Introduction to Six Sigma
Introduction to
Six Sigma
Six Sigma: An overviewWhat is Sigma and Six Sigma?Why Six Sigma?Six Sigma LevelsSix Sigma Methodology and ManagementKey Roles for Six SigmaTools for Six SigmaTrainings and CertificationsConclusion
• Genesis• Six Sigma: An overview• What is Six Sigma• Six Sigma focus• Six Sigma Scale• Six Sigma Companies• Six Sigma – The statistical background• DMAIC/DMADV• Benefits
GENESIS• Motorola in early 80s• Mikel Harry formalized the process for targeting the
inputs to the quality problems rather than the outputs of the those problems
• Input oriented approach leads to: A problem solving methodology and a set of tools to manage the problems
• Adapted gradually by other Fortune 500 Co.• Another very famous proponent – Jack Welch (GE)• Its had evolved to mean different things to different
people, sometimes any QI improvement process is also termed as SS
Six Sigma Companies
Six Sigma and Financial Services
6
Six Sigma
• A term (Greek) used in statistics to representstandard deviation from mean value, an indicator of the degree of variation in a set of a process.
• Six Sigma - A highly disciplined process that enables organizations deliver nearly perfect products and services.
• A rigorous, data based problems solving approach to improving the performance of an organization
• DMAIC / DMADV Cycle
Six Sigma• A performance goal, representing 3.4 defects for
every million opportunities to make one.• A series of tools and methods used to improve or
design products, processes, and/or services.• A statistical measure indicating the number of
standard deviations within customer expectations.• A disciplined, fact-based approach to managing a
business and its processes.• A means to promote greater awareness of customer
needs, performance measurement, and business improvement.
Six Sigma
Six Sigma can be defined as a specific methodology to
develop and implement quality improvements in an
organization’s critical processes by rigorously measuring
and analyzing and identifying variations from customer
specifications in those processes and improving them or
designing entirely new processes to keep variations at an
acceptable level and sustaining and institutionalizing or
verifying the improvements for future as well.
Six Sigma• CTQ/CTC/CTD: Attributes which are important to
customers• Defect: Failing to deliver what the customers wants• Process Capability: What your process can deliver• Variation: What the customers see and feels • Stable Operations: Ensuring consistent, stable
processes• DFSS: Designing to meet customers needs and
process capability
10
Six Sigma Focus is on
• Defining users requirements• Aligning processes to meet those requirements• Using metrics to minimize the variations• Rapidly and permanently improve the process
(Try and incorporate the best of the options in process)• Sustain and hold on to the improvement achieved
(Check the design for its use, usability & performance)
Sigma ScaleIn a world at 3 Sigma
• There are 964 U.S. flight cancellations per day.
• The police make 7 false arrests every 4 minutes.
• In MA, 5,390 newborns are dropped each year.
• In one hour, 47,283 international long distance calls are accidentally disconnected.
In a world at 6 Sigma
• 1 U.S. flight is cancelled every 3 weeks.
• There are fewer than 4 false arrests per month.
• 1 newborn is dropped every 4 years in MA.
• It would take more than 2 years to see the same number of dropped international calls.
Statistical Background
Target = m
Some Key measure
+/ - 3s
Statistical Background
Target = m
‘Control’ limits
+/ - 3s
LSL USL
Statistical Background
Required Tolerance
Target = m
+/ - 3s
+/ - 6s
LSL USL
Statistical Background
Tolerance
Target = m
Six-Sigma
+/ - 3s
+/ - 6s
LSL USL
ppm1350
ppm1350
Statistical Background
Tolerance
Target = m
+/ - 3s
+/ - 6s
LSL USL
ppm0.001
ppm1350
ppm1350
ppm0.001
Statistical Background
Tolerance
Target = m
LSL
0 ppm ppm3.4
1.5s USL
ppm3.4ppm
66803
m
+/ - 6s
Statistical Background
Tolerance
Statistical Background
• Six-Sigma allows for un-foreseen ‘problems’ and longer term issues when calculating failure error or re-work rates
• Allows for a process ‘shift’• So what constitutes an acceptable level of
quality for any business?• While a 4 sigma is acceptable for restaurants
but then for a hospital medication process this seems to be too low
DPMO or PPM Table
Managing Up the Sigma Scale
Sigma % Good % Bad DPMO
1 30.9% 69.1% 691,462
2 69.1% 30.9% 308,538
3 93.3% 6.7% 66,807
4 99.38% 0.62% 6,210
5 99.977% 0.023% 233
6 99.9997% 0.00034% 3.4
Performance Standards
23456
30853766807
62102333.4
PPM
69.1%93.3%99.38%99.977%99.9997%
Yield
Processperformance
Processperformance
Defects permillion
Defects permillion
Long term yield
Long term yield
Current standardCurrent standard
World ClassWorld Class
24
WHAT IS DMAICDefine,Measure,Analyse,Improve,Control
• A logical and structured approach to problem solving and process improvement.
