GBT27408-2010实验室质量控制非标准测试方法的有效性评价线性关系.pdf 21页

'ICS03.120.30CCS41中华人民共和国国家标准GB/T27408—2010实验室质量控制非标准测试方法的有效性评价线性关系Qualitycontrolinlaboratoriesevaluatingvalidityofnon-standardtestmethodforalinearrelationship2011-01-14发布2011-07-01实施中华人民共和国国家质量监督检验检疫总局发布中国国家标准化管理委员会 GB/T27408-2010前言本标准按照GB/T1.1-2009给出的规则起草。本标准参考采用以下两个ASTM标准：ASTMD7235：2005《使用ASTM标准建立在线分析仪与标准检测方法结果之间的线性相关关系》（StandardGuideforEstablishingaLinearCorrelationRelationshipBetweenAnalyzerandPrimaryTestMethodResultsUsingRelevantASTMStandardPractices）。ASTMD6708：2007《同物料特性度量下两个检测方法之间预期一致性的统计评价与改进》（StandardPracticeforStatisticalAssessmentandImprovementofExpectedAgreementBetweenTwoTestMethodsthatPurporttoMeasuretheSamePropertyofaMaterial）。本标准的附录A为规范性附录，附录B和附录C为资料性附录。本标准由全国认证认可标准化技术委员会提出并归口。本标准起草单位：辽宁出入境检验检疫局、中国合格评定国家认可中心、山东出入境检验检疫局、中国质量认证中心、中国石油天然气股份有限公司大连石化分公司、广东出入境检验检疫局、大连理工大学数学科学学院。本标准主要起草人：王斗文、孙海容、王东、沈烽、吴建国、昃向君、黄道臣、陈世山、郑仙淑、刘健斌、于孝展、冯敬海、王惠。1 GB/T27408-2010实验室质量控制非标准测试方法的有效性评价线性关系1范围本标准规定了：——非标准测试方法（以下简称X法）及其对应标准测试方法（以下简称Y法）之间的线性关系评价。——X法和Y法之间的无偏、常数、比例和线性的偏倚修正分级计算。——X法和Y法之间的方法间精密度。本标准适用于：——在线分析技术（X法）与其对应Y法所用物料特性范围内线性关系的评价。——同一物料特性下相同或不同测量原理的X法和Y法结果间预期一致性的评价。——均匀和稳定物料测量下产生连续数值结果的测量系统。——测量系统性能处于统计受控状态假定下的正态模型描述和预测。2规范性引用文件下列文件对于本文件的应用是必不可少的。凡是注日期的引用文件，仅注日期的版本适用于本文件。凡是不注日期的引用文件，其最新版本（包括所有的修改单）适用于本文件。GB/T27407实验室质量控制利用统计质量保证和控制图技术评价分析测量系统的性能（ASTMD6299，MOD）ASTMD5191TestMethodforVaporPressureofPetroleumProducts(MiniMethod)3术语、定义和符号JJF1001中确立的以及下列术语、定义和符号适用于本标准。3.1术语和定义3.1.1测量复现性measurementreproducibility复现性reproducibility在复现性测量条件下的测量精密度注1：复现性测量条件（reproducibilityconditionofmeasurement）是指不同地点、不同操作者、不同测量系统，对同一或类似被测对象重复测量的一组测量条件。注2：不同的测量系统可采用不同的测量程序。注3：在给出复现性时应说明改变和未变的条件及实际改变到什么程度。注4：有时把在不同实验室，由不同操作者使用不同设备，按相同测量方法，对同一被测对象重复测量的一组测量条件，称为再现性测量条件或再现性条件。3.1.2期间测量精密度测量条件intermediateprecisionconditionofmeasurement期间精密度条件intermediateprecisioncondition除了相同测量程序、相同地点，还可能有改变的其它条件下，在一个较长时间内重复测量同一或相类似被测对象的一组测量条件。注1：改变的条件可包括新的校准、测量标准器、操作者和测量系统。注2：对条件的说明应包括改变和未变的条件以及实际改变到什么程度。注3：在化学中，术语“序列间精密度测量条件”有时用于指“期间精密度测量条件”。3.1.3质量控制样品qualitycontrolsampleQC样品一种存储完整、用量充足的稳定和均质化物料，其物理或化学特性近似于测量系统的常规样品，用于期间精密度条件下测量系统的精密度和稳定性确定和监控。3.1.4总平方和TotalSumofSquares，TSS样品平均值的总变异。2 GB/T27408-20103.1.5近似度平方和closenesssumofsquares，CSS偏倚修正后两个检测方法结果间一致性程度的统计量。注：偏倚修正函数关系式分别有：CSS（无偏修正）、CSS（常数修正）、CSS（比例修正）和CSS2（线性修正）。01a1b3.1.6方法间精密度betweenmethodprecisionR∧XY由操作人员分别按X法和Y法、使用不同的测量设备、在同一物料度量的期间精密度测量条件下，通∧过本标准的评价和适宜的偏倚修正后，利用X法结果预测Y法的估计值Y，以95%概率表示的两个独立测量结果的精密度。