12 montecarlo(bp) final
TRANSCRIPT
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 1/44
© 2001 ConceptFlow 1
Monte Carlo Analysis
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 2/44
© 2001 ConceptFlow 2
Objectives
By the end of this module, the participant will be able to:• Apply Monte Carlo analysis to business processes.
• Create a Monte Carlo analysis worksheet in MinitabTM.
• Conduct a Monte Carlo simulation using Minitab.
• Apply capability analysis to the output of a Monte Carlo analysis.
• Determine the proper centering and spread of the input variables to
achieve six sigmaTM capability in the output variable.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 3/44
© 2001 ConceptFlow 3
Why Use Monte Carlo Analysis?
Monte Carlo analysis can be used to:• Estimate the location of a response variable (Y)
• Estimate the variation of a response variable (Y)
• By using information from the input variables (Xs)
• Through use of the transfer function, Y = f(x)
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 4/44
© 2001 ConceptFlow 4
What Is Monte Carlo Analysis?
Monte Carlo analysis:• Generates approximate solutions
• To a variety of practical problems
• Using a computer to perform statistical sampling simulation
experiments.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 5/44
© 2001 ConceptFlow 5
Minitab Diversion
In order to perform Monte Carlo analysis efficiently in Minitab, it ishelpful to have Minitab automatically update the result column from a
formula. This allows the user to make modifications in the input values
and the output values will be updated without having to re-calculate the
formula.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 6/44
© 2001 ConceptFlow 6
Minitab: Auto Update of Columns
Minitab can automatically update columns by using the followingprocedure:
1. Selec t (highlight) the input data column headings
2. Choose Edit > Copy Cells
3. Choose Edit > Links > Manage Link s
4. Click Add
5. In Act ion , select Execute commands on ly (last in list)
6. In Commands , type the Y = f(X) formula (begin with Let): for
example: Let Y = X1 + X2
7. Click Add 8. In Manage Link s , click OK
9. The Y column will now automatically update.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 7/44© 2001 ConceptFlow 7
Minitab Auto Update Example
•
As a simple example to illustrate the automatic column update featureof Minitab, we will add two columns together and store the result in a
third column.
• Create a worksheet with input column headings as X1 and X2 and
output column heading as Y. The formula is Y = X1 + X2.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 8/44© 2001 ConceptFlow 8
Minitab Example Continued
1. Select (highlight) the input data column headingsIn the worksheet, highlight the X1 and X2 column headings
2. Choose Edit > Copy Cel ls
3. Choose Edit > Links > Manage Link s
4. Click Add
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 9/44© 2001 ConceptFlow 9
Minitab Example Continued
5. In Act ion , select Execute commands on ly (last in list)6. In Commands , type the Y = f(X) formula (begin with Let):
for example: Let Y = X1 + X2
7. Click Add
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 10/44© 2001 ConceptFlow 10
Minitab Example Continued
8. In Manage Links, click OK
9. The Y column will now automatically update.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 11/44© 2001 ConceptFlow 11
Monte Carlo Analysis Example
•
In order to illustrate the usefulness of Monte Carlo analysis, we willanalyze an order-entry through order-delivery system.
• Some questions to answer are
1. What is the average time to complete a client order?
2. What is the standard deviation of order completion?
3. What is the capability (in DPM) of the system?
4. What input characteristics are required for a six sigma process?
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 12/44© 2001 ConceptFlow 12
Monte Carlo Analysis Example
•
The requirement for total time from order entry through order deliveryis 14 days.
