正交试验设计与方差分析

1、正交试验设计与方差分析例6：例5.4.2某纺织厂在梳棉机上纺粘锦混纺纱为了降低棉结粒数, 想通过试验确定有关的三个因素（即因子）的一个较好方案,这个因素的 各个水平如表5.4.7.表5.4.7因素水平表水平因12金属针布A日本青岛产量水平B6 kg10 kg锡林速度C238转/分320转/分21121.003121-2.004122.005211-3.0062124.007221-3.0082222+ Univariate Analysis of VarianceBetween-Subjects FactorsN金属 14针布 24产重 14水平24锡林 14速度24Tests of Betw

2、eeii-Subjects Effectsependent Mariable:棉 数SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model31.37泸310.4533.633.122Intercept.1251.125.043.845金属耳布.1251.125.043.845产量水平3.12513.1251.087.356锡林速度23.125123.1259.783.035Error11.50042.375Total43.0008Corrected Total42.8757a. R Squared = .732 (Adjus

3、ted R Squared = .531)Estimated Marginal Means1.金属针布日p日n寸日nt Mari able:棍结粒数95% Confidence Inten/al金属针布MeanStd. ErrorLower BoundUpper Bound12-.250.000.843.843-2.604-2.3542.1042.3542.产量水平Dependent Vari able:根结粒数95% Confidence Interval产量水平MeanStd. ErrorLower BoundUpper Bound12.500-.750.843.843-1.354-3.1

4、042.8541.6043.哲林速度叩加日用Mari able：棉MS&数福林速度MeanStd. Error95% Confidence IntervalLower BoundUpper Bound1-2.000.843-4.354.35421.750.843-.6044.1043k最优组合水平：C1B2A1例7、多变量（指标）正交试验设计与方差分析，题目:表126水平A水份/%B粒度/%。碱度1841. 12961. 33781. 5表 12.7列号 试验号123ABC各指标的试验结果抗压强度/kg/个落下强度/o. 5m/次裂纹度1111223312223311332133211. 54

5、. 511. 07.0018. 508. 013. 41. 1661. 11. 615. 11. 14.6-20. 2L抗 压 强 度K、 尺2 爪327. 027.538.033. 520.524.930. 442.928.0片239.09. 212. 711. 26. 88. 310. 114.39.3极差2. 27. 54. 4123ABC优方案& b3 g裂纹度KKz_K311958859落 下 强 度Ki k2 k39. 33.320.89.824.939.97.3KfC233. 73.01.772.72.701.73.0与3. 11.16.95- 93.38.38- 613.32.

6、4极差2. 01. 31. 3极差5. 512. 25. 9优方案a2 b3 g优方案&饱C2SPSS求解:File Edi t Vi ew Data Tr ：=ltle orm ArL：alyzt! Gi- aphs Ut ili ties jV i rLilow Help闵口僵1噂|小|由叫#4Eg冒庄庸I际期NameTypeWidthDecimalsLabel1因素水份String1N(2因素粒度String1N(3因素碱度String1N(4指标抗压强度Numeric82N(5指标落下强度Numeric82N(6指标裂绞度NumericI82N(应用多变量方差分析方法:MulthAir

7、iate Tests0EffectValueFHypothesis dfError dfSig.Intercept Pillais Trace1.0001 584.551 a2.0001.000.018Wilks Lambda.0001 584.551 a2.0001.000.018Hotellings Trace3169.1011 584.551 a2.0001.000.018Roys Largest Root3169.1011 584.551 a2.0001.000.018因素水份 Pillais Trace1.4102.3904.0004.000.210Wilks Lambda.0075

8、.588a4.0002.000.158Hotellings Trace85.459.0004.000.000Roys Largest Root84.73084.730b2.0002.000.012因素粒度 Pillais Trace1.88916.9894.0004.000.009Wilks Lambda.00118.29534.0002.000.052Hotellings Trace155.091.0004.000.000Roys Largest Root146.5121 46.51 2b2.0002.000.007因素碱度 Pillais Trace1.5673.6204.0004.000

9、.120Wilks Lambda.00113.87734.0002.000.068Hotellings Trace355.897.0004.000.000Roys Largest Root354.572354.572b2.0002.000.003Exact statisticThe statistic is an upper bound on F that yields a lower bound on the significance levelDesign: lntercept+因素水份旧素粒度+因素喊匿Tests of Between-Suhjects EffectsSourceDepe

10、ndent VariableType III Sum of SquaresdfMean SquareFSig.Corrected Model指标吭压强度 指标落下强度指标裂纹度125.8403356.673b12.667c620.97359.4462.1114.4724.1372.794Intercept指标抗压强度指标落下强度指标裂纹度918.090312.11153.7781918.09031 2.11153.778195.75521.72369.143.005.043.014因素水价指标抗压强度 指标落下强度 指标裂纹度7.04745.9366.88923.52322.9683.444.

