QUALITY TOOLS & TECHNIQUES
By: -Hakeem–Ur–Rehman
IQTM–PU 1
TQ TINTRODUCTION TO SIX SIGMA
SIX SIGMA DEFINED In a narrow sense…
A metric based on Statistical Measure called Standard Deviation
In a 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”
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.
WHAT IS A SIX SIGMA … As a
Measure?
1.5 Sigma Shift
Theory
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. Defects2. Defects Per Unit (DPU)3. Parts Per Million (PPM)4. Defects Per Million Opportunities (DPMO)5. Yield6. First Time Yield7. Rolled Throughput Yield (RTY)8. Sigma Level
SIX SIGMA: Metrics (Cont…)
DPU(Defects / Unit)
(# of Defects / # of Units)
Say: 10 Defects, 100 PairsDPU = 10/100 = 0.1 (10%)
DPO(Defects /
Opportunity)
(# of Defects) / (# of Units X # of Defect Opportunities / Unit)
Say: 10 Defects, 100 Pairs,2 Opportunities / CartonDPO = 10/(100 X 2) = 0.05 or 5% for each type
SIX SIGMA: Metrics (Cont…)
DPMO(Defects / M.
Opportunities)
DPO X 106
Say: 10 Defects, 100 Pairs2 types of defectsDPMO = 0.05 X 106 = 50,000
SIGMAConsult Z–Table or
Excel
Sigma Level
Yield =1–DPO =1–0.05 = 95 %
From M.S. Excel:=Normsinv(%Yield)
+1.5
50,000 DPMO = 3.145σ
SIGMA LEVEL: CONVERSION TABLEDefects per1,000,000
Successrate
SigmaLevel
Defects per1,000,000
Successrate
SigmaLevel
933,000 7% 0.0 54,800 94.52% 3.1919,000 8% 0.1 44,600 95.54% 3.2903,000 10% 0.2 35,900 96.41% 3.3885,000 12% 0.3 28,700 97.13% 3.4864,000 14% 0.4 22,800 97.72% 3.5841,000 16% 0.5 17,900 98.21% 3.6816,000 18% 0.6 13,900 98.61% 3.7788,000 21% 0.7 10,700 98.93% 3.8758,000 24% 0.8 8,200 99.18% 3.9726,000 27% 0.9 6,210 99.379% 4.0691,000 31% 1.0 4,660 99.534% 4.1655,000 34% 1.1 3,470 99.653% 4.2618,000 38% 1.2 2,560 99.744% 4.3579,000 42% 1.3 1,870 99.813% 4.4540,000 46% 1.4 1,350 99.865% 4.5500,000 50% 1.5 968 99.903% 4.6460,000 54.0% 1.6 687 99.931% 4.7421,000 57.9% 1.7 483 99.952% 4.8382,000 61.8% 1.8 337 99.966% 4.9345,000 65.5% 1.9 233 99.9767% 5.0309,000 69.1% 2.0 159 99.9841% 5.1274,000 72.6% 2.1 108 99.9892% 5.2242,000 75.8% 2.2 72 99.9928% 5.3212,000 78.8% 2.3 48 99.9952% 5.4184,000 81.6% 2.4 32 99.9968% 5.5159,000 84.1% 2.5 21 99.9979% 5.6136,000 86.4% 2.6 13 99.9987% 5.7115,000 88.5% 2.7 9 99.9991% 5.896,800 90.32% 2.8 5 99.9995% 5.980,800 91.92% 2.9 3.4 99.99966% 6.066,800 93.32% 3.0
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
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
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
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
EXAMPLE: Calculate Sigma LevelA 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. Criticalii. Majoriii. Minoriv. 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: 5Total # of Major Defects: 20Total # of Minor Defects: 120Total # 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
SIGMA TABLE
SIGMA
LEVEL
SHORT TERM (PROCESS NOT
SHIFTED)
LONG TERM (PROCESS SHIFTED 1.5
SIGMA)
Yield (OK)%
RejectPPM
Yield (OK)%
RejectPPM
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
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.
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
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:
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:
SIX SIGMA TOOLS
Q
• QFD• FMEA• SPC• QC
TOOLS• New
Management Tools
S
• Control Charts
• Capability
Analysis
• Probability
Distribution
• Sampling
• Confidence
Interval
• Regression
Analysis
M
• Project Management
• Organizationa
l Behavi
or• Human
Resource
Management
• Knowledge
Management
SIX SIGMA TOOLS1. Quality Tools2. Statistical Tools3. Management Tools
Every tool is a JUNK unless used appropriately
SIX SIGMA FRAMEWORKS
SIX SIGMA Lean Six Sigma DFSS
VARIATIONDefects
Cost of Poor Quality
WASTE / SPEEDCycle Time, Delivery
Cost of Operation
RELIABILITY & ROBUSTNESS
Design Features
DMAIC DMAIC DMADV
SIPOC, CTQ, SPC, FMEA, DOE, QFD,
CoQ, ANOVA, Hypothesis, Regression, MSA (R & R)
5S, Value Mapping, Time
Study, TPM,Cellular Prod.,Supply Chain,
Takt Time,Poke Yoke
VOC, QFD, FMEA, CTQ, Gage R & R, DOE, Reliability Analysis, SPC,
Systems Engineering
Program
Focus / Theme
Methodology
Tools
QUESTIONS
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