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Page 1: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts
Page 2: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Duncan Miller MBChB FRCA

Anaesthesia Registrar

Former QI fellow

Variation and Basic Queue Theory

Page 3: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Topics

• Variation

• Basics of queue theory

• Practical examples

• Gantt Charts

• Other Variation Concepts

Page 4: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Variation

Duncan Miller

Duncstable

Dunc

‘Intended Variation’

Daniel

Page 5: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Intended

and

Unintended Variation

Page 6: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Sir Ronald

Fisher

(1890 - 1962)

William Sealy

Gosset

(1876 - 1937)

Page 7: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Walter

Shewhart

(1891 – 1967)

W. Edwards

Deming

(1900 - 1993)

Page 8: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Common Cause Variation

Page 9: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

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

Page 10: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Common Cause Variation

Page 11: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

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

Page 12: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

0

20

40

60

80

100

120

Consecutive trips

Min.

Special Cause - My trip to work

Mean

Upper process limit

Lower process limit

Page 13: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

RULE 1 – THE OUTLIER

Point above Upper Control Limit (UCL)

MEAN

LCL

UCL

Page 14: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Or point below Lower Control Limit (LCL)

RULE 1 – THE OUTLIER

MEAN

LCL

UCL

Page 15: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

MEAN

Eight points above centre line

RULE 2 – THE SHIFT

LCL

UCL

Page 16: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

MEAN

RULE 2 – THE SHIFT

LCL

UCL Or eight points below centre line

Page 17: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

MEAN

Six points in a downward direction

RULE 3 – THE TREND

LCL

UCL

Page 18: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

MEAN

RULE 3 – THE TREND

LCL

Or six points in an upward direction

UCL

Page 19: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Considerably less than 2/3 of all the points fall in this zone

LCL

UCL

RULE 4 – ALL ON THE EDGE

MEAN

Page 20: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

RULE 4 – ALL IN THE MIDDLE

Or considerably more than 2/3 of all the points fall in this zone

MEAN

UCL

LCL

Page 21: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Variation – what to do?

21

Page 22: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

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

Page 23: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Variation and Queues

Page 24: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

“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

Page 25: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Variation & Queues

Consecutive Patients

Pro

cedure

Tim

e (

Min

ute

s)

50%

100% 80%

80% rule is the most efficient balancing waiting and waste

Page 26: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Erlangs rule of thumb

Jan 1878 - Feb 1929

Page 27: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts
Page 28: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts
Page 29: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

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)

Page 30: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Plan Cycle Time = 20m

Page 31: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

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

Page 32: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

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

Page 33: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

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

Page 34: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

PDSA – Do & Study

Page 35: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Demand is increasing....

More slots needed...

Page 36: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

80% = 21mins

3hrs = 8 Patients

Page 37: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

80% = 21mins

3hrs = 8 Patients

80% = 18mins

3hrs = 10 Patients

Page 38: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

80% = 21mins

3hrs = 8 Patients

80% = 18mins

3hrs = 10 Patients

80% = 14mins

3hrs = 12 Patients

Page 39: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

HOW DO YOU REDUCE

COMMON CAUSE VARIATION?

Page 40: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

GSM

Page 41: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

More Queuing....

Page 42: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Capacity required = 27

Page 43: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Capacity required = 27

Page 44: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts
Page 45: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Capacity required = 49

(5 beds less than separate units ~£400,000)

Page 46: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

46

5 15 35 150 500 1500

Dunbar’s Number

The maximum number of meaningful relationships a person can maintain

Page 47: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Lung Cancer Clinic

47

13 + 11 = 24

Page 48: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Lung Cancer - pooled

Page 49: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

And Finally - More Queuing....

Page 50: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

Which is best?

C Q

C Q

C Q

S

S

S

C Q

S

S

S

C Q C Q

Page 51: Duncan Miller MBChB FRCA · Variation and Basic Queue Theory . Topics • Variation • Basics of queue theory • Practical examples • Gantt Charts • Other Variation Concepts

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

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

THANKS!