Six Sigma is defined in multiple ways: as a philosophy, set of tools, methodology, and metric. As a metric, it uses the concept of sigma (σ) to measure quality levels and defects. A Six Sigma level process would produce just 3.4 defects per million opportunities. Metrics like defects per unit, defects per million opportunities, sigma level, and yield are used to measure process performance. Examples show how to calculate these metrics from data on defects, units, and opportunities to determine a process's sigma level.

1. QUALITY TOOLS &
TECHNIQUES
Q T T
INTRODUCTION TO SIX SIGMA
By: -
Hakeem–Ur–Rehman
IQTM–PU 1

2. SIX SIGMA DEFINED
 Ina narrow sense…
 A metric based on Statistical Measure called Standard Deviation
 Ina broader, business sense…
 WORLD CLASS QUALITY providing a BETTER product or
service, FASTER, and at a LOWER COST than our competitors.
 VARIATION… “the enemy of the customer satisfaction”

3. WHAT IS SIX SIGMA?
 DIFFERENT OPINIONS ON THE DEFINITION OF SIX
SIGMA:
 Six Sigma is a PHILOSOPHY: This perspective views all work as processes
that can be defined, measured, analyzed, improved and controlled. Processes
require inputs (x) and produce outputs (y). If you control the inputs, you will
control the outputs: This is generally expressed as y = f(x).
 Six Sigma is a SET OF TOOLS: The Six Sigma expert uses qualitative and
quantitative techniques to drive process improvement. A few such tools
include statistical process control (SPC), control charts, failure mode and
effects analysis and flowcharting.
 Six Sigma is a METHODOLOGY: This view of Six Sigma recognizes the
underlying and rigorous approach known as DMAIC (define, measure,
analyze, improve and control). DMAIC defines the steps a Six Sigma
practitioner is expected to follow, starting with identifying the problem and
ending with the implementation of long-lasting solutions. While DMAIC is not
the only Six Sigma methodology in use, it is certainly the most widely adopted
and recognized.
 Six Sigma is a METRIC: it uses the measure of sigma, DPMO (Defect Per
Million Opportunities), RTY (Rolled Throughput Yield) etc.

4. WHAT IS A SIX SIGMA
… As a Measure?
1.5 Sigma
Shift
Theory

5. WHAT IS A SIX SIGMA
… As a Metric?
Each of these metrics serves a different purpose and may be
used at different levels in the organization to express the
performance of a process in meeting the organization’s (or
customer’s) requirements. We will discuss each in detail as we
do through the course.
1. Defects
2. Defects Per Unit (DPU)
3. Parts Per Million (PPM)
4. Defects Per Million Opportunities (DPMO)
5. Yield
6. First Time Yield
7. Rolled Throughput Yield (RTY)
8. Sigma Level

6. SIX SIGMA:
Metrics (Cont…)
DPU Say:
(Defects / Unit) 10 Defects, 100 Pairs
(# of Defects / # of Units) DPU = 10/100 = 0.1 (10%)
DPO Say:
(Defects / Opportunity) 10 Defects, 100 Pairs,
2 Opportunities / Carton
(# of Defects) / (# of Units DPO = 10/(100 X 2) = 0.05 or
X # of Defect Opportunities 5% for each type
/ Unit)

7. SIX SIGMA:
Metrics (Cont…)
DPMO Say:
(Defects / M. 10 Defects, 100 Pairs
Opportunities) 2 types of defects
DPO X 106 DPMO = 0.05 X 106 = 50,000
Yield =1–DPO =1–0.05 = 95 %
SIGMA
Consult Z–Table or Excel From M.S. Excel:
=Normsinv(%Yield)+1.5
Sigma Level
50,000 DPMO = 3.145σ