• An iterative process (continuous improvement)
• A quality tool which focus on change management style.
DMAIC
Define Determine purpose and scope of project
Measure Collect info which indicates process perf.
Analyze R’ship betn key process input variables
Improve Expt. inputs variables to get right outputs
Control Std. & sustain change for improvements
Six-Sigma - A Roadmap for Improvement
DMAIC – The Improvement Methodology
Objective:DEFINE the
opportunity
Objective:MEASURE current performance
Objective:ANALYZE the root causes of problems
Objective:IMPROVE the process to eliminate root causes
Objective:CONTROL the process to sustain the gains.
Key Define Tools:• Cost of Poor
Quality (COPQ)• Voice of the
Stakeholder (VOS)
• Project Charter• As-Is Process
Map(s)• Primary Metric
(Y)
Key Measure Tools:
• Critical to Quality Requirements (CTQs)
• Sample Plan• Capability
Analysis• Failure Modes
and Effect Analysis (FMEA)
Key Analyze Tools:
• Histograms, Boxplots, Multi-Vari Charts, etc.
• Hypothesis Tests• Regression
Analysis
Key Improve Tools:
• Solution Selection Matrix
• To-Be Process Map(s)
Key Control Tools:
• Control Charts• Contingency
and/or Action Plan(s)
Define Measure Analyze Improve Control
Define – DMAIC ProjectWhat is the project?
• What is the problem? The “problem” is the Output (a “Y” in a math equation Y = f(x1,x2,x3) etc).
• What is the cost of this problem• Who are the stake holders / decision makers• Align resources and expectations
Six Sigma
Project Charter
Voice of the
Stakeholder
S takeho lders
$
Cost of Poor
Quality
Define – Customer RequirementsWhat are the CTQs? What motivates the customer?
Voice of the Customer Key Customer Issue Critical to QualitySECONDARY RESEARCH
PRIMARY RESEARCH
Surveys
Surveys
OTM
Market Data
Ind
ust
ry
Inte
lLi
sten
ing
Po
sts
Industry Benchmarking
Focus Groups
Customer Service
Customer Correspondence
Obser-vations
Measure – Baselines and CapabilityWhat is our current level of performance?
50403020100
95% Confidence Interval for Mu
26.525.524.523.522.521.520.519.5
95% Confidence Interval for Median
Variable: 2003 Output
19.7313
8.9690
21.1423
Maximum3rd QuartileMedian1st QuartileMinimum
NKurtosisSkewnessVarianceStDevMean
P-Value:A-Squared:
26.0572
11.8667
25.1961
55.290729.610023.147516.4134 0.2156
1000.2407710.238483
104.34910.215223.1692
0.8540.211
95% Confidence Interval for Median
95% Confidence Interval for Sigma
95% Confidence Interval for Mu
Anderson-Darling Normality Test
Descriptive Statistics
• Sample some data / not all data• Current Process actuals measured
against the Customer expectation• What is the chance that we will succeed
at this level every time?
OthersAmount
Late
41779 4.017.079.0
100.0 96.0 79.0
100
50
0
100
80
60
40
20
0
Defect
CountPercentCum %
Pe
rce
nt
Co
unt
Pareto Chart for Txfr Defects
Six Sigma
Analyze – Potential Root CausesWhat affects our process?
y = f (x1, x2, x3 . . . xn)
Ishikawa Diagram
(Fishbone)
Analyze – Validated Root CausesWhat are the key root causes?
OthersAmount
Late
41779 4.017.079.0
100.0 96.0 79.0
100
50
0
100
80
60
40
20
0
Defect
CountPercentCum %
Pe
rce
nt
Co
unt
Pareto Chart for Txfr Defects
OtherClerical
Currency
2 31211.817.670.6
100.0 88.2 70.6
15
10
5
0
100
80
60
40
20
0
Defect
CountPercentCum %
Pe
rce
nt
Co
unt
Pareto Chart for Amt Defects
Six Sigma
y = f (x1, x2, x3 . . . xn)Critical Xs
Process Simulatio
n
Data Stratificatio
n
Regression Analysis
Experim ental Design
Improve – Potential SolutionsHow can we address the root causes we identified?