注：只有当两个方法之间不存在统计可测的样品偏倚时，R∧才有意义。XY3.2符号N——共用QC样品的水平数Xi，Yi——分别为X法和Y法的第i个QC样品测量结果X，Y——分别为X法和Y法所有QC样品的加权平均值wi——第i个QC样品测量结果差的权数s——期间精密度标准偏差R"s，s——分别为X法和Y法的期间精密度标准偏差RX"()RY"()R"，R"——分别为X法和Y法的期间精密度限XY∧Yi——第i个QC样品X法预测出的Y法结果值∧a，b——分别为Yab=+X的线性相关参数xi，yi——分别为第i个QC样品测量结果平均值与X和Y的离差∧εi——Yi与Yi之差的加权残差值v——ε的标准化值iin——重复测量次数4统计程序4.1QC样品组规定4.1.1同时段选择X法和Y法的物料类型和水平范围。4.1.2N的水平数不少于30。4.1.3样品水平范围之间大于Y法给出的2RY。4.1.4在期间精密度测量条件下，样品低水平和高水平的重复测量大于6次。4.1.5水平下的重复可来自于不同批次物料，这些物料应接近标称的基体和水平（处于1.2RY的范围内）。4.2TSS的统计检验4.2.1按照GB/T27407，分别求得低水平和高水平QC样品的s和s。RX"()RY"()4.2.2X法的TSS和F计算见式（1）：TSSF=X…………………………………………………（1）XN−1式中：3 GB/T27408-20102Xi−XXi1TSSX——∑()，其中，X=∑∑()22/()。isR"()XiissRR""()XX()4.2.3Y法的TSS和F计算见式（2）：TSSF=Y…………………………………………………（2）YN−1式中：2YYi−Yi1TSSY——∑()，其中，Y=∑∑()22/()。isR"()YiissRR""()YY()4.2.4若F计算值大于表A.1中F分布的95％分位数，表明共用QC样品间的变异足够大，继续往下进行；否则，停止本标准的使用。4.3CSS的计算4.3.1无偏修正，CSS0CSS计算见式（3）：02CSS0=−∑wXiii()Y………………………………………（3）i式中：1wi——22。ss+RR""()YX()4.3.2常数偏倚修正，CSS1aCSS计算见式（4）：1a2CSS1a=−∑wYii⎡⎣()Xi+a⎤⎦………………………………（4）i式中：1wi——22；ss+RR""()YX()∑∑wYiiwXiia——ii−。∑∑wwiiii4.3.3比例偏倚修正，CSS1b4.3.3.1假定零特性值具有物理意义、且[(最大Yi)/(最小Yi)]≥2。4.3.3.2b计算见式（5）：0∑wXYiiib0=2222……………………（5）∑∑wXii−−wsiR"()X()YbXii式中：1wi——222。sb+sRR""()YX()4.3.3.3设定b=1。若|b-b0|>0.001b，用b0替代b，继续计算wi；否则停止迭代。4.3.3.4CSS计算见式（6）：1b4 GB/T27408-20102CSS1b=−∑wYii()bXi……………………………………（6）i4.3.4线性偏倚修正，CSS24.3.4.1X和Y计算分别见式（7）和式（8）：∑wXiiX=i………………………………………………（7）∑wii∑wYiiY=i…………………………………………………（8）∑wii式中：1wi——222。sb+sRR""()YX()4.3.4.2xi和yi计算分别见式（9）和式（10）：x=X−X…………………………………………………（9）iiy=Y−Y………………………………………………（10）ii4.3.4.3b计算见式（11）：0∑wxyiiib0=2222………………（11）∑∑wxii−−wsiR"()X()ybxii4.3.4.4设定b=1。若|b-b0|>0.001b，用b0替代b，重新计算wi、X和Y、xi和yi、以及b0；否则停止迭代。4.3.4.5CSS和a计算分别见式（12）和式（13）：22CSS2=−∑wyii()bxi……………………………………（12）iaYbX=−…………………………………………………（13）4.4CSS的统计检验4.4.1相关性的F检验4.4.1.1按式（14），比较F计算值与表A.1中F分布的95％分位数：()TSSXY+TSS−CSS2/N…………………………（14）F=CSS/(N−2)2∧4.4.1.2若F计算值大，表明可以使用X法的结果来预测Y法的Yi，继续往下进行；否则，无法建立Y∧法Yi的预测关系，停止本标准的使用。4.4.2一致性改进的F检验4.4.2.1按式（15），比较F计算值与表A.1中F分布的95％分位数：()CSS−CSS/2F=02……………………………………（15）CSS/(N−2)24.4.2.3若F计算值大，表明使用CSS偏倚修正能改进方法间的预期一致性，继续往下进行；否则，可使用CSS0，进入4.5。4.4.3偏倚修正选择的t检验5 GB/T27408-20104.4.3.1按式（16）或式（17），比较t计算值与表A.2中t分布的97.5％分位数：CSS−CSSt=01………………………………………（16）1CSS/(N−2)2CSS−CSSt=12………………………………………（17）2CSS/(N−2)2式中：CSS1——CSS1a和CSS1b的较小者。4.4.3.2若t2计算值大于分位数，选择CSS2，进入4.5；若t2计算值小于分位数，计算t1。4.4.3.3若t1计算值大于分位数，选择CSS1，进入4.5；若t1计算值小于分位数，选择CSS2。