8. SIGMA LEVEL: CONVERSION TABLE
Defects per Success Sigma Defects per Success Sigma
1,000,000 rate Level 1,000,000 rate Level
933,000 7% 0.0 54,800 94.52% 3.1
919,000 8% 0.1 44,600 95.54% 3.2
903,000 10% 0.2 35,900 96.41% 3.3
885,000 12% 0.3 28,700 97.13% 3.4
864,000 14% 0.4 22,800 97.72% 3.5
841,000 16% 0.5 17,900 98.21% 3.6
816,000 18% 0.6 13,900 98.61% 3.7
788,000 21% 0.7 10,700 98.93% 3.8
758,000 24% 0.8 8,200 99.18% 3.9
726,000 27% 0.9 6,210 99.379% 4.0
691,000 31% 1.0 4,660 99.534% 4.1
655,000 34% 1.1 3,470 99.653% 4.2
618,000 38% 1.2 2,560 99.744% 4.3
579,000 42% 1.3 1,870 99.813% 4.4
540,000 46% 1.4 1,350 99.865% 4.5
500,000 50% 1.5 968 99.903% 4.6
460,000 54.0% 1.6 687 99.931% 4.7
421,000 57.9% 1.7 483 99.952% 4.8
382,000 61.8% 1.8 337 99.966% 4.9
345,000 65.5% 1.9 233 99.9767% 5.0
309,000 69.1% 2.0 159 99.9841% 5.1
274,000 72.6% 2.1 108 99.9892% 5.2
242,000 75.8% 2.2 72 99.9928% 5.3
212,000 78.8% 2.3 48 99.9952% 5.4
184,000 81.6% 2.4 32 99.9968% 5.5
159,000 84.1% 2.5 21 99.9979% 5.6
136,000 86.4% 2.6 13 99.9987% 5.7
115,000 88.5% 2.7 9 99.9991% 5.8
96,800 90.32% 2.8 5 99.9995% 5.9
80,800 91.92% 2.9 3.4 99.99966% 6.0
66,800 93.32% 3.0

9. EXAMPLE: Calculate Sigma Level
Calculate the Sigma Level and DPMO of a telecom network had
500 minutes of downtime in 2005.
 Product: Network (Connectivity)
 CTQ: Up time / Down time
 CTQ Measure: Minutes
 CTQ Specs: no downtime
 Defect measure: One minute of Network down
 Opportunity/Unit: 1
 Total Defects in 2005: 500 minutes
 Total Time (Minutes): 365days X 24hours X 60min. = 525,600
 DPU = 500/525,600 = 0.000951
 DPO = 500 / (525600 X 1) = 0.000951
 DPMO= 0.000951 X 106 = 951
 Yield = 1 – DPO = 1 – 0.000951 = 0.999049
 SIGMA LEVEL = Normsinv(%Yield)+1.5 = 4.6σ

10. EXAMPLE: Calculate Sigma Level
A manufacturer of computer hard drives wants to measure their
Six Sigma level. Over a given period of time, the manufacturer
creates 83,934 hard drives. The manufacturer performs 8
individual checks to test quality of the drives. During testing
3,432 are rejected.
 # of Defects = 3432
 # of Units = 83934
 # of Defect Opportunities per Unit = 8
 DPU = 3432/83934 = 0.041
 DPO = 3432/(83934 X 8) = 0.0051
 DPMO= DPO X 106 = 5111
 Yield = 1 – DPO = 1 – 0.0051 = 0.9949
 SIGMA LEVEL = Normsinv(%Yield)+1.5 = 4.07σ

11. EXAMPLE: Calculate Sigma Level
A project is focused on a billing process. The team wants to
have correct bills sent to the customer. They have defined one
opportunity for this process - either the bill is correct or not. All
of the bills produced are the same in terms of complexity. The
team took a sample of 250 bills and found 60 defects.
 # of Defects = 60
 # of Units = 250
 # of Defect Opportunities per Unit = 1
 DPU = 6/250 = 0.24
 DPO = 6/(250 X 1) = 0.24
 DPMO= DPO X 106 = 240,000
 Yield = 1 – DPO = 1 – 0.24 = 0.76
 SIGMA LEVEL = Normsinv(%Yield)+1.5 = 2.21σ

12. EXAMPLE: Calculate Sigma Level
If you have a total of 500 delivery orders and you find out that
41 of those were delivered late, and 17 were incorrect orders.
 # of Defects = 41+17 = 58
 # of Units = 500
 # of Defect Opportunities per Unit = 2
(delivery time and correct order)
 DPU = 58/500 = 0.116
 DPO = 58/(500 X 2) = 0.058
 DPMO= DPO X 106 = 58,000
 Yield = 1 – DPO = 1 – 0.058 = 0.942
 SIGMA LEVEL = Normsinv(%Yield)+1.5 = 3.07σ

13. EXAMPLE: Calculate Sigma Level
A telecom service provider complies the defects of one year from the inspection of
100 sites. The severity of each defect is classified in the following:
i. Critical
ii. Major
iii. Minor
iv. Trivial
The complete checklist comprises of 50 types of defects. The data of 2005 of 100
sites reveals the following figures:
Total # of Critical Defects: 5
Total # of Major Defects: 20
Total # of Minor Defects: 120
Total # of Trivial Defects: 155
Calculate the Sigma Value and the DPMO for the year 2005.
 # of Defects = 5 + 20 + 120 + 155 = 300
 # of Units (Opportunities) = 100
 # of Defect Opportunities per Unit = 50
 DPU = 300/100 = 3.0
 DPO = 300/(100 X 50) = 0.0600
 DPMO= DPO X 106 = 60,000
 Yield = 1 – DPO = 1 – 0.0600 = 0.9400
 SIGMA LEVEL = Normsinv(%Yield)+1.5 = 3.05σ