• There are five steps to the process:
1. Order entry
2. Manufacturing at site A
3. Ship to site B
4. Manufacturing at site B
5. Ship to client
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 13/44© 2001 ConceptFlow 13
Process Map for Example
Order
Entry
Mfg at
site A
Ship to
site B
Ship to
client
Mfg at
site B
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 14/44
© 2001 ConceptFlow 14
Data Summary of Process Steps
Data was collected at each process step with the sample
statistics (in days) recorded below:
Step Mean SD Min Max
Order Entry 1.2 0.1 0.9 1.5Mfg at Site A 3.3 0.3 2.4 4.2
Ship to Site B 2.1 0.2 1.5 2.7
Mfg at Site B 3.5 0.4 2.3 4.7
Ship to Client 2.8 0.3 1.9 3.7
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 15/44
© 2001 ConceptFlow 15
Example Continued
Create a worksheet with column headings:• S1 S2 S3 S4 S5 Y
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 16/44
© 2001 ConceptFlow 16
Example Continued
Generate 1000 Normal values for Step 1:• Calc > Random Data > Normal
• Use Mean = 1.2 and Std Dev = .1
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 17/44
© 2001 ConceptFlow 17
Example Continued
Generate 1000 Normal values for Step 2:• Calc > Random Data > Normal
• Use Mean = 3.3 and Std Dev = .3
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 18/44
© 2001 ConceptFlow 18
Example Continued
Generate 1000 Normal values for Step 3:• Calc > Random Data > Normal
• Use Mean = 2.1 and Std Dev = .2
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 19/44
© 2001 ConceptFlow 19
Example Continued
Generate 1000 Normal values for Step 4:• Calc > Random Data > Normal
• Use Mean = 3.5 and Std Dev = .4
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 20/44
© 2001 ConceptFlow 20
Example Continued
Generate 1000 Normal values for Step 5:• Calc > Random Data > Normal
• Use Mean = 2.8 and Std Dev = .3
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 21/44
© 2001 ConceptFlow 21
Example Continued
Set up the worksheet for automatic column updating:1. Select (highlight) the input data column headings
2. Choose Edit > Copy Cells
3. Choose Edit > Links > Manage Links
4. Click Add
5. In Act ion , select Execute commands on ly (last in list)
6. In Commands , type the Y = f(X) formula (begin with Let):
for example: Let Y = X1 + X2
7. Click Add
8. In Manage Link s , click OK 9. The Y column will now automatically update.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 22/44
© 2001 ConceptFlow 22
Example Continued
1. Select (highlight) the input data column headingsIn the worksheet, highlight the S1 S2 S3 S4 S5 column headings
2. Choose Edit > Copy Cel ls
3. Choose Edit > Links > Manage Link s
4. Click Add
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 23/44
© 2001 ConceptFlow 23
Example Continued
5. In Act ion , select Execute commands on ly (last in list)6. In Commands , type the Y = f(X) formula (begin with Let):
for example: Let Y = S1 + S2 + S3 + S4 + S5
7. Click Add
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 24/44
© 2001 ConceptFlow 24
Example Continued
8. In Manage Links, click OK
9. The Y column will now automatically update.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 25/44
© 2001 ConceptFlow 25
Example Continued
The worksheet should appear as below. The values will not be thesame – they are random.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 26/44
© 2001 ConceptFlow 26
Answering Questions
The first 3 questions can be answered using capability analysis:1. What is the average time to complete a client order?
2. What is the standard deviation of order completion?
3. What is the capability (in DPM) of the system?
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 27/44
© 2001 ConceptFlow 27
Capability Analysis
Stat > Quality Tools > Capability Analysis (Normal)
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 28/44
© 2001 ConceptFlow 28
Capability Analysis Output
The output from the Minitab capability analysis is
10 11 12 13 14 15 16
USLUSL
Process Capability Analysis for Y
USL
Target
LSLMean
Sample N
StDev (Within)
StDev (Overall)
Cp
CPU
CPLCpk
Cpm
Pp
PPU
PPL
Ppk
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
14.0000
*
*12.9067
1000
0.610514
0.610514
*
0.60
*0.60
*
*
0.60
*
0.60
*
28000.00
28000.00
*
36658.52
36658.52
*
36658.52
36658.52
Process Data
Potential (Within) Capability
Overall Capability Observed Performance Exp. "Within" Performance Exp. "Overall" Performance
Within
Overall
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 29/44
© 2001 ConceptFlow 29
Answering Questions 1, 2, 3
1. What is the average time to complete a client order?• Y average is 12.91 days.
2. What is the standard deviation of order completion?
• Y standard deviation is 0.61 days
3. What is the capability (in DPM) of the system?
• Y capability is 36,659 DPM
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 30/44
© 2001 ConceptFlow 30
Answering Question 4
4. What input characteristics are required for a six sigma process?• The are at least three ways to answer question 4:
1. Re-center the Step means
2. Reduce the Step standard deviations
3. Re-center the Step means and reduce the Step standard
deviations
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 31/44
© 2001 ConceptFlow 31
Answering Question 4 Continued
If the Step means are re-centered as follows, the capability is near 3.4DPM:
New Original
Step 1 1.0 1.2
Step 2 3.0 3.3
Step 3 2.0 2.1Step 4 3.0 3.5
Step 5 2.2 2.8
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 32/44