• Address the causes, not the symptoms.
y = f (x1, x2, x3 . . . xn)
Critical Xs
Decision
Evaluat
e
Clarify
Generat
e
Divergent | Convergent
Improve – Solution SelectionHow do we choose the best solution?
Solution Sigma Time CBA Other Score
Time
Quality
Cost
Six Sigma
Solution Implementatio
n Plan
Solution Selection Matrix
☺ Nice Try
Nice Idea X
Solution Right Wrong
Imp
lem
enta
tion
Bad
G
ood
Control – Sustainable BenefitsHow do we ”hold the gains” of our new process?
0 10 20 30
15
25
35
Observation Number
Indi
vidu
al V
alue
Mean=24.35
UCL=33.48
LCL=15.21
• Some variation is normal and OK• How High and Low can an “X” go yet not materially impact the “Y”• Pre-plan approach for control exceptions
Process Owner: Date:Process Description: CCR:
Measuring and Monitoring
Key Measurements
Specs &/or
Targets
Measures (Tools)
Where & Frequency
Responsibility (Who)
Contingency (Quick Fix)
Remarks
P1 - activity duration, min.
P2 - # of incomplete loan applications
Process Control System (Business Process Framework)
Direct Process Customer:
Flowchart
Custom er Sales Branch ManagerProcessingLoan Service
Manager
1.1
Ap
plic
atio
n &
Re
vie
w1
.2P
roce
ssin
g1
.3C
red
it re
vie
w1
.4R
evi
ew
1.5
Dis
clo
sure
Apply forloan
Reviewappliation for
com pleteness
ApplicationCom plete?
Com pletem eeting
inform ationNo
Six Sigma
Six Sigma can be defined as a specific methodology to
develop and implement quality improvements in an
organization’s critical processes by rigorously measuring
and analyzing and identifying variations from customer
specifications in those processes and improving them or
designing entirely new processes to keep variations at an
acceptable level and sustaining and institutionalizing or
verifying the improvements for future as well (control).
36
BENEFITS OF SIX SIGMA
• Generates sustained success• Sets performance goal for everyone• Enhances value for customers• Accelerates rate of improvement• Promotes learning across boundaries• Executes strategic change
SIX SIGMA – PERFORMANCE MEASURES
TOP: Total number Of Opportunities
DPU: Defect Per Unit
DPO: Defect Per Opportunity
DPMO: Defects Per Million Opportunities
PPM: Parts Per Million
RTY/FPY: Rolled Throughput Yield or First Pass Yield
TOP• TOP: Total number Of Opportunity: In any given product or
service, this refers to the total number of defect opportunities possible.
• TOP = TOTAL NUMBER OF OPPORTUNITY = NUMBER OF SAMPLE UNITS INSPECTED * OPPORTUNITY PER UNIT
• For example: If there are 10 columns/spaces in a form to be filled then, we can say in each form there the TOP = 10 per form, so if we are inspecting 100 forms then the
• TOP = 10 * 100 = 1000 number of opportunities.
DPU• DPU: Defect Per Unit: Average number of defects per unit.
Numerically it is the ratio between the total number of defects found in a sample to the total number of samples inspected.
• DPU = DEFECT PER UNIT = NUMBER OF DEFECTS IN A SAMPLE / NUMBER OF SAMPLE INSPECTED
• For example: If we had inspecting 100 forms and found that there are 140 defects (mistakes) in all the forms inspected then the
• DPU = 140/100 = 1.4 defects per unit
DPO• DPO: Defect Per Opportunity: Average number of defects per opportunity.
This is the ratio of total number of defects found in a sample with the total number of defect opportunities available in the sample.
• DPO = DEFECT PER OPPORTUNITY = TOTAL NUMBER OF DEFECTS DETECTED IN A SAMPLE / TOTAL NUMBER OF DEFECT OPPORTUNITIES IN THE SAMPLE
• DPO = TOTAL NUMBER OF DEFECTS DETECTED IN A SAMPLE / (SAMPLE INSPECTED * NUMBER OF DEFECT OPPORTUNITIES PER UNIT IN THE SAMPLE)
• DPO = TOTAL NUMEBR OF DEFECTS DETECTED IN A SAMPLE / TOP
• For example: If we had inspecting 100 forms and there are 10 fields of information i.e. opportunities to make errors. If only 15 forms are sampled/inspected and 25 defects are found, then the
• DPO = 25 / (10*15) = 25/150 = 0.166667 defects per opportunity
DPMO• DPMO: Defects Per Million Opportunities: Ratio of total number of defects in one million
opportunities when an item can contain more than one defect. (This pertains to defects). This is the ratio of total number of defects found in a sample in one million opportunities.
