the application of six-sigma dmaic to a distribution...
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Dr. Edgardo J. Escalante 1
The Application of Six-Sigma
DMAIC to a Distribution SystemEdgardo J. Escalante, Ph.D.
ITESM | México
Pan-American Advanced Studies Institute on Modeling,
Simulation and Optimization of Globalized Physical Distribution
Systems (PASI)
August 9, 2013
Santiago, Chile
Dr. Edgardo J. Escalante 2
C O N T E N T S
� Brief introduction to Six-Sigma
� Case development and hands-on exercises
� Conclusions
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Dr. Edgardo J. Escalante 3
The Scientific Method
The quality movement and continuous
improvement can be seen as the
application of the Scientific Method
– a tool to obtain new knowledge
Box (1995)
Dr. Edgardo J. Escalante 4
The Meaning of Six Sigma
It is a
metric,
a working philosophy, and
a target
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Dr. Edgardo J. Escalante 5
The meaning of Six Sigma
As a metrics →way of measuring the performance of a process
As a working philosophy → continuous improvement of processes
As a target → world class performance process (3.4 part-per-million opportunities)
Dr. Edgardo J. Escalante 6
SIX SIGMA is a BUSINESS
STRATEGY to satisfy CUSTOMER
requirements
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DR. GENICHI TAGUCHI’S CONCEPTS
� An important product quality dimension is the total
loss to society
� In a competitive economy, quality continual
improvement and cost reductions are needed to
survive
� A quality continual improvement program includes a
constant variation reduction of a product’s
characteristics with respect to their target value
Taguchi (1987)
Dr. Edgardo J. Escalante 8
Lower specificationlimit (LSL)
Conforming product
Non conforming
product
Classic definition of Quality
Conformance to specifications for fitness for consumer
use
Target value
Non conforming
product
Upper specificationlimit (USL)
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Dr. Edgardo J. Escalante 9
Modern definition of Quality
Uniformity around a target value
Lower specificationlimit (LSL)
Upper specificationlimit (USL)
Non conforming
product
Target value
Non conforming
product
Sullivan (1984)
Dr. Edgardo J. Escalante 10
Dr. Taguchi’s Definition of Quality
The loss a product causes to society if it’s not
performing at its target value (m)
LSL USL LSL USL
m m
Good BadBad Good
Taguchi (1987)
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Two important things regarding process
control and improvement:
� Process variation
� Process mean
Dr. Edgardo J. Escalante 12
Definition of variation
For Shewhart (1931), sampling variation or
fluctuations are defined as differences between
things even if produced under presumably the
same conditions.
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Importance of Variation and Centering
Service evaluation in a bank in ten occasions:
Badservice
Excellentservice
Variation
1 2 3 4 5 6
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Is reducing variation enough?
Badservice
Excellentservice
1 2 3 4 5 6
Variation
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What about centering too?
Badservice
Excellentservice
Target
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The planning of statistical experiments is used to identify
the optimum values of the parameters that reduce variation
QUALITY
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“σ” is a Greek letter used to represent a measure of a
process’ variation
Graphical meaning of Six Sigma
3σ
process
LSL USL
3σ
Cp=Cpk=1
σ
0.4
0.3
0.2
0.1
0.0
14131211109876
Dr. Edgardo J. Escalante 18
Graphical meaning of Six Sigma…
Centered 6σ
process
LSL USL
6σ
Cp=Cpk=2
σ
14131211109876
0.4
0.3
0.2
0.1
0.0
1615154
10
Dr. Edgardo J. Escalante 19
Graphical meaning of Six Sigma…
Official 6σ
processCp=2, Cpk=1.5
LSL USL
4.5σ
14131211109876
0.4
0.3
0.2
0.1
0.0
1615154
1.5σ
Dr. Edgardo J. Escalante 20
Defects per million opportunitiesProcess capability
3.46
2335
6,2104
66,8073
308,5372
PPMσ
Historic standard
US companies
New standard
World class standard evolution
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Distinctive characteristics
CEO’s direct involvement and leading Six Sigma
Project evaluation, approval and following by the finance