© 2001 ConceptFlow 32
Answering Question 4 Continued
8 9 10 11 12 13 14
USLUSL
Process Capability Analysis for Y
USL
Target
LSL
Mean
Sample NStDev (Within)
StDev (Overall)
Cp
CPU
CPL
Cpk
Cpm
Pp
PPU
PPL
Ppk
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
14.0000
*
*
11.1979
10000.639234
0.639234
*
1.46
*
1.46
*
*
1.46
*
1.46
*
0.00
0.00
*
5.84
5.84
*
5.84
5.84
Process Data
Potential (Within) Capability
Overall Capability Observed Performance Exp. "Within" Performance Exp. "Overall" Performance
Within
Overall
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 33/44
© 2001 ConceptFlow 33
Answering Question 4 Continued
If the Step standard deviations are reduced as follows, the capability isless than 3.4 DPM:
New Original
Step 1 0.1 0.1
Step 2 0.1 0.3
Step 3 0.1 0.2Step 4 0.1 0.4
Step 5 0.1 0.3
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 34/44
© 2001 ConceptFlow 34
12.0 12.5 13.0 13.5 14.0
USLUSL
Process Capability Analysis for Y
USL
Target
LSL
Mean
Sample N
StDev (Within)
StDev (Overall)
Cp
CPU
CPL
Cpk
Cpm
Pp
PPU
PPL
Ppk
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
14.0000
*
*
12.9011
1000
0.224935
0.224935
*
1.63
*
1.63
*
*
1.63
*
1.63
*
0.00
0.00
*
0.52
0.52
*
0.52
0.52
Process Data
Potential (Within) Capability
Overall Capability Observed Performance Exp. "Within" Performance Exp. "Overall" Performance
Within
Overall
Answering Question 4 Continued
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 35/44
© 2001 ConceptFlow 35
Answering Question 4 Continued
It is typical that the means must be re-centered, along with the standard
deviations being reduced. The following will achieve six sigma
capability:
New Original
Step Mean SD Mean SD
Order Entry 1.0 0.1 1.2 0.1Mfg at Site A 3.0 0.2 3.3 0.3
Ship to Site B 2.1 0.2 2.1 0.2
Mfg at Site B 3.0 0.2 3.5 0.4
Ship to Client 2.7 0.2 2.8 0.3
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 36/44
© 2001 ConceptFlow 36
10 11 12 13 14
USLUSL
Process Capability Analysis for Y
USL
Target
LSL
Mean
Sample N
StDev (Within)
StDev (Overall)
Cp
CPU
CPL
Cpk
Cpm
Pp
PPU
PPL
Ppk
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
PPM < LSL
PPM > USL
PPM Total
14.0000
*
*
11.8088
1000
0.467779
0.467779
*
1.56
*
1.56
*
*
1.56
*
1.56
*
0.00
0.00
*
1.40
1.40
*
1.40
1.40
Process Data
Potential (Within) Capability
Overall Capability Observed Performance Exp. "Within" Performance Exp. "Overall" Performance
Within
Overall
Answering Question 4 Continued
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 37/44
© 2001 ConceptFlow 37
Class Example
Use Monte Carlo analysis to analyze a call-in order filling system.
• Answer the following questions:
1. What is the average time to complete a client order?
2. What is the standard deviation of order completion?
3. What is the capability (in DPM) of the system?
4. What input characteristics are required for a six sigma process?
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 38/44
© 2001 ConceptFlow 38
Class Example
The requirement to fill a call-in order is 24 hours.
• There are three steps to the process:
1. Order entry
2. Item collection
3. Ship to client
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 39/44
© 2001 ConceptFlow 39
Process Map for Class Example
CollectItems
Ship toClient
Order Entry
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 40/44
© 2001 ConceptFlow 40
Data Summary of Process Steps
Data was collected at each process step with the sample statistics (in
hours) recorded below:
Step Mean SD Min Max
Order Entry 1.2 0.1 0.9 1.5Item Collection 7.5 0.5 6.0 9.0
Ship to Client 13.5 1.5 9.0 18.0
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 41/44
© 2001 ConceptFlow 41
Class Example
Use Monte Carlo analysis to answer the following questions:
1. What is the average time to complete a client order?
2. What is the standard deviation of order completion?
3. What is the capability (in DPM) of the system?
4. What input characteristics are required for a six sigma process?
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 42/44
© 2001 ConceptFlow 42
Key Learning Points
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 43/44
© 2001 ConceptFlow 43
Objectives Review
By the end of this module, the participant will be able to:
• Apply Monte Carlo analysis to business processes.
• Create a Monte Carlo analysis worksheet in Minitab.
• Conduct a Monte Carlo simulation using Minitab.
• Apply capability analysis to the output of a Monte Carlo analysis.
• Determine the proper centering and spread of the input variables toachieve six sigma capability in the output variable.
8/22/2019 12 Montecarlo(BP) Final
http://slidepdf.com/reader/full/12-montecarlobp-final 44/44
Trademarks and Service Marks
Six Sigma is a federally registered trademark of Motorola, Inc.
Breakthrough Strategy is a federally registered trademark of Six Sigma Academy.
VISION. FOR A MORE PERFECT WORLD is a federally registered trademark of Six Sigma Academy.
ESSENTEQ is a trademark of Six Sigma Academy.
FASTART is a trademark of Six Sigma Academy.
Breakthrough Design is a trademark of Six Sigma Academy.
Breakthrough Lean is a trademark of Six Sigma Academy.
Design with the Power of Six Sigma is a trademark of Six Sigma Academy.
Legal Lean is a trademark of Six Sigma Academy.
SSA Navigator is a trademark of Six Sigma Academy.
SigmaCALC is a trademark of ix Sigma Academy.
SigmaFlow is a trademark of Compass Partners, Inc.
SigmaTRAC is a trademark of DuPont.
MINITAB is a trademark of Minitab, Inc.