4.5无偏倚效应的R∧XY24.5.1χ检验24.5.1.1所选CSS值与表A.3中χ分布的95％分位数进行比较，其中，CSS0的自由度为N；CSS1a和CSS1b的自由度为N-1；CSS2的自由度为N-2。4.5.1.2若CSS值小于分位数，按式（18）计算R∧：XY()Rb""22+()R2YXR∧=………………………………（18）XY2式中：b——选择CSS0和CSS1a时，b=1。∧∧Y——X法的偏倚修正结果，在对同一样品进行测量时，95%概率下区间Y±R∧涵盖Y法的结果。XY4.5.2A*检验∧4.5.2.1A*统计来自GB/T27407。基于所选CSS，利用Xi预测Yi，按式（19）计算数据集的εi：∧ε=−wYY()……………………………………………（19）iiii4.5.2.2将升序排列后的εi换算为vi，见式（20）：()/sνii=−εεε……………………………………………（20）式中：ε——εi的平均值；sε——εi的标准偏差。4.5.2.3利用表A.4，将vi换算成pi值。将pi值带入式（21）和式（22）：n∑(2ip−+1)[ln(in)ln(1−p+−1i)]………………（21）i=1An=−−n0.752.25AA*=++(1)…………………………………（22）nn24.5.2.4若计算值A*＜0.752，表明系列εi值呈正态分布，准备报告X法和Y法两者间所选的CSS偏倚修正式和R∧；否则，停止本标准的使用。XY4.6有偏倚效应的R∧XY24.6.1若所选CSS值大于表A.3中χ分布的95％分位数，进入4.5.2。6 GB/T27408-20104.6.2若计算值A*＜0.752，表明样品偏倚可以作为随机效应处理，此时使用式（23）来计算R∧；否则，XY停止本标准的使用。⎡⎤⎡⎤bR22()()""R2⎢2(1.96)(2CSSNkN−+)⎥=++XY⎢⎥R∧⎢⎥1……………（23）XY⎢⎥22⎢bR22()()""+R2⎥⎣⎦XY⎢()Nk−∑⎥222⎣bsRX"()+sRY"()⎦式中：CSS——所选的偏倚修正函数式；b——所选CSS函数式的参数；k——选CSS0时，k=0；选CSS1a或CSS1b时，k=1；选CSS2时，k=2。4.6.4准备报告X法和Y法两者间所选的CSS偏倚修正式和R∧。XY4.7评价示例、流程图与调查分析表参见附录B和附录C。5CSS的后续使用与持续确认5.1CSS的使用5.1.1根据X法的预期应用，对所选CSS一致性程度的有效性进行解释：a）所发现样品偏倚的处理；b）s和εi两者间的比较；RY"()c）所选CSS的X法结果使用。5.1.2若认为所选CSS的一致性程度有效，在X法的日常使用中，即可对其测量结果进行偏倚修正。5.2CSS的确认5.2.1参照GB/T27407，绘制时间序列的εi残差图，检查是否出现异常图形。∧5.2.2参照GB/T27407，利用I/MR/EWMA控制图，持续对Yi和Yi之间拟合的CSS偏倚修正进行确认。5.2.3建立跟踪程序，并针对统计失控状态，依次回答和消除可能出现的以下原因：a）是否由于方法间的样品差异所致？b）是否由于X法的统计受控所致？c）是否由于Y法的统计受控所致？5.2.4如果排除了a）~c）的原因，则失控状态有可能来自不同于CSS偏倚修正时所用的QC样品基体。5.2.5基于控制图的性能，使用更多数据结果，重新按第4章进行评价。5.2.6建议日常交替使用X法和Y法，通过GB/T27407，定期监控两个方法之间的偏倚。7 GB/T27408-2010附录A（规范性附录）统计数值表表A.1F分布分位数表（F0.95）n1n223456789101214161820253060120219.0019.1619.2519.3019.3319.3519.3719.3819.4019.4119.4219.4319.4419.4519.4619.4619.4819.4939.559.289.129.018.948.898.858.818.798.748.718.698.678.668.638.628.578.5546.946.596.396.266.166.096.046.005.965.915.875.845.825.805.775.755.695.6655.795.415.195.054.954.884.824.774.744.684.644.604.584.564.524.504.434.4065.144.764.534.394.284.214.154.104.064.003.963.923.903.873.833.813.743.7074.744.354.123.973.873.793.733.683.643.573.533.493.473.443.403.383.303.2784.464.073.843.693.583.503.443.393.353.283.243.203.173.153.113.083.012.9794.263.863.633.483.373.293.233.183.143.073.062.992.962.942.892.862.792.75104.103.713.483.333.223.143.073.022.982.912.862.832.802.772.732.702.622.58123.893.493.263.113.002.912.852.802.752.692.642.602.572.542.502.472.382.34143.743.343.112.962.852.762.702.652.602.532.482.442.412.392.342.312.222.18163.633.243.012.852.742.662.592.542.492.422.372