function
Integration of existing techniques into a structured methodology
Six Sigma is an important part of the individual performance
evaluation
Of immediate application to GB or BB projects
It can be applied to any area within an organization
Dr. Edgardo J. Escalante
Metrics (Ys) linked to
CTQs
Define the Problem
Project Objective
Project Goal
PROCESS
X1X2X3X4
Y1Y2Y3
Establish Controls on the critical Xs so the
improvements will be maintained
Identify ways
to improve
the process
and validate
the solution
Measure and Analyze data
and process performance to
determine the critical
variables and root cause of
the problem
DMAIC Process
Little (2002)
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Dr. Edgardo J. Escalante
Overall Approach
Practical Problem Statistical Problem
Statistical SolutionPractical Solution
y f x x xk= ( , , ... , )1 2
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Zinkgraf S. y Snee R. (1999)
Dr. Edgardo J. Escalante 24
SIX SIGMA-DMAIC phases
Previous activities
Identify project, champion and project owner
Team defined and fully trained
Define customers and CTQs
Define project charter
Title, Business Case (Problem definition, COPQ,
baseline and entitlement), objective and goals, scope,
resource requirements, financial benefits, project approval
team members and estimated time
Define project plan
Develop a high-level process map
DEFINE
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Dr. Edgardo J. Escalante 25
Develop a detailed process map
Identify inputs and outputs
Perform measurement system analysis
Establish process capability baseline and entitlement
Identify potential critical inputs
Determine the critical inputs
Adjust the process
Evaluate new process capability
MEASURE
ANALYZE
Dr. Edgardo J. Escalante 26
Optimize critical inputs
Generate and test possible solutions
Select the best solution
Design implementation plan
Evaluate new process capability
Develop a monitoring and control plan
Verify final process capability
Obtain owner sign-off
Elaborate a final report
IMPROVE
CONTROL
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Dr. Edgardo J. Escalante 27
Define
problem
Describe process
Stable/capable
measurementImprove
N
Determine & validate significant
variables. Adjust process
Evalute process
stability & capability
Capable
process
N
D
M
M
A
A
OptimizeI
Stable
processEliminate
special
causes
N
Control
processC
Improve
continuouslyC
Y
Y
Y
Evaluate process capability & stabilityr
(baseline/entitlement)
M
DMAIC FLOW
Dr. Edgardo J. Escalante
Case development
Rent – A – Linen company
Products: bed sheets, towels, medical linen, etc.
Customers: major hospitals in a large metropolitan area
and in neighboring towns
One important customer satisfaction indicator (CTQ):
Response time to customer’s orders (OTD), target no
more than 8 hours since order reception
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Problem description
The % of late shipments has increased as shown
SepAugJulJunMayAprMarFebJanDecNov
6
5
4
3
2
Month
%LateShipments
Time Series Plot of %LateShipments
Dr. Edgardo J. Escalante 30
OctSepJulJunMayAprMarFebJanDecNov
7
6
5
4
3
2
Index
Individual Value _
X=5.045
UCL=6.721
LCL=3.370
56
1
1
I Chart of %LateShpments
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Dr. Edgardo J. Escalante 31
SepAugJulJunMayAprMarFebJanDecNov
7
6
5
4
3
2
Index2
Sample Mean
__X=5.788
UCL=6.953
LCL=4.622
1 2
Xbar Chart of Cap by Stage2
B
E
Dr. Edgardo J. Escalante 32
Project Charter
Problem definition/Response variable
� The % late shipments has significantly increased since Feb.
Response variable (Y): % Late shipments, measured as the
(number of late shipments divided by the total number of
shipments)*100 .
Business Case
Project title
Reduction of the percent of late shipments
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Cost of poor quality (COPQ)
� The monthly average % late shipments is 5.79 (B, baseline)
since February. Each late shipment costs $300 and there are
an average of 400 shipments/month (100/weekly)
� The average monthly total cost is
0.0579*300*400=$6,948/month or $83,376 a year
Business Case (cont.)
Dr. Edgardo J. Escalante 34
Goal and target
� To reduce the % late shipments to no more than 2% (E)
(entitlement) by 1st March (6 months).
