D D D Dr Dr Dr Dr O O O
Patient 8L L L W N D D D D Dr Dr Dr Dr O O O
Patient 9L L L W N D D D D Dr Dr Dr Dr O O O
Patient 10L L L W N D D D D Dr Dr Dr Dr O O O
Patient 11L L L W N D D D D Dr Dr Dr Dr O O O
Patient 12L L L W N D D D D Dr Dr Dr Dr O O O
Patient 13L L L W N D D D D Dr Dr Dr Dr O O O
Patient 14L L L W N D D D D Dr Dr Dr Dr O O O
Patient 15L L L W N D D D D Dr Dr Dr Dr O O O
Patient 16L L L W N D D D D Dr Dr Dr Dr O O O
Patient 17L L L W N D D D D Dr Dr Dr Dr O O O
Patient 18L L L W N D D D D Dr Dr Dr Dr O O O
1.15 1.30 2.00 2.30 3.00 3.30 4.00 4.30 5.00
Patient 1L L L W N D D D D Dr Dr Dr Dr O O O
Patient 2L L L W N D D D D Dr Dr Dr Dr O O O
Patient 3L L L W N D D D D Dr Dr Dr Dr O O O
Patient 4L L L W N D D D D Dr Dr Dr Dr O O O
Patient 5L L L W N D D D D Dr Dr Dr Dr O O O
Patient 6L L L W N D D D D Dr Dr Dr Dr O O O
Patient 7L L L W N D D D D Dr Dr Dr Dr O O O
Patient 8L L L W N D D D D Dr Dr Dr Dr O O O
Patient 9L L L W N D D D D Dr Dr Dr Dr O O O
Patient 10L L L W N D D D D Dr Dr Dr Dr O O O
Patient 11L L L W N D D D D Dr Dr Dr Dr O O O
Patient 12L L L W N D D D D Dr Dr Dr Dr O O O
Patient 13L L L W N D D D D Dr Dr Dr Dr O O O
Patient 14L L L W N D D D D Dr Dr Dr Dr O O O
Patient 15L L L W N D D D D Dr Dr Dr Dr O O O
Patient 16L L L W N D D D D Dr Dr Dr Dr O O O
Patient 17L L L W N D D D D Dr Dr Dr Dr O O O
Patient 18L L L W N D D D D Dr Dr Dr Dr O O O
1.15 1.30 2.00 2.30 3.00 3.30 4.00 4.30 5.00
Patient 1L L L W N D D D D Dr Dr Dr Dr O O O
Patient 2L L L W N D D D D Dr Dr Dr Dr O O O
Patient 3L L L W N D D D D Dr Dr Dr Dr O O O
Patient 4L L L W N D D D D Dr Dr Dr Dr O O O
Patient 5L L L W N D D D D Dr Dr Dr Dr O O O
Patient 6L L L W N D D D D Dr Dr Dr Dr O O O
Patient 7L L L W N D D D D Dr Dr Dr Dr O O O
Patient 8L L L W N D D D D Dr Dr Dr Dr O O O
Patient 9L L L W N D D D D Dr Dr Dr Dr O O O
Patient 10L L L W N D D D D Dr Dr Dr Dr O O O
Patient 11L L L W N D D D D Dr Dr Dr Dr O O O
Patient 12L L L W N D D D D Dr Dr Dr Dr O O O
Patient 13L L L W N D D D D Dr Dr Dr Dr O O O
Patient 14L L L W N D D D D Dr Dr Dr Dr O O O
Patient 15L L L W N D D D D Dr Dr Dr Dr O O O
Patient 16L L L W N D D D D Dr Dr Dr Dr O O O
Patient 17L L L W N D D D D Dr Dr Dr Dr O O O
Patient 18L L L W N D D D D Dr Dr Dr Dr O O O
1.15 1.30 2.00 2.30 3.00 3.30 4.00 4.30 5.00
Patient 1L L L W N D D D D Dr Dr Dr Dr O O O
Patient 2L L L W N D D D D Dr Dr Dr Dr O O O
Patient 3L L L W N D D D D Dr Dr Dr Dr O O O
Patient 4L L L W N D D D D Dr Dr Dr Dr O O O
Patient 5L L L W N D D D D Dr Dr Dr Dr O O O
Patient 6L L L W N D D D D Dr Dr Dr Dr O O O
Patient 7L L L W N D D D D Dr Dr Dr Dr O O O
Patient 8L L L W N D D D D Dr Dr Dr Dr O O O
Patient 9L L L W N D D D D Dr Dr Dr Dr O O O
Patient 10L L L W N D D D D Dr Dr Dr Dr O O O
Patient 11L L L W N D D D D Dr Dr Dr Dr O O O
Patient 12L L L W N D D D D Dr Dr Dr Dr O O O
Patient 13L L L W N D D D D Dr Dr Dr Dr O O O
Patient 14L L L W N D D D D Dr Dr Dr Dr O O O
Patient 15L L L W N D D D D Dr Dr Dr Dr O O O
Patient 16L L L W N D D D D Dr Dr Dr Dr O O O
