【正文】 1%A Basic Sample Size Table Applies to Continuous Data Only δ/σ For example : The 1st adhesive has an average of and a standard deviation of The practical significance is such that any alternative Adhesive must have an average strength of 20 or more to make the change worth while. Q: For α=5% β=10% what should be the sample size in each level of the experiment? Ans: How big of a change is important? δ/σ=()/= α=5% β=10% So follow the table we find the sample size is 5 : Comparing Means : Comparing Variances (Between 2 Groups) :(Analysis Of Variance) (Between multigroups) Improve Statistical Control ? PokaYoke Plan (if Applicable) ? Confirmed Vital X’s ……Are They Statistically Significant ? ? Sample Size Calculation For Confirmation Run ? DOE Plan (if Applicable) ? Regression Equation Linked to statistical Problem ? SOP Changes and/or Optimal Solution Identified ? Plan to Implement SOP Changes and/or Optimal Solution What contribution did each vital X have to the Y ? How can we control the Xs ? What do we want to know ? How do we determine a model Correlation Regression Correlation tells if you have a relationship between two variables(Y and X, or two Xs) Regression is used to identify the nature of the relationship, and be able to predict Y while better understanding Y and possibly improving the controllability of Y 10987654152151150p u l ltempCorrelation Correlations (Pearson) Correlation of pull and temp = 210120 . 50 . 0 0 . 5 1 . 0N o r m a l S c o r eResidualN o rm a l Pro b a b i l i t y Pl o t o f t h e R e s i d u a l s(res po ns e is pu ll)Regression Analysis (Minitab software) The regression equation is pull = 353 temp Predictor Coef StDev T P Constant temp S = RSq = % RSq(adj) = % Analysis of Variance Source DF SS MS F P Regression 1 Error 30 Total 31 Unusual Observations Obs temp pull Fit StDev Fit Residual St Resid 12 150 31 151 DOE (Design of experiment) 找尋最佳之生產(chǎn)條件 (製程參數(shù) ) Design of Experiments 6? Overview SCREENING OPTIMIZATION CHARACTERIZATION ? For Experiments Involving a Large Number of Factors ? Useful in Isolating the “Vital Few “ from the “Trivial Many” ? For Experiments Involving a Relatively Small Number of Factors ? Useful When Studying Relatively Unplicated Effects Interactions ? For Experiments Involving Only 2 or 3 Factors ? Useful When Studying Highly Complicated Effects Relationships DOE is More Effective Than Testing One Factor at a Time Control What do we want to know ? Statistical Control ? PokaYoke Plan (if Applicable) ? Measurement of Final Capability Using Confirmation Run ? Comparison of Before and After Distributions ? How Do You Control or PokaYoke the Vital Xs ? ? Is the Learning Transferrable Across the Business ……What’s the Plan ? ? Who Owns the Project Documentation File ? ? Final Financial Results Signed Off ? What Spin Off Projects Are There ? How will this change the way we work ? ?Mistake proofing ?FMEA ?Process Monitor(SPC, Control chart…) ?Risk vs. Benefit Control tools Short Term Capability Short Term Capability Ratio (Cp) Cp = [ ] LSL 6? USL ] Example USL LSL ? = = ? 6? [ ? ( ? ? Cp = Cp = 1 LSL USL ? ? ? Process Mean 181。s as Motorola responded to the threat of Japanese petition which had far lower defective rates. The approach spread to AlliedSignal and to General Electric, whose Chief Executive Officer, Jack Welch, has been the most passionate advocate of SixSigma. Since introducing it worldwide in 1996, GE has made over $1 billion of cost savings. ?1979 年 ，當(dāng)時 Motorola一位資深業(yè)務(wù)主管 Arthur Sundry 在高階主管會議上說： Our quality levels really stink ! ? Six Sigma Quality Program 此名稱乃為 Motorola工程師 Bill Smith所建議，為Robert Galvin所採納。 ? ? 在動態(tài)的真實世界中，每一件事都在不停的變化著 ?溫度 ?溼度 ?工具的磨耗 ?原料的差異 ...... ? ?乃由機(jī)率、估計、經(jīng)驗而來 參考資料 :Evans, . (1975) : Statistical Tolerancing : The State of the Art, Part III. Shifts and Drifts. 6?的四個假設(shè) ?常態(tài)分配 ? 177。 The Potential Performance of a Process, Corrected for an OffTarget Mean LSL USL ? ? ? Process Mean 181。t know much about it, we cannot control it) ，那只有靠運(yùn)氣了 (If we cannot control it, we are at the mercy of chance) Why “Six Sigma”? ? Proven Successful in “QualityDemanding” Industries ., Motorola, Texas Instruments (many process steps in series) ? Proven Method to Reduce Costs ? Highly Quantitative Method – Science and Logic Instead of Gut Feel ? Includes Manufacturing Service (close to customer) and Provides Bridge to Design for Quality Concepts ? Has Support and Commitment of Top Management It Works!!! 6?有多小 ? Sigma ?? ?? ?? ?? ?? ?? PPM 2,700 45,500 317,310 面積 一般教室 2倍 約 6甲地 約 30個天安門廣場 略大於臺北市 東莞市 臺灣省的面積 時間 1 秒鐘 分鐘 9 小時 半個月 約 9 個月 5 年 6Sigma 狹隘解釋 DPPM 6? Overview Sigma 3? 4? 5? 6? Spelling Money Time Misspelled Words per Page in a Book 1 Misspelled Word per 30 Pages in a Book 1 Misspelled Word in a set of Encyclopedias 1 Misspelled Word in all of the Books in a Small Library $ Million Indebtedness per $1 Billion in Assets $570 Indebtedness per $1 Billion in Assets $63,000 Ind