5全因子試驗設計

1、第五章全因子試驗設計第一節(jié)概述第二節(jié)單因子四水平試驗第三節(jié)三因子兩水平試驗第四節(jié)二因子四水平試驗第一節(jié)概述一.什么是全因子試驗設計將每一個因子的不同水平組合做同樣數目的試驗二.特點及使用場合1.特點A.所有因子和水平的完全組合B.試驗次數為ek次，即K因子E水平C.完全組合，結果真實可靠2.適用場合水平數和因子數不多，以獲得精確的結論第二節(jié)單因子四水平試驗設計例冰箱故障增加，有四家供應商提供壓縮機，項目小組懷疑某家供應商的MTBF比其它供應商短，為此進行實驗。1 .實驗目標不同供應商對冰箱壽命的影響2 .確定測量指標即輸出變量冰箱的MTBF實驗計劃表項目負責人：譚XX.參加人員：日期：項目：冰

2、箱投訴增加目標：不同供應商對冰箱壽命的影響相關背景：我司冰箱的市場服務請求升為10起/天,且有增高之勢輸出特性指標：1.MTBF常溫下運轉出現故障，要求10000H,用于DOE3 .確定影響因子XS4 .確定噪音因子5 .列出計劃表可控因素表可控因子對輸出的影響試驗時改變難易度是否作為實驗因子目前水平目標水平如非實驗因子控制指標供應商是重在影響易改變?A影響一般，相對易改變O影響低，很難改變噪音因子表噪音因素對輸出的影響試驗時改變難易度是否作為實驗因素實驗因素非實驗因素策略水平設置水平設備環(huán)境溫度否2010濕度O否45-65%振動O否自然C中等影響，相對易改變重大影響，易改變A影響小，難改變實

3、驗次數丫RESI1FITS1110200-16756.526956.519850071543.526956.5111300-15656.526956.5112530-14426.526956.5211900-8067.419967.4212890-7077.419967.4212100-7867.419967.4210910-9057.419967.4313930951.712978.3310210-2768.312978.338300-4678.312978.339500-3478.312978.34124006410.9598995989.1489652975.9

4、5989.1496403650.95989.1One-wayANOVA:Yversus實驗次數SourceDFSSMSFP實驗次數314866635554955545181.040.4110.05供應商不是顯著因子Error125726234644477186220Total157212898198S=21845R-Sq=20.61%90%相關性不強R-Sq(adj)=0.76%與R-Sq相差遠，不能很好模擬實驗結果.Individual95%CIsForMeanBasedonPooledStDevLevelNMeanStDev143313343589241195081434104852428

5、44103241486(+-置信區(qū)間有重合，差異不明顯+-0200004000060000PooledStDev=21845MainEffectsPlot(datameans)forYMainEffectsPlot(datameans)forY35000一YfonaeM1000030000.250002000015000Illi1234可以看出供應商1為主要影響水平.TheregressionequationisY=33946-6989實驗次數PredictorCoefSECoefConstant3394612924實驗次數-69894719S=21105.1R-Sq=13.5%Analysi

6、sofVarianceSourceDFTP2.630.0200.05不時顯著因子R-Sq(adj)=7.4%SSMSFPRegressionAnalysis:Yversus實驗次數Regression19769573659769573652.190.1610.05相關性不顯著ResidualError146235940833445424345Total157212898198UnusualObservationsObs實驗次數YFitSEFitResidualStResid21.0098500269578829715443.73RRdenotesanobservationwithalarges

7、tandardizedresidual.ResidualsvsFitsforYaupseRResidualsVersustheFittedValues(responseisY)700006000050000400003000020000100000-10000-2000025000300005000100001500020000FittedValue殘值與擬合值沒有明顯關系RegressionAnalysis:Yversus實驗次數TheregressionequationisPredictorCoefSECoefConstant3394612924實驗次數-69894719TP2.630.0

8、200.05不是顯著因子Y=33946-6989實驗次數S=21105.1R-Sq=13.5%R-Sq(adj)=7.4%與R-Sq相差遠，方程模擬不強AnalysisofVarianceSourceDFSSMSFPRegression19769573659769573652.190.1610.05相關性不顯著ResidualError146235940833445424345Total157212898198UnusualObservationsObs實驗次數YFitSEFitResidualStResid21.0098500269578829715443.73RRdenotesanobse