11、7511.5994.429.571.385.184因素粒度指标抗压强度指标落下强度指标裂纹度87.547254.2022.889243.773127.1011.4449.3338.8461.357.097.102.350因素碱度指标抗压强度指标落下强度指标裂纹度31.24756.5362.889215.62328.2681.4443.3311.9671.857.231.337.350Error指标抗压强度指标落下强度指标裂纹度9.38028.7361.55624.69014.368.778Total指标抗压强度 指标落下强度 指标裂纹度1053.310697.52068.0009Correct

12、ed Total指标抗压强度指标落下强度指标裂纹度135.220385.40914.2228R Squared = .931 (Adjusted R Squared = .723)R Squared = .925 (Adjusted R Squared = .702)R Squared = .891 (Adjusted R Squared = .563)Estimated Marginal Means1.因素水粉Dependent Variable因素水份MeanStd. Error95% Confidence IntervalLower BoundUpper Bound指林;虫亟度19.00

13、01.2503.62014.380211.1671.2505.73716.546310.1331.2504.75415.513指晞卜强度13.1002.100-6.31612.51625.9332.138-3.48315.34930.6332.103-.73310.049指睽纹度13.667.5091.4765.05721.667.509-.5243.85732.000.509-.1914.191之.因素粒度Dependent Variable因素粒度MeanStd. Error95% Confidence IntetvalLower BoundUpper Bound指林;虫敢度19.1671

14、.2503.73714.54626.3331.2501.45412.213314.3001.2508.92019.680指晞I、强度11.1002.138-8.31610.51623.2672.108-6.14912.683313.3002.1003.00422.716指标裂纹度13.000.509.0095.19122.667.509.4764.85731.667.509-.5243.3573.因素麻度Dependent Variable因素膝度MeanStd. Error95% Confidence IntervalLower BoundUpper Bound指晌压度112.6671.25

15、07.28718.04623.3001.2502.92013.68039.3331.2503.95414.713指扉I、强度16.9332.183-2.48316.34923.3002.188-1.11617.71632.4332.188-6.98311.849指睽纹度11.667.509-.5243.85722.667.509.4764.85733.000.509.3095.191最优组合水平：B3 C1 A2例8、混合水平正交试验设计与方差分析，题目:例12. 3. 1某农科站进行品种试验共有4个因素;刀（品种）、8（氮肥量）、（氮、磷、 钾肥比例）、Q（规格）因素4是4水平的，另外3个因

16、素都是2水平的，具体数值如表 12. 11所示.试验指标是产量，数值越大越好试用混合正交表安排试验，找出最好的试验 方案.表 12. 11因素ABCD水平品种氮肥量/kg氮、磷、钾肥比例规格甲253 ： 3 ： 16X62乙302 ： 1 ： 27X73丙4丁表 12.12试验因素ABCD试验指标（产量Ag）减去200111111955212222055321122202042221225255312121010632122151574122185一1584211190一10匕010202045352525k325一25明02. 55. 05. 0k222. 58. 86. 36. 3们12.

17、 5A12*5极差35. 06. 31. 31- 3方123756=1113U151013214212122121Univariate: Model Specify ModelFull factorialFactors & Covariates:因素AIFI因素BR因素CR因素DFJ因素C因素口 实验指标1-5.0022112215.00 20.00 25.00 10.00 15.00 -15.00 -10.00Build Term(sCustomModel:ABC素素素因因因因素口实验指称-5.005.0020.0025.0010.0015.00-15.00-10.00varOptions.

