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# 2. intro. to six sigma

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Intro. to Six Sigma

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### 2. intro. to six sigma

1. 1. QUALITY TOOLS & TECHNIQUES Q T T INTRODUCTION TO SIX SIGMA By: - Hakeem–Ur–Rehman IQTM–PU 1
2. 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. 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. 4. WHAT IS A SIX SIGMA … As a Measure?1.5 Sigma Shift Theory
5. 5. WHAT IS A SIX SIGMA … As a Metric?Each of these metrics serves a different purpose and may beused at different levels in the organization to express theperformance of a process in meeting the organization’s (orcustomer’s) requirements. We will discuss each in detail as wedo 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. 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 orX # of Defect Opportunities 5% for each type / Unit)
7. 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 % SIGMAConsult Z–Table or Excel From M.S. Excel: =Normsinv(%Yield)+1.5 Sigma Level 50,000 DPMO = 3.145σ
8. 8. SIGMA LEVEL: CONVERSION TABLEDefects 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. 9. EXAMPLE: Calculate Sigma LevelCalculate the Sigma Level and DPMO of a telecom network had500 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. 10. EXAMPLE: Calculate Sigma LevelA manufacturer of computer hard drives wants to measure theirSix Sigma level. Over a given period of time, the manufacturercreates 83,934 hard drives. The manufacturer performs 8individual checks to test quality of the drives. During testing3,432 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. 11. EXAMPLE: Calculate Sigma LevelA project is focused on a billing process. The team wants tohave correct bills sent to the customer. They have defined oneopportunity for this process - either the bill is correct or not. Allof the bills produced are the same in terms of complexity. Theteam 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. 12. EXAMPLE: Calculate Sigma LevelIf you have a total of 500 delivery orders and you find out that41 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. 13. EXAMPLE: Calculate Sigma LevelA telecom service provider complies the defects of one year from the inspection of100 sites. The severity of each defect is classified in the following: i. Critical ii. Major iii. Minor iv. TrivialThe complete checklist comprises of 50 types of defects. The data of 2005 of 100sites reveals the following figures: Total # of Critical Defects: 5 Total # of Major Defects: 20 Total # of Minor Defects: 120 Total # of Trivial Defects: 155Calculate 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. 14. SIGMA TABLE SHORT TERM LONG TERM (PROCESS NOT SHIFTED) (PROCESS SHIFTED 1.5 SIGMA)SIGMALEVEL 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. 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 numeratorand 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. 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. 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. 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. 19. SIX SIGMA TOOLS • QFD • FMEAQ • SPC • QC TOOLS • New Management Tools • Control Charts • Capability Analysis S • Probability Distribution • Sampling • Confidence Interval • Regression Analysis • Project Management • Organizational BehaviorM • Human Resource Management • Knowledge Management
20. 20. SIX SIGMA TOOLS1. Quality Tools2. Statistical Tools3. Management ToolsEvery tool is a JUNK unless used appropriately
21. 21. SIX SIGMA FRAMEWORKSProgram 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 FeaturesMethodology 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. 22. QUESTIONS 22