9、rvationwithalargestandardizedresidual.我們嘗試用非線性關系來描述PolynomialRegressionAnalysis:Yversus實驗次數TheregressionequationisY=60222-33266實驗次數+5255實驗次數*2S=21111.5R-Sq=19.7%R-Sq(adj)=7.3%與R-Sq=19.7%相差遠方程模擬不良AnalysisofVarianceSourceDFSSMSFPRegressionError14188503177094251581.590.2410.05相關性不強135794047882445695991

10、Total157212898198SequentialAnalysisofVarianceSourceDFSSLinear19769573652.190.161Quadrati990.3380.05方程模擬不良FittedLine:Yversus實驗次數*2FittedLinePlotY=60222-33266+5255S21111.5R-Sq19.7%R-Sq(adj)7.3%我們再用三次方程來描述FittedLine:Yversus實驗次數PolynomialRegressionAnalysis:Yversus實驗次數Theregressionequationis

11、*2-3069實驗次數*3Y=92446-84517實驗次數+28272實驗次數S=21844.6R-Sq=20.6%R-Sq(adj)=0.8%AnalysisofVarianceSourceDFSSMSFRegression314866635554955545181.040.411Error125726234644477186220Total157212898198PSequentialAnalysisofVarianceSourceDFSSFPLinear19769573652.190.161Quadrati990.338Cubic1678132380.140.

12、7130.05三次方關系不顯著FittedLine:Yversus實驗次數FittedLinePlotY=92446-84517+28272*2-3069*3結論:線性非線性關系都不能模擬X與Y的關系，說明X與Y都不存在重要相關關系我不是影響Y的主要因素.第三節(jié)三因子二水平試驗設計1 .試驗目標：將外滑軌的內部尺寸保證在目標以內并使偏差最小，內外軌尺寸配合決定滑動力的大小.2 .實驗計劃表項目負責人：譚洪華參與人員：日期：項目名稱：滾珠成型過程改善實驗目標：將外滑軌的內部尺寸保證在目標以內并使偏差最小化相關背景：市場上此款滑軌的滑動力超規(guī)格，經小組調查分析，決定實施DO改善輸出特性指標：關鍵特

13、性測量儀器規(guī)格是否用于DOE滑動力測力#22-175否配合間隙內外滑軌尺寸差異-0.01-0.03否滑軌尺寸內軌的外部尺寸，外軌的內部尺寸19.07i0.119.07i0.15否是可控因素表可控因素對輸出的實驗時改是否作為如是實驗因素非實驗因素水影響變難易度試驗因素平設置材料硬度OA否使用現在水平滾珠固定座的位置O是滾珠10的角度是滾珠壓力是裝配速度O否使用現在水平C中等影響，相對易改變有重大影響，容易改變A影響很小，很難改變噪音因素表噪音因素對輸出的影響試驗時改變難易度是否作為實驗因素如是實驗因素非實驗因素水平滾珠的磨損AA否策略何種水平穩(wěn)健設計中和保持現有狀態(tài)3.確定測量指標即輸出變量外滑

14、軌的內部尺寸4.確定影響因素XS三個：滾珠固定座的位置滾珠10的角度滾珠壓力5 .實驗方案為三因素兩水平6 .試3效,每個實驗抽三個樣品并算平均值19.119.019.2MainEffectsPlot(datameans)forY218.918.819.09821060d991111YfonaeMABCy1y2y3平均丫丫11117.988819.0219.4218.809617.988812220.090219.4019.1219.536720.090212117.982919.4519.3418.924317.982911218.352718.8518.7218.640918.352722

15、119.552818.8918.0618.834319.552821219.230818.6318.8818.913619.230821118.665718.7618.9018.775218.665722219.852219.4619.4319.580719.852211119.020012219.400012119.450011218.850022118.890021218.630021118.760022219.460011119.420012219.120012119.340011218.720022118.060021218.880021118.900022219.4300任何兩個因素

16、都交叉或接近交叉,所以存在交互作用。B,C越陡，說明影響越大。再分析交互作用ANOVA:YversusA,B,CFactorTypeLevelsValuesAfixed21,2Bfixed21,2Cfixed21,2AnalysisofVarianceforYSourceDFSSMSFPA10.01390.01390.050.822B11.13101.13104.240.0530.05不是顯著因子，但接近0.05可視為顯著C10.66190.66192.480.131因子ErrorTotal205.3358237.14260.2668S=0.516519R-Sq=25.30%0.05交互作用不

17、顯著可/、計A*B*C10.01120.01120.040.844Error164.49760.2811Total237.1426S=0.530186R-Sq=37.03%R-Sq(adj)=9.48%RegressionAnalysis:YversusA,B,CTheregressionequationisY=17.8+0.048A+0.434B+0.332CPredictorCoefSECoefTPConstant17.78040.557931.870.000顯著因子A0.04810.21090.230.822B0.43420.21092.060.0530.05不是顯著因子C0.33210