Scope and limitations
� Applicable to deliveries within the metropolitan area
Estimated resources
� $6,000 (tests, personnel, meeting room, statistical software)
Expected economic benefits
� Expected new COPQ=2%*300*400=$2,400/month or $28,800
yearly
� The expected yearly benefits are $83,376–$28,800=$54,576
� Benefits from first year will be $54,576–$6,000=$48,576
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Champion (name/signature) Finance approval (name/signature)
H. Virtos J. Moredo
Process owner (name/signature) Estimated time
L. Moranteso 6 months
Black Belt (name/signature) Team members (name/signature)
R. Martecas R. Mataes, L. Recado, G. Gorid
Dr. Edgardo J. Escalante 36
% Late
shipments
(No. late shipments/total
No. shipments)*100Customer
requirements
Orders
on-time
Orders
delivered
on-time
ResponseResponsevariable
(Y)
Measurement
TargetNo more than 2%
of late shipments
Critical-to-quality characteristics (CTQ) tree
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Dr. Edgardo J. Escalante 37
SIPOC DIAGRAM
S=Suppliers I=Inputs
P=Process O=outputs C=Customers
Suppliers Inputs Process Outputs Customers
Sales dept.
Suppliers of
services
Suppliers of
linens
Suppliers of eq.
& chemicals
HR dept.
Orders
Gas,
Water
Electricity
Linens
Chemicals
People
Order
reception
Order
processing
Schedule
delivery
Lots of
linens
delivered
Local and
neighbo-
ring
hospitals
Dr. Edgardo J. Escalante 38
Quick exercise
A tools distribution company has seen a decrease of its on-time
deliveries and decided to analyze the situation. Based on a sample
of its last 100 shipments the problem-solving team elaborated the
following histogram depicting the characteristic (CTD) “delivery
time”. Specs are less or equal 24h and the team set an
improvement target of 50%. Briefly define the problem.
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Dr. Edgardo J. Escalante 39
12 24
0
10
20
Hours
Fre
cue
ncy
USLHISTOGRAM
0
Dr. Edgardo J. Escalante 40
DEFINE THE PROBLEM
Define the problem using one or more of the
following tools:
Pareto chart
Histogram
Run chartAudits
Critical-to-Quality (CTQ)
Problem
Target
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Dr. Edgardo J. Escalante 41
Develop a detailed process map
Identify inputs and outputs
Perform measurement system analysis
Establish process capability baseline and entitlement
MEASURE
Dr. Edgardo J. Escalante
StartOrder
receptionSchedule
deliverySend
items
-Quantity & type-Processing time
-Delivery time-No. of
available trucks
-Informationaccuracy
-Scheduleddelivery time
Prepare
order
End
Example. Rent – A – Linen distribution company
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PROCESS MAP
%Late shipments = f (Inf. accuracy, processing t,…, No. of avail. trucks)?
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Dr. Edgardo J. Escalante 43
Measurement System Analysis
� Reliability and dependability of measurements
�Make appropiate decisions
Studies→ stability, linearity, bias, repeatability &
reproducibility
Dr. Edgardo J. Escalante 44
Example. Rent – A – Linen distribution company
The order reception systems is automated and
remotely accessed by customers for placing orders.
This system is serviced at appropriate time intervals.
Order’s reception time is set by the customer when he
signs an electronic reception sheet connected directly
to Rent‒A‒Linen.