.332.302.282.232.192.112.06183.553.162.932.772.662.582.512.462.412.342.292.252.222.192.142.112.021.97203.493.102.872.712.602.512.452.392.352.282.222.182.152.122.072.041.951.90253.392.992.762.602.492.402.342.282.242.162.112.072.042.011.961.921.821.77303.322.922.692.532.422.332.272.212.162.092.041.991.961.931.881.841.741.68603.152.762.532.372.252.172.102.041.991.921.861.821.781.751.691.651.531.471203.072.682.452.292.182.092.021.961.911.831.781.731.691.661.601.551.431.358 GB/T27408-2010表A.2t分布双侧情形分位数表nt0.975112.706224.302733.182442.776452.570662.446972.364682.306092.2622102.2281112.2010122.1788132.1604142.1448152.1314162.1199172.1098182.1009192.0930202.0860212.0796222.0739232.0687242.0639252.0595262.0555272.0518282.0484292.0452302.0423312.0395322.0369332.0345342.0322352.0301362.0281372.0262382.0244392.0227402.0211412.0195422.0181432.0167442.0154452.0141462.0129472.0117482.0106492.0096502.0086552.0040602.0003651.9971701.9944751.9921801.99006851.98827901.98667951.985251001.983979 GB/T27408-20102表A.3χ分布单侧情形分位数表2nχ0.95714.1815.5916.91018.31119.71221.01322.41423.71525.01626.31727.61828.91930.12031.42132.72233.92335.22436.42537.72638.92740.12841.32942.63043.83549.84055.84561.75067.56079.17090.580101.910 GB/T27408-2010表A.4pi数值表v-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.010.00i-3.50.00020.00020.00020.00020.00020.00020.00020.00020.00020.0002-3.40.00020.00030.00030.00030.00030.00030.00030.00030.00030.0003-3.30.00030.00040.00040.00040.00040.00040.00040.00050.00050.0005-3.20.00050.00050.00050.00060.00060.00060.00060.00060.00070.0007-3.10.00070.00070.00080.00080.00080.00080.00090.00090.00090.0010-3.00.00100.00100.00110.00110.00110.00120.00120.00130.00130.0013-2.90.00140.00140.00150.00150.00160.00160.00170.00180.00180.0019-2.80.00190.00200.00210.00210.00220.00230.00230.00240.00250.0026-2.70.00260.00270.00280.00290.00300.00310.00320.00330.00340.0035-2.60.00360.00370.00380.00390.00400.00410.00430.00440.00450.0047-2.50.00480.00490.00510.00520.00540.00550.00570.00590.00600.0062-2.40.00640.00660.00680.00690.00710.00730.00750.00780.00800.0082-2.30.00840.00870.00890.00910.00940.00960.00990.01020.01040.0107-2.20.01100.01130.01160.01190.01220.01250.01290.01320.01360.0139-2.10.01430.01460.01500.01540.01580.01620.01660.01700.01740.0179-2.00.01830.01880.01920.01970.02020.02070.02120.02170.02220.0228-1.90.02330.02390.02440.02500.02560.02620.02680.02740.02810.0287-1.80.02940.