14. SIGMA TABLE
SHORT TERM LONG TERM
(PROCESS NOT SHIFTED) (PROCESS SHIFTED 1.5 SIGMA)
SIGMA
LEVEL Yield (OK) Reject Yield (OK) Reject
% PPM % PPM
1σ 68.27 317,300 30.23 697,700
2σ 95.45 45,500 69.13 308,700
3σ 99.73 2,700 93.32 66,810
4σ 99.9937 63 99.3790 6,210
5σ 99.999943 0.53 99.97670 233
6σ 99.9999998 0.002 99.999660 3.4

15. SIX SIGMA: Metrics (Cont…)
 Final Yield (FY)
 Final Yield represents the acceptable pieces at the end of the process divided by
the pieces started. The FY excludes scrap.
FY = (Total Unit Passed) / (Total Unit Tested)
Calculation from above example: The unit of measure must be the same for the numerator
and denominator throughout the calculation.
 Process 1 Yield: 46 passed / 50 entered = 92.0%
 Process 2 Yield (itself): 46 passed / 46 passed = 100%
 Yield AFTER Process 2: 46 passed / 50 entered: 92.0%
 Process 3 Yield (itself): 37 passed / 46 entered = 80.4%
 Yield AFTER Process 3 (also the same as the final yield of entire process): 37 passed /
50 entered = Final Yield = 74%
Process 3 has the lowest yield and probably the most cost associated since all the material, labor,
and overhead costs are already in the pieces from the previous processes.

16. SIX SIGMA: Metrics (Cont…)
 Throughput Yield (TPY):
 Also called:
 FIRST PASS YIELD or
 FIRST TIME YIELD (FTY)
 Throughput Yield (TPY) is the number of acceptable
pieces at the end of a process divided by the
number of starting pieces excluding scrap and
rework.
 TPY is the traditional quality metric for yield
 Unfortunately, it does not account for any
necessary rework

17. SIX SIGMA: Metrics (Cont…)
Throughput Yield (TPY): Also called FIRST PASS YIELD (FIRST TIME YIELD)
Calculation (assuming all rework only takes one time to correct):
Process 1 TPY:
40 of the 50 pieces that entered Process 1 went through Process 1 correctly the first time.
Therefore Process 1 TPY = 40 / 50 = 80.0%
Process 2 TPY:
34 of the 46 pieces that entered into Process 2 went through Process 2 correctly the first time
through. Therefore Process 2 TPY = 34 / 46 = 73.9%
Process 3 TPY:
37 of the 46 pieces that entered Process 3 went through Process 3 correctly the first time.
Therefore Process 3 TPY = 37/46 = 80.4%
There is another method to calculate TPY for a single process. If the DPU or defects and units
are known then:

18. SIX SIGMA: Metrics (Cont…)
 Rolled Throughput Yield (RTY):
 Rolled Throughput Yield is the probability of the entire process producing zero
defects. RTY is more important as a metric to use where the process has
excessive rework.
Calculation from above example:
RTY = Process 1 TPY * Process 2 TPY * Process 3 TPY
RTY = 0.800 * 0.739 * 0.804
RTY = 0.475 = 47.5%
There is a 47.5% of the entire process producing zero defects.
Another method to estimate RTY if the defects per unit or defects and units are
known:

19. SIX SIGMA TOOLS
• QFD
• FMEA
Q • SPC
• QC TOOLS
• New Management
Tools
• Control Charts
• Capability Analysis
S • Probability Distribution
• Sampling
• Confidence Interval
• Regression Analysis
• Project Management
• Organizational Behavior
M • Human Resource
Management
• Knowledge
Management

20. SIX SIGMA TOOLS
1. Quality Tools
2. Statistical Tools
3. Management Tools
Every tool is a JUNK unless used appropriately

21. SIX SIGMA FRAMEWORKS
Program SIX SIGMA Lean Six Sigma DFSS
Focus / VARIATION WASTE / SPEED RELIABILITY &
Defects Cycle Time, Delivery ROBUSTNESS
Theme Cost of Poor Quality Cost of Operation Design Features
Methodology DMAIC DMAIC DMADV
Tools SIPOC, CTQ, 5S, Value
VOC, QFD, FMEA,
SPC, FMEA, Mapping, Time
CTQ, Gage R & R,
DOE, QFD, Study, TPM,
DOE, Reliability
CoQ, ANOVA, Cellular Prod.,
Analysis, SPC,
Hypothesis, Supply Chain,
Systems
Regression, Takt Time,
Engineering
MSA (R & R) Poke Yoke

22. QUESTIONS
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