18、WLS Weight:InteractionSum of squares:|Type III = V Include intercept in model-;|npContinue |匚am-l | Help97?IIIIIII厂 Compare main effectsConfidence interval adjustment:| LSD (none)|11 Univariat e实验指标-5.005.0020.0025.0010.0016.00-15.00-1U .ULI123因素B21因素A12因素C214 222Model.Contrasts.Plots.Post Hoc. ISav

19、e.Options.D 索 因ABC 素素素 因因因ALR A B c D 素素索索 因因因因Estimated Marginal Means - Factor(s) and Factor Interactions:13U1516171819202?2223242526272829-DisplayI- Descriptive statisticsI- Estimates of effect sizeI- Observed powerI- Parameter estimatesContrast coefficient matrixI- Homogeneity testsI- Sfiread vs

20、. level plotI- Residual plot Lack of fitI- General estimable function30Significance level: |.O5Confidence intervals are 95%ContinueCancel I HelpTests of Between-Sul)jects EffectsDe pen dent用riab厄:实明旨标SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model1468.75036244.79278.333.086Intercept25

21、3.1251253.1 2501.000.070因素A1384.3753461.453147.667.060因素B78.125170.12525.000.126因素。3.12513.1251.000.500因素口3.12513.1251.000.500Error3.12513.125Total1725.0008Corrected Total1471.8751a. R Squared = .993 (Adjusted R Squared = .985)Estimated Marginal Means1.因素ADe pen dent用riab厄:实幼旨标因素四MeanStd. Error95% C

22、onfidence IntervalLower BoundUpper Bound1.0001.250-15.08315.833222.5001.2506.61733.383312.5001.250-3.38320.3334-12.5001.250-28.3833.3832.因素BDe pen dent Mari able：实验指标因素日MeanStd. Error95% Confidence IntervalLower BoundUpper Bound12.500.834-0.73113.73123.750.834-2.48119.9813.因素e的n dent诡ri able：实验指标因素c

23、MeanStd. Error95% Confidence IntervalLower BoundUpper Bound15.000.004-6.23116.23126.250.004-4.98117.4314.因素DDe pen dent Mari able：实瑜指标因素口MeanStd. Error95% Confidence IntervalLower BoundUpper Bound15.000.004-6.23116.23126.250.384-4.98117.431最优组合水平：A2 B2 C2 D2。例9、拟水平单变量试验正交试验与方差分析，题目：例12. 3.2今有某一试验，试验

24、指标只有一个，它的数值越小越好，这个试验有4个 因素其中因素。是2水平的，其余3个因素都是3水平的，具体数值如表12. 13 所示,试安排试验，并对试验结果进行分析，找出最好的试验方案.表 12. 13水平因素ABCD135015606522505807533001085Z 二/ 表 12. 14水平XBCD135015606522505807533001085表 12. 15因素ABCD实验指标测试结果试验号11 1 111452.12222363133231242122315522321406231121573132210832113593322147K】937065132k2708116

25、061K3627432Ki31. 023. 321. 744.0k223. 327. 026. 720. 320. 724. 710. 7极差10. 33. 75. 033. 3优方案&B,gd3单变量方差分析SPSS求解:因素A因素A8 9 10 77 12实验指标45.0036.0012.0015.0040.0015.0010.005.0047.00Tests of Between-Siihjects EffectsDe pen dent用riab厄:实幼旨标SourceType III Sum of SquaresdfMean SquareFSig.Corrected Model2003

26、.000a1236.8571.320.506Intercept4672.22214672.22221.631.135因素A172.667236.333.400.745因素B20.667210.333.040.955因素。50.000150.000.231.715因素D1764.6672882.3334.085.330Error216.0001216.000Total7049.0009Corrected Total2224.0003a. R Squared = .903 (Adjusted R Squared = .223)Estimated Marginal Means1.因素A日 pen d

27、ent Mari able：实物旨标因素AMeanStd. Error95% Confidence IntervalLower BoundUpper Bound130.1673.660-79.072140.206222.5003.660-37.539132.539319.8338.660-90.206129.872De pen dent Mari able：实勤旨标因素日MeanStd. Error95% Confidence Inten/alLower BoundUpper Bound122.5008.660-87.539132.539226.167S.660-83.072136.20632

28、3.0330.660-86.206133.3723.因素CDe pen dent Mari able：实勤旨标因素cMeanStd. Error95% Confidence InternalLower BoundUpper Bound121.6678.435-36.149129.482226.6676.000-49.571102.9044.因素De pen dent Mari able：实验指标因素口MeanStd. Error95% Confidence IntervalLower BoundUpper Bound143.1678.660-66.372153.206219.5008.660-