03010.03070.03140.03220.03290.03360.03440.03510.0359-1.70.03670.03750.03840.03920.04010.04090.04180.04270.04360.0446-1.60.04550.04650.04750.04850.04950.05050.05160.05260.05370.0548-1.50.05590.05710.05820.05940.06060.06180.06300.06430.06550.0668-1.40.06810.06940.07080.07210.07350.07490.07640.07780.07930.0808-1.30.08230.08380.08530.08690.08850.09010.09180.09340.09510.0968-1.20.09850.10030.10200.10380.10560.10750.10930.11120.11310.1151-1.10.11700.11900.12100.12300.12510.12710.12920.13140.13350.1357-1.00.13790.14010.14230.14460.14690.14920.15150.15390.15620.1587-0.90.16110.16350.16600.16850.17110.17360.17620.17880.18140.1841-0.80.18670.18940.19220.19490.19770.20050.20330.20610.20900.2119-0.70.21480.21770.22060.22360.22660.22960.23270.23580.23890.2420-0.60.24510.24830.25140.25460.25780.26110.26430.26760.27090.2743-0.50.27760.28100.28430.28770.29120.29460.29810.30150.30500.3085-0.40.31210.31560.31920.32280.32640.33000.33360.33720.34090.3446-0.30.34830.35200.35570.35940.36320.36690.37070.37450.37830.3821-0.20.38590.38970.39360.39740.40130.40520.40900.41290.41680.4207-0.10.42470.42860.43250.43640.44040.44430.44830.45220.45620.46020.00.46410.46810.47210.47610.48010.48400.48800.49200.49600.5000表注：vi为左列和顶行数字的和。11 GB/T27408-2010续表A.4v0.000.010.020.030.040.050.060.070.080.09i0.00.50000.50400.50800.51200.51600.51990.52390.52790.53190.53590.10.53980.54380.54780.55170.55570.55960.56360.56750.57140.57530.20.57930.58320.58710.59100.59480.59870.60260.60640.61030.61410.30.61790.62170.62550.62930.63310.63680.64060.64430.64800.65170.40.65540.65910.66280.66640.67000.67360.67720.68080.68440.68790.50.69150.69500.69850.70190.70540.70880.71230.71570.71900.72240.60.72570.72910.73240.73570.73890.74220.74540.74860.75170.75490.70.75800.76110.76420.76730.77040.77340.77640.77940.78230.78520.80.78810.79100.79390.79670.79950.80230.80510.80780.81060.81330.90.81590.81860.82120.82380.82640.82890.83150.83400.83650.83891.00.84130.84380.84610.84850.85080.85310.85540.85770.85990.86211.10.86430.86650.86860.87080.87290.87490.87700.87900.88100.88301.20.88490.88690.88880.89070.89250.89440.89620.89800.89970.90151.30.90320.90490.90660.90820.90990.91150.91310.91470.91620.91771.40.91920.92070.92220.92360.92510.92650.92790.92920.93060.93191.50.93320.93450.93570.93700.93820.93940.94060.94180.94290.94411.60.94520.94630.94740.94840.94950.95050.95150.95250.95350.95451.70.95540.95640.95730.95820.95910.95990.96080.