18、.21091.580.131S=0.516519R-Sq=25.3%R-Sq(adj)=14.1%與R-Sq相差遠，方程模擬實驗結果不良AnalysisofVarianceFP2.260.113相關性不強SourceDFSSMSRegression31.80680.6023ResidualError205.33580.2668Total237.1426SourceDFSeqSSA10.0139B11.1310C10.6619UnusualObservationsResidual-1.046-1.017StResid-2.22R-2.16RObsAYFitSEFit31.0017.98319.0

19、290.211212.0018.06019.0770.211ResponseOptimizationParametersGoalLowerTargetUpperWeightImportYTarget18.919.0519.211GlobalSolutionA=1.00000B=1.00000C=-0.42501數據為假設數據，所以找不到關鍵因子。如果真的數據出現這種情況需要分析原因，重新設置實驗方案。第四節(jié)二因素四水平實驗設計1.測量指標：PCA假焊DPMO2.試驗因素：焊接溫度，松香比重因素水平1水平2水平3水平4溫度240245250255松香比重0.760.780.800.823.實驗方

20、案及結果ABDPMO1181428943129411253380341004410823107326131681283241061430216213632285Two-wayANOVA:DPMOversusA,BSourceABErrorTotalDF33915SS5124.7491.24545.110160.9MS1708.233.380.0680.05非顯著因子，但比A顯著163.730.32505.010.808S=22.47果不良R-Sq=55.27%R-Sq(adj)=25.45%與R-Sq相差遠所以方程模擬實驗結ResidualsVersustheFittedValues(resp

21、onseisDPMO)aunrseRoo-2-3o-460708090100110120130FittedValue殘值與按擬合值圖，其分布隨機、離散、未顯示有特別形狀，故不能得出關于試驗對象的其它信息。30ResidualsVersusA(responseisDPMO)aurtpseRooo-31.01.52.02.5A3.03.54.030ResidualsVersusB(responseisDPMO)20100-10-20-30-401.01.52.03.03.54.02.5B從A圖可看出隨著A水平的提高，殘值變小，其它看不出別的信息。InteractionPlot(datameans)

22、forDPMOnaeMX一KJ:從上圖可看出A,B存在非線性關系，并有交互作用。ResponseSurfaceRegression:DPMOversusA,BTheanalysiswasdoneusingcodedunits.EstimatedRegressionCoefficientsforDPMOTermCoefSECoefTPConstant82.37556.4731.4590.175A-10.08733.243-0.3030.768B-3.73733.243-0.1120.913A*A2.4386.0900.4000.6970.05非顯著項.B*B-1.0636.090-0.1740.

23、865A*B4.4704.8720.9180.380S=24.36R-Sq=41.6%R-Sq(adj)=：12.4%方程模擬不良AnalysisofVarianceforDPMOSourceDFSeqSSAdjSSAdjMSFPRegression54227.54227.47845.4951.420.296Linear23614.857.7428.8710.050.953Square2113.1113.1356.5630.100.910線性，交互作用系都不顯著Interaction1499.5499.52499.5220.840.380ResidualError105933.55933.47

24、593.347Total1510160.9UnusualObservationsforDPMOObsStdOrderDPMOFitSEFitResidualStResid44125.00094.10519.10330.8952.04R131330.00060.65519.103-30.655-2.03RRdenotesanobservationwithalargestandardizedresidual.EstimatedRegressionCoefficientsforDPMOusingdatainuncodedunitsTermCoefConstant121.6528A-17.1083B-

25、5.0972A*A1.0833B*B-0.4722A*B1.9867B因素最大值，A因素最小值DPMO最小.RegressionAnalysis:DPMOversusA,BTheregressionequationisDPMO=47.6+13.3A+2.13BPredictorCoefSECoefConstant47.5618.612.5613.2755.0182.650.0240.0200.05顯著因子2.1255.0180.420.679S=22.4399R-Sq=35.6%R-Sq(adj)=25.7%AnalysisofVarianceSourceDFSSMSRegressionResidualError3614.81807.43.590.057136546.1503.5Total1510160.9SourceDFSeqSS3524.590.3UnusualObservationsObsADPMOFitSEFitResidualStResid131.0030.0069.3412.03-39.34-2.08RRdenotesanobservationwithalargestandardizedresidual.PredictedVa