SPC-VI-Training[1]

Classified-InternalUseOnly1STATISTICALHYPOTHESISTESTING统计假设检验Chi-Square-Test–检验F-TestF─检验T-TestT─检验2RonChen陈荣生Classified-InternalUseOnly2TerminologyAndConcepts术语和概念•Nullhypothesis.原假设(无差异假设)•Alternativehypothesis(Experimentalhypothesis).备择假设(调查假设)．•Allhypothesistestingisdoneundertheassumptionthatthenullhypothesisistrue.无差异推定．•Goodness-of-fittest(frequencydistributiontest).吻合性检验(频率分布检验)．•Thereisnoenoughevidencetoindicatethat….没有充分证据表明….•Thereisevidencetoindicatethat….有证据表明…Classified-InternalUseOnly3TerminologyAndConcepts术语和概念•Degreesoffreedomv=n-1自由度:v=自由度n=样品数或类型数•Confidencelevel(1–a)a=假警率置信度•MereChanceCoincidence随机符合•Ifyourtestdoesnotresultinasignificantdifferenceyoucannotsaythesubjectstestedare“equal”,theyarejustnotdifferent.如检验统计值未显示显著差异，可认为受检验对象无差异，但不能说“等同”．Classified-InternalUseOnly4SampleDistribution样本分布NumberofFlowers(orDigits)in10TossesofaCoinNumberofHeads(orDigits)ProbabilityClassified-InternalUseOnly5─检验的应用TheApplicationOfChi-squareTest2Classified-InternalUseOnly6Chi-SquareProceduresForTheAnalysisOfCategoricalFrequencydata(goodness-of-fittest)方法用于频率分布检验2Classified-InternalUseOnly7AVersionofChi-SquareToTestExpectedDistribution预期分布的检验鱼1鱼2鱼3总数测得频率8929.7%12040.0%9130.3%300100%预期频率10033.3%10033.3%10033.3%300100%O=ObservedFrequency(测得频率)E=ExpectedFrequency(预期频率)鱼1=鱼2=鱼3==1.21+4.0+0.81=6.022Classified-InternalUseOnly8EmpiricalApproximationOfASamplingDistribution重复采样得出的分布222样本值2样本百分率Ournullhypothesis:Threespeciesoffishinhabittheriverinidenticalproportionsofonethirdeach.Whatdoestheleftdistributiontellus?isthehypothesistruein95.01%cases.我们的无差异假设是三种鱼在大河中生长的比例各1/3．左图表明了什么？有充分证据认为三种鱼在大河中各为1/3的比例已发生显著改变了吗？Classified-InternalUseOnly9FrequencyDistributionOfProcessVariance过程方差的频率分布向正值方向偏斜的不对称曲线,带有一明显的峰(众数)Nonsymmetricalandpositivelyskewedcurvewithahump(mode)方差频率密度频率分布Classified-InternalUseOnly10TheoreticalSamplingDistributionOfChi-square(=2)自由度为2时的分布22Obviously,thehighertheconfidencelevel(1–)thebiggerthevalue.置信度要求越高，则值(临界值)也越高222Classified-InternalUseOnly11鱼1鱼2鱼3O8912091E100100100=1.21+4.0+0.81=6.022思考题：HowConfidenceLevelChangesTheCriticalValueOf?提示：你需要多大的把握作判断(选择多大的置信度)?2Classified-InternalUseOnly12Chi-SquareDistributionFordifferentDegreesOfFreedom不同自由度的分布2Classified-InternalUseOnly13Example：JudgeIfConsumers’TastePreferenceHasChanged用─检验判断消费者口味的变化某厂10年前根据市场调查确定可乐／雪碧／芬达产品中消费者首选比例为0.3/0.4/0.3.最近的问卷调查数据如右表．请采用－检验判断消费者的口味选择是否已发生变化．可乐雪碧芬达O11010090E0.30900.401200.30909012090Note:NumberOfSamples:300提示：1.计算检验值．2.计算自由度．3.