29、90.539129.53939.8338.660-100.206119.872最优组合水平：D3 A3 C1 B1。例10、单变量试验指标三因素三水平交互作用的正交试验与方差分 析，题目：例12. 5. 7用烟灰和煤砰石作原料制造烟灰砖的试验.试验指标是干坯的扯断力 （10，Pa）.考虑3个因素，每个因素3个水平，具体情况如表12. 36所示.水平因素A成形水份/%碾压时间/min料重/kg/盘）1983302101036031112400选用乙（34）正交表作试验，因素A ,C分别列在第1,2,3列，见表12. 37.每号试验生产出 若干块干坯，采用重复取样的方法,每号试验中随机地取5块，测

30、出扯断力，列于表12. 37右 边.%表示第=1,2,，9）号试验中的第顶（顶=1,2,，5）个样品的测试结果.因素表 12.21产量/kg34. 2334. 2733. 0459. 16单变量方差分析SPSS求解：列号13.406. 2735. 2132. 9434. 6634. 2133. 13因素表 12.21产量/kg34. 2334. 2733. 0459. 16单变量方差分析SPSS求解：列号13.406. 2735. 2132. 9434. 6634. 2133. 1333. 3333. 0433. 437.073-470. 330. 636.506. 803. 976. 573

31、6. 73 33. 4635. 6334. 3030. 70 31- 3032. 0831. 7332. 98100.64解因素A因素El因素AE1因素AB2因素c因素AC1因素AC2因素BC1因素BC2产量11111111111.3021111222224.6331111333337.234122211123.6051222222313.6761222333126.2371333111321.3781333222134.7391333333217.0710212312311.47112123231223.47122123312336.1313223112323.33142231231313.

32、40152331312125.8016231212332.63172312231133.97182312312216.5019313213211.03203132213223.40213132321336.8022321313223.57233213213313.97243213321126.83253321132321.07263321213133.97273321321216.57File Edi t Vi ew Lata TrarLEformGraphs Utilities Window Help洛旧每国g|c|由爵Reports,方Des:riptive Statisti:e 1 27

33、 :产星6.57Tables卜因素A 因素BCompare卜|因素AC1 |因素AC2 |因素BC1因素BC2 |产量Gener：il Linear ModelUni v：ai_i ate.2111Milted ModelsCorrelate卜Regieszi on卜Muitiv：ai_i ate.Repeated M它.24.63311137.234122V：ai- i:anc e Comporient e.3.505122Logline：ir13.67Zzj6122L-lassi#Data Reducti on卜2 ale,llonp ar:am e tr i c Tests*Tjme S

34、eries卜Smvi v：al*Multiple ReEponze卜Mieeing V：alue.Complen S：ajnples*33126.23713311321.37813322134.73913三33217.07102122311.471121231223.471221212336331422三31313.40Iz152331312125.8016231212332.63172312231133.97182312312216.5019313213211.03203132213223.40213132321336.8022321313223.572332132

35、13313.97243213321126.83253321132321.07263321213133.977-I-!1-I11rTTIr Univariate: lodel1 2B B c c c c abaacaabb 素素素素素素素索索Tests of Between-Subjects Effectsependent Variable:产量SourceType III Sum of SquaresdfMean SquareFSig.Model535.81 9a1928.201443.309.0002.34921.17410.461.0011.0022.5017.878.013因 AB1.8

36、502.4256.679.020因 AB2.4892.2443.042.068150.970275.4091 186.661.000因赢D1.2922.1462.297.163因素.1402.0701.097.379因素SB.1352.0671.059.391因羲芝.1212.060.950.426Error.5098.064Total536.32827a. R Squared = .999 (Adjusted R Squared = .997)1.因素此Dependent Variable:；因素四MeanStd. Error95% Confidence IntervalLower BoundUpper Bound14.081.0343.S874.27523.354.0353.1583.55133.690.0343.4963.S04占因素Be pen dent Mari able:产堂因素日MeanStd. Error95% Confidence IntervalLower BoundUpper Bound13.710.0343.5243.91223.449.0933.2353.66333.959.0323.7694.149e p