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Dr. Edgardo J. Escalante 45
Order # 1 2 3 4 5 6 7 8 9 10
Time 1 {1} 7.1 2.3 5.9 4.3 6.6 8.1 9.2 5.4 8.4 7.8
Time 2 {2} 7.3 2.6 6.2 3.9 6.9 8.2 8.9 4.9 8.5 7.9
Example. Rent – A – Linen distribution company
Gage R&R
Study Var %Study Var
Source StdDev (SD) (6 * SD) (%SV)
Total Gage R&R 0.20494 1.2296 9.75
Repeatability 0.20494 1.2296 9.75
Part-To-Part 2.09223 12.5534 99.52
Total Variation 2.10225 12.6135 100.00
{1} from automated system {2} by hand
MEASUREMENT SYSTEM EVALUATION
Dr. Edgardo J. Escalante 46
Process capability baseline and entitlement
USL
Based on 8 previous months of weekly data
3128252219161310741
10
8
6
4
2
Obser vation
Individual Value
_X=5.871
U C L=9.559
LC L=2.182
3128252219161310741
4
3
2
1
0
Obser vation
Moving Range
__M R=1.387
U C L=4.531
LC L=0
I-MR Chart of %LT-week
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Dr. Edgardo J. Escalante 47
876543
99
95
90
80
70
60
50
40
30
20
10
5
1
%LT-week
Percent
Mean 5.871
StDev 1.026
N 32
AD 0.445
P-Value 0.267
Probability Plot of %LT-weekNormal
Dr. Edgardo J. Escalante 48
8765432
USL
LSL *
Target *
USL 2
Sample Mean 5.87074
Sample N 32
StDev (Within) 1.22952
StDev (O v erall) 1.02603
Process Data
C p *
C PL *
C PU -1.05
C pk -1.05
Pp *
PPL *
PPU -1.26
Ppk -1.26
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL *
PPM > USL 1000000.00
PPM Total 1000000.00
O bserv ed Performance
PPM < LSL *
PPM > USL 999178.54
PPM Total 999178.54
Exp. Within Performance
PPM < LSL *
PPM > USL 999919.20
PPM Total 999919.20
Exp. O v erall Performance
Within
Overall
Process Capability of %LT-weekUSL=target<=02
25
Dr. Edgardo J. Escalante 49
Identify potential critical inputs
Determine the critical inputs
Adjust the process
Evaluate new process capability
Optimize critical inputs
Generate and test possible solutions
Select the best solution
Design implementation plan
Evaluate new process capability
ANALYZE
IMPROVE
Dr. Edgardo J. Escalante 50
Process variables 1 2 3 4 5 TOTAL Rank
Information accuracy 2 2 1 2 2 9
Quantity & type 3 1 2 3 3 12
Processing time 6 6 5 5 6 28 1
Scheduled delivery time 5 5 3 5 5 23 3
Delivery time 1 6 6 1 1 15
No. of available trucks 4 3 5 6 6 24 2
NOMINAL GROUP TECHNIQUE
GROUP MEMBERS
Process variables
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Dr. Edgardo J. Escalante 51
TIME
PROCESSING
HIGH
ROUTES
PROCEDURES TRUCKS
PEOPLE
Errors
Lack of superv ision
Lack of motiv ation
Lack of training
Not enough
Broken down
Unav ailable
Not standardized
Not automated
O bsolete
Not appropriate
Wrong programming
Lack of driv ers
Suboptimized
Not up to date
Cause-and-Effect Diagram
Dr. Edgardo J. Escalante 52
Experiential exercise-product/process optimization
One wishes to build a helicopter prototype that has the
longest Y=Flying time {Processing time} once dropped
from a certain height.
A: Wing length (2”, 3”)
No. of trucks {a, b}
B: Body length (2”, 3”)
No. of routes {c, d}
C: Body width (1”, 1.5”)
No of drivers {e, f}Adapted from Box (1992)
What kind of design is it?