确定置信度(此案例中，不一定需要选择高置信度)．4.查表得临界值比较检验值与临界值．2222Classified-InternalUseOnly14Example:JudgeIfConsumers’TastePreferenceHasChanged用─检验判断消费者口味的变化0.500.300.200.0510.4551.0741.6423.84121.3862.4083.2195.99132.3663.6654.6427.81543.3574.8785.9899.488可乐雪碧芬达总和O11010090300E9012090300E90=4.444120=3.33390=0=7.777=2)(2EO)120100(22)90110(2)9090(2检验值大于临界值(=0.05):7.7775.991.222我们有95%的把握相信，消费者的首选发生了变化．Classified-InternalUseOnly152CHI-SQUARETABLE─表表左侧为自由度v表上行为假警率阴影部分为假警率2Classified-InternalUseOnly16Chi-SquareProceduresForComparingTheVariabilityOfAProcessWithTheStandardOrSatedOrImpliedVariabilityOfTheProcess-检验用于将实际过程的变异度与标准，或承诺的，或隐示的过程变异度进行比较．2Classified-InternalUseOnly17FormulaforTestingProcessVariance检验过程方差的公式222))(1(sn22式中：n=subgroupsamplesize分组样品数=variancederivedfromsubgroupofsizen样品数为n的分组方差=varianceofthestandardorthemeasurederivedfromthemanufacturer’sstatedspecification标准或根据供应商承诺的规格得出的方差v=degreesoffreedom=n–1自由度=n–1s22Classified-InternalUseOnly18应用验证过程能力MakeDecisionsAboutProcessVariabilityUsing22过程方差可能是一个规定的标准或要求，也可能是设备供应商承诺的规格。Avariance（变异）canbeastandardorarequirement,oritcanbederivedfrom（源自于）asupplier’sstatement（声明）.Interpretation（解释）issometimesnecessaryforasupplier’sstatementofaccuracy.Forexample,whenasupplierstatesitsequipmentwilldeliverproductwithanaccuracyof±2%,itmayactuallymeanthedeliveredvalueswillbewithin±2%ofthetarget.供应商承诺所隐涵的过程能力供应商的承诺有时需要作正确的“译释”．例如：供应商所说的准确度±2%,可能是指其设备的输出值与设定目标的偏离不超出±2%(如右)．Classified-InternalUseOnly19InterpretationOfTheStated“±2%OfAccuracy”供应商承诺的“±2%准确度”的实际含意一个合理的前提是±2%应在±3σ的范围内，即：4%=6σ,σ=4%÷6=0.6667%Itappearsthatthesupplierdidnotreallymeanaccuracywhenstatingtheprocessperformanceof±2%.Thestatementappearstoimplytherangeofvaluesexpectedfromtheprocess.Avalueofσcanbederivedfromthestatement.2testshouldthenbeperformedtoverifythestatement用─检验验证供应商承诺22Classified-InternalUseOnly20PerformingA-testForProcessVariance-检验分析过程方差的步骤222Step1Determinethevalueofσfortheprocess确定过程的标准偏差．Step2Randomlysamplefromtheprocessandcalculatethe3keypiecesofinformation.对过程随机采样，计算３个过程数据．Step3Calculate─teststatistic.计算的统计数据．Step4Calculateappropriatedegreesoffreedom.取合适的自由度．Step5Decideonanacceptablelevelof(falsealarm).确定值．Step6Determinethecriticalvalueoffromthetables.查表确定临界值．Step7Evaluatetheresults.评价结果．222Classified-InternalUseOnly21Example:ComparingProcessVariabilityToAStandard例：将过程的变异度与标准比较Amanufacturerstatesthatitsproportioner（比例调节器，定量器，配合加料器（漏斗））candeliversugarproductwithBrixvarying（变更，变化）nomorethan±1.5%ofthetarget.制造商声称其混比器能做到白利度偏差不超过目标值的±1.5%.Inordertoverifys