Patient 17L L L W N D D D D Dr Dr Dr Dr O O O
Patient 18L L L W N D D D D Dr Dr Dr Dr O O O
PDSA - Plan
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PDSA - Plan
1.15 1.30 2.00 2.30 3.00 3.30 4.00 4.30 5.00
Patient 1L L L W N D D D D Dr Dr Dr Dr O O O
Patient 2L L L W N D D D D Dr Dr Dr Dr O O O
Patient 3L L L W N D D D D Dr Dr Dr Dr O O O
Patient 4L L L W N D D D D Dr Dr Dr Dr O O O
Patient 5L L L W N D D D D Dr Dr Dr Dr O O O
Patient 6L L L W N D D D D Dr Dr Dr Dr O O O
Patient 7L L L W N D D D D Dr Dr Dr Dr O O O
Patient 8L L L W N D D D D Dr Dr Dr Dr O O O
Patient 9L L L W N D D D D Dr Dr Dr Dr O O O
Patient 10L L L W N D D D D Dr Dr Dr Dr O O O
Patient 11L L L W N D D D D Dr Dr Dr Dr O O O
Patient 12L L L W N D D D D Dr Dr Dr Dr O O O
Patient 13L L L W N D D D D Dr Dr Dr Dr O O O
Patient 14L L L W N D D D D Dr Dr Dr Dr O O O
Patient 15L L L W N D D D D Dr Dr Dr Dr O O O
Patient 16L L L W N D D D D Dr Dr Dr Dr O O O
Patient 17L L L W N D D D D Dr Dr Dr Dr O O O
Patient 18L L L W N D D D D Dr Dr Dr Dr O O O
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PDSA – Do & Study
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Demand is increasing....
More slots needed...
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80% = 21mins
3hrs = 8 Patients
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80% = 21mins
3hrs = 8 Patients
80% = 18mins
3hrs = 10 Patients
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80% = 21mins
3hrs = 8 Patients
80% = 18mins
3hrs = 10 Patients
80% = 14mins
3hrs = 12 Patients
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HOW DO YOU REDUCE
COMMON CAUSE VARIATION?
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GSM
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More Queuing....
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Capacity required = 27
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Capacity required = 27
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Capacity required = 49
(5 beds less than separate units ~£400,000)
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46
5 15 35 150 500 1500
Dunbar’s Number
The maximum number of meaningful relationships a person can maintain
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Lung Cancer Clinic
47
13 + 11 = 24
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Lung Cancer - pooled
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And Finally - More Queuing....
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Which is best?
C Q
C Q
C Q
S
S
S
C Q
S
S
S
C Q C Q
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And Finally - Which is best?
C Q
Long
C Q
Short
S
S
C Q
Long
S
S
S
C Q
Short
C Q
Long
![Page 52: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts](https://reader033.vdocuments.mx/reader033/viewer/2022041417/5e1c354be054d465292d3153/html5/thumbnails/52.jpg)
DISCUSSION
![Page 53: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts](https://reader033.vdocuments.mx/reader033/viewer/2022041417/5e1c354be054d465292d3153/html5/thumbnails/53.jpg)
THANKS!