• DPMO = DEFECT PER MILLION OPPORTUNITIES = TOTAL NUMBER OF DEFECTS DETECTED IN A SAMPLE * ONE MILLION / TOTAL NUMBER OF DEFECT OPPORTUNITIES
• DPMO = TOTAL NUMBER OF DEFECTS DETECTED IN A SAMPLE * ONE MILLION / (SAMPLE INSPECTED * NUMBER OF DEFECT OPPORTUNITIES PER UNIT IN THE SAMPLE)
• DPMO = TOTAL NUMEBR OF DEFECTS DETECTED IN A SAMPLE * 10,00,000 / TOP
• For example: If in a form, there are 10 fields of information i.e. opportunities to make errors. If only 15 forms are sampled/inspected and 25 defects are found, then the
• DPMO = 25 * 1000000 / (10*15) = 25 * 1000000 /150 = 166666.7 defect per million opportunity
PPM• PPM: Parts Per Million: The number of defective units in one million
units. Usually, preferred when the fraction defective figures are too small to consider in normal circumstances. (This pertains to defectives).
• PPM = PARTS PER MILLION = TOTAL NUMBER OF DEFECTIVE UNITS DETECTED IN SAMPLE * 10,00,000/ NUMBER OF SAMPLES INSPECTED
• For example: If we had inspected 100 forms and there was 100% inspection done and 25 forms were found to be unacceptable, then the
• PPM = 25 * 1000000 / 100 = 250000 parts per million defective
RTY/FPY• RTY/FPY: Rolled Throughput Yield or First Pass Yield: It is the probability (or the
percentage chances) that a process will complete all required steps without any failures. The computations of RTY is based on reliability principle.
• Reliability of a system in series with n steps in the process = R1*R2*R3….Rn• Where, R is the reliability of each process from 1 to n.
• Similarly, yield of any process is the product of yield at every stage when quality is the performance metric: RTY = FPY = Y1 * Y2 * Y3 *….Yn ,Where, Y is the yield (proportion accepted/good) for each step in a n step process
• For example: In a three step process, the yield rate of different step is as: Step 1=0.97, Step 2=0.92 and Step 3=0.95. Then the RTY = 0.97 * 0.92 * 0.95 = 0.8478 It means that only 84.78% of the units completed through all this three step process will make it through without needing any repair work.
RTY & DPU
• RTY = e –DPU = e - 0.01666667 = 0.9835 = 98.35%
• The yield of a certain process is known and is around 0.836. Find DPU.
• RTY = 0.836 • RTY = e –DPU
• Therefore, DPU = - Logn (RTY) = - Logn (0.836) = 0.179127
DEFECTS OR
REJECTS
UNITS OF
PRODUCTION
OPPORTUNITIES/UNIT
OF PRODUCTION
DPU = DEFECTS PER UNITS
DPO = DEFECTS/(UNITS*OPPORTUNIT
Y/UNIT)
DPMO = DPO
* MILLIO
N
SIGMA SHORT TERM = ABS(NORMSINV(DPO))
SIGMA LONG
TERM = SSST +
1.5
RTY = E TO THE POWER MINUS
DPU
DPU FROM RTY =
MINUS LN
(RTY)
10 200 5
15 50 10
80 50 8
DEFECTS OR
REJECTS
UNITS OF
PRODUCTION
OPPORTUNITIES/UNIT
OF PRODUCTION
DPU = DEFECTS PER UNITS
DPO = DEFECTS/(UNITS*OPPORTUNIT
Y/UNIT)
DPMO = DPO
* MILLIO
N
SIGMA SHORT TERM = ABS(NORMSINV(DPO))
SIGMA LONG
TERM = SSST +
1.5
RTY = E TO THE POWER MINUS
DPU
DPU FROM RTY =
MINUS LN
(RTY)
10 200 5 0.05 0.01 10000 2.326 3.826 0.9512 0.05
15 50 10 0.3 0.03 30000 1.880 3.380 0.7408 0.3
80 50 8 1.6 0.2 200000 0.841 2.341 0.2018 1.6
THANK YOU