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1、 Introduction to Six SigmaPat Hammett TQM - University of Michigan1 1 Introduction to Six Sigma See Course Website for the following Reference Paper: An Introduction to Six Sigma with A Design Example, Robert White, IEEE 1992. 2 Outline ?Six Sigma - History and Philosophy ?Six Sigma - Statistical Fo
2、undation ?Six Sigma Methodology Introduction to Six SigmaPat Hammett TQM - University of Michigan2 3 Six Sigma - Short History ?Pioneered by Motorola in 1980s ?Methodology used to focus resources on solving problems and increasing customer satisfaction with an emphasis on profits (bottom line). ?Som
3、e Key Players in Six Sigma History: ?Mikel Harry - one of the original Motorola architects who later founded Six Sigma Academy. ?Jack Welch, CEO General Electric ?Larry Bossidy, CEO Allied Signal ?These CEOs are largely responsible for the spread of Six Sigma by embracing the methodology and demonst
4、rating its potential in their respective companies. 4 Six Sigma Philosophy ?Key to business success is to drive out product variation. ?Need better than 99% quality levels ?Consider some outcomes for 99% levels ?20,000 lost articles of mail per hour ?5000 incorrect surgical operations per week ?200,
5、000 wrong prescription drugs each year ?No electricity for almost 7 hours each month Introduction to Six SigmaPat Hammett TQM - University of Michigan3 5 Six Sigma and Bottom Line ?Much of six sigma buzz results from executives claiming huge savings. ?GE - Jack Welch ?Operating Margin Before Six Sig
6、ma 13.6% (95); after Six Sigma 16.7% (98) $600 Million* . ?Allied Signal - Larry Bossidy ?Operating Margin from 12% to 14.1% in 99. ?Cumultative Six Sigma Savings 94-99 = $2 billion in direct costs*. *Harry, M. and Schroeder, S. (2000). Six Sigma: The Breakthrough Management Strategy, Currency. 6 Si
7、x Sigma 3.4 DPMO ?So, if Cp = 2.0, mean may deviate up to +/- 1.5 from nominal and still achieve 1.5) 10 Opportunities ?Characteristic Level - # defects for some component characteristic (e.g., tire pressure) ?In this class, we have been examining defects on a characteristic or feature level basis.
8、?But, a component has multiple characteristics and a system has multiple components. ?Definition of Opportunity any chance for error ?So, Total # Opportunities in a system = ?( # characteristics/component) * # produced. ?If part A 10 characteristics, B 50, C 30 characteristics ?Then, System ABC has
9、90M opportunities/1M produced Introduction to Six SigmaPat Hammett TQM - University of Michigan6 11 Yield Vs. Rolled Yield ?First Time Yield - # Acceptable Units (w/o scrap or rework) / Total Units Produced. ?Rolled Throughput yield is the probability of being able to pass a unit of product through
10、entire process - defect free. ?It is more sensitive to product complexity. ?Rolled Yield YRT= 0.93*0.89*0.84*0.9 = 0.63 10 708393 100 units63 units Scrap 10Scrap 3 93/100 = .9383/93 = .8970/83 = .8463/70 = .9 77 Op1Op2Op3Op4 12 Rolled Yield Calculations ?Rolled Throughput Yield (YRT) decreases as ad
11、d operations (unless operation yield is 100%) Yields 0 0.2 0.4 0.6 0.8 1 1234 Operation # Yield Proportion Operation YieldCum Rolled Yield Process Operation# Units # Good Units Operation Yield (per unit) Cum Rolled Yield per unit Op1100930.930.93 Op293830.890.83 Op383700.840.70 Op470630.900.63 Rolle
12、d Throughput Yield0.63 Introduction to Six SigmaPat Hammett TQM - University of Michigan7 13 Concerns with Yield by Unit ?Suppose: ?Case A: 10 parts are inspected, part #3 has 1 defect and part #4 has 1 defect - yield is 80%. ?Case B: 10 parts are inspected, part #3 has 2 defects and part #4 has 5 d
13、efects - yield is 80%. ?Are these two processes performing the same? 14 Rolled Yield w/ Multiple Defect Opportunities per unit ?Rolled throughput yield on a unit basis is not defect sensitive. ?An alternative approach is to consider defects per million opportunities (DPMO). Process Operation # Units
14、 # Rework/ Scrap # Opportunities/ unit # DefectsTotal # OP DPO (defects per opportunity) Op110074104000.03 Op293105104650.02 Op383135154150.04 Op470710107000.01 Sum4519800.02 DPMO22,727 Introduction to Six SigmaPat Hammett TQM - University of Michigan8 15 Assessing Performance of Multiple Products ?
15、Similarly, rolled yield may be calculated using defect per unit (DPU) rather than DPMO. ?To determine probability of zero defects when you inspect multiple characteristics per part and the likelihood of a defect is small, use special case of Poisson where. ?Yproduct i= e-dpu ?So, if you have 5 defec
16、ts in 523 units of Product A (note: a unit may have more than 1 defect), then Yield = e-(5/523)= 0.99049 16 Rolled Yield using DPU and Multiple Products (or operations) ProductUnitsDefects Throughput Yield A52350.99049 B851750.91564 C10000010.99999 D850.53526 E100750.47237 sum101482161 YRT23% (.9904
17、9*.91564*.99999*) Introduction to Six SigmaPat Hammett TQM - University of Michigan9 17 Normalized Yield, Ynorm ?To compare two product lines with different # operations, it may be useful to normalize yield. ?If m entities (operations, products, etc) ?Ynorm= (Yield)1/m ?So, the Ynorm in the prior ex
18、ample with 4 operations and YRT= 0.63, ?Ynorm= 0.8909 18 Other Six Sigma Speak ?Some Six Sigma trainers use six sigma conversion tables to equate a DPM in terms of # sigma quality. ?These tables include a 1.5 shift. ?So, for 4.5 sigma value would correspond to a Z = 4.5 - 1.5 = 3.0, which would be 1
19、350 DPM. ?Alternatively, if you are producing 3.4 DPM, then Z = 4.5 + 1.5 would be called a 6sigma process. ?I strongly disagree with this practice, I think it shows a lack of understanding for the difference between achieving a variation level and producing parts to specification. Introduction to S
20、ix SigmaPat Hammett TQM - University of Michigan10 19 Design for Six Sigma ?Design for Six Sigma simply involves utilizing identifying the appropriate processes and/or process settings necessary to achieve less than 3.4 DPM. ?Finding the “knobs” to insure high capability ?Key Tools Used in Design fo
21、r Six Sigma: ?Design of Experiments ?Reliability Analysis ?Tolerance Analysis 20 Six Sigma Implementation ?Comprehensive Training for following classifications: ?Master Black Belts - project selection and training of black and green belts. ?Black Belts - Apply Six Sigma tools to specific projects (100% of their time). ?Green Belts - Work part-time on six sigma projects. They receive more simplified black belt training. They might limit their involvement to collecting and analyzing data.