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Dr. Edgardo J. Escalante 53
Design Matrix (coded units)
StdOrder WINGS BODY WIDTH TIME
1 -1 -1 -1
2 1 -1 -1
3 -1 1 -1
4 1 1 -1
5 -1 -1 1
6 1 -1 1
7 -1 1 1
8 1 1 1
Dr. Edgardo J. Escalante 54
StdOrder WINGS BODY WIDTH TIME
1 2 2 1
2 3 2 1
3 2 3 1
4 3 3 1
5 2 2 1.5
6 3 2 1.5
7 2 3 1.5
8 3 3 1.5
Design Matrix (uncoded units)
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Dr. Edgardo J. Escalante 55
Cut
Fold
A
B
C (1”(-1), 1.5”(+1))
Material needed:
8 letter-sized sheets
8 scissors
8 small paper clips
2 glue sticks to share
1 chronograph
2” (-1)
3” (+1)
2” (-1)
3” (+1)
3”
1” (fixed)
Not to scale
Wings
Body
Width
Dr. Edgardo J. Escalante 56
Depending on the dimensions of your prototype it should look like this
Glue
here
Final prototype
Paper
clip
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Dr. Edgardo J. Escalante 57
Design matrix in original or uncoded units (inches) in random order using Minitab®
Study of mean flight time
Factors influencing flying time:
Optimum levels to maximize flying time:
Dr. Edgardo J. Escalante 58
765432
Processing time
Processing time-new
Data
Dotplot of Processing time, Processing time-new {h}
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Dr. Edgardo J. Escalante 59
4137332925211713951
10.0
7.5
5.0
2.5
0.0
Observation
Individual Value
_X=1.64
UC L=2.95
LC L=0.32
1 2
4137332925211713951
4
3
2
1
0
Observation
Moving Range
__MR=0.496
UC L=1.620
LC L=0
1 2
I-MR Chart of %LT-week by stage
Before improvements
After improvements
Dr. Edgardo J. Escalante 60
Process capability after improvements
121110987654321
3
2
1
0
Observation
Individual Value
_X=1.636
UC L=2.955
LC L=0.318
121110987654321
1.6
1.2
0.8
0.4
0.0
Observation
Moving Range
__MR=0.496
UC L=1.620
LC L=0
I-MR Chart of %LT-week
31
Dr. Edgardo J. Escalante 61
2.52.01.51.00.5
99
95
90
80
70
60
50
40
30
20
10
5
1
%LT-week3
Percent
Mean 1.636
StDev 0.3887
N 12
AD 0.241
P-Value 0.711
Probability Plot of %LT-week3Normal
Dr. Edgardo J. Escalante 62
Evaluate new process capability after adjustments
2.42.01.61.20.8
USL
LSL *
Target *
USL 2
Sample Mean 1.63615
Sample N 12
StDev (Within) 0.439504
StDev (O v erall) 0.388709
Process Data
C p *
C PL *
C PU 0.28
C pk 0.28
Pp *
PPL *
PPU 0.31
Ppk 0.31
C pm *
O v erall C apability
Potential (Within) C apability
PPM < LSL *
PPM > USL 83333.33
PPM Total 83333.33
O bserv ed Performance
PPM < LSL *
PPM > USL 203873.65
PPM Total 203873.65
Exp. Within Performance
PPM < LSL *
PPM > USL 174624.63
PPM Total 174624.63
Exp. O v erall P erformance
Within
Overall
Process Capability of %LT-week
32
Dr. Edgardo J. Escalante 63
Develop a monitoring and control plan
Verify final process capability
Obtain owner sign-off
Elaborate a final report
CONTROL
Dr. Edgardo J. Escalante 64
�In addition to optimizing the process, some
SOP where developed to keep them
enforced
�Control charts were set in place to monitor
KPIVs/KPOVs
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Dr. Edgardo J. Escalante 65
Final remarks
Six Sigma Scientific
methodKnowledge
Improvement
ability
Quality &
productivity
improvement
Systematic
innovation
BUSINESS STRATEGY
Bisgaard and DeMast (2006); Escalante (2008)
Dr. Edgardo J. Escalante 66
REFERENCES
Bisgaard S., De Mast J. (2006). “After Six Sigma, what’s Next?”. Quality Progress, January.
Box G. (1995). “Total Quality: Its Origins and Its Future”. Report No. 123,
CQPI, UW. January.
Box G. (1992). “Teaching engineers experimental design with a paper helicopter” (George’s
Column). Quality Engineering, Vol. 4, No. 3.
Escalante E. (2008). Full Speed Ahead. Six Sigma Forum Magazine, May.
Little T. (2002). “Six Sigma Executive Overview”. Thomas Little Consulting.
Shewhart W. (1931). Economic Control of Quality of Manufactured Product. D. Van Nostrand
Co. Inc.
Sullivan L. P. (1984). Reducing Variability: A New Approach to Quality. Quality Progress, July.
Taguchi G. (1987). Introduction to Quality Engineering. A.P.O.
Zinkgraf S. y Snee R. (1999). Institutionalizing Six Sigma in Large Corporations: A Leadership
Roadmap. Quality and Productivity Research Conference.