96160.96250.96331.80.96410.96490.96560.96640.96710.96780.96860.96930.96990.97061.90.97130.97190.97260.97320.97380.97440.97500.97560.97610.97672.00.97720.97780.97830.97880.97930.97980.98030.98080.98120.98172.10.98210.98260.98300.98340.98380.98420.98460.98500.98540.98572.20.98610.98640.98680.98710.98750.98780.98810.98840.98870.98902.30.98930.98960.98980.99010.99040.99060.99090.99110.99130.99162.40.99180.99200.99220.99250.99270.99290.99310.99320.99340.99362.50.99380.99400.99410.99430.99450.99460.99480.99490.99510.99522.60.99530.99550.99560.99570.99590.99600.99610.99620.99630.99642.70.99650.99660.99670.99680.99690.99700.99710.99720.99730.99742.80.99740.99750.99760.99770.99770.99780.99790.99790.99800.99812.90.99810.99820.99820.99830.99840.99840.99850.99850.99860.99863.00.99870.99870.99870.99880.99880.99890.99890.99890.99900.99903.10.99900.99910.99910.99910.99920.99920.99920.99920.99930.99933.20.99930.99930.99940.99940.99940.99940.99940.99950.99950.99953.30.99950.99950.99950.99960.99960.99960.99960.99960.99960.99973.40.99970.99970.99970.99970.99970.99970.99970.99970.99970.99983.50.99980.99980.99980.99980.99980.99980.99980.99980.99980.9998表注：vi为左列和顶行数字的和。12 GB/T27408-2010附录B（资料性附录）评价示例B.1简介在汽油饱和蒸气压的测量过程中，根据GB/T27407和本标准的统计程序，研究和评价在线分析（X法）和ASTMD5191（Y法）之间的相关函数式。B.2sR"估计B.2.1根据4.1，选择N=27的同时段样品水平，基于GB/T27407，分别利用X法和Y法，对低水平9psi（61.9kPa）和高水平15psi（103.2kPa）的QC样品进行测量，给出sR"的估计值：a）在9psi（61.9kPa）水平下，s=0.020psi（0.14kPa），s=0.040psi（0.27kPa）；R"()XR"()Yb）在15psi（103.2kPa）水平下，s=0.040psi（0.27kPa），s=0.070psi（0.48kPa）。R"()XR"()Y方法间水平下的sR"插值估计见表B.1。表B.1X法和Y法之间水平下的sR"插值估计，psiNXisRX"()YisRY"()110.450.02510.270.046210.440.02510.230.046310.450.02510.180.046410.410.02510.240.04658.900.0208.820.039610.460.02510.250.046710.470.02510.250.046810.410.02510.300.047910.280.02410.040.0451012.590.03212.340.0571112.630.03212.240.0561210.440.02510.360.0471312.520.03212.180.0561412.630.03212.430.0571512.500.03212.300.0571612.650.03212.370.0571714.090.03713.780.0641812.540.03212.200.0561914.040.03713.720.0642015.360.04115.010.0702115.740.04215.360.0722215.700.04215.230.0712315.760.04215.270.0712415.800.04215.390.0722515.750.04215.400.0722615.800.04215.450.0722715.780.04215.520.073B.2.2F检验表明，表B.1中不同水平间的sR"存在显著性差异，则需使用线性拟合来对sR"进行估计，估计的结果如下：a）s=0.020+0.0033(X-9)，R"=0.009141(X-2.9394)；R"()XXb）s=0.040+0.005(Y-9)，R"=0.01385(Y-1)。R"()YY13 GB/T27408-2010B.3TSS的统计检验B.3.1TSS计算根据4.2，表B.2分别给出了X法和Y法的TSS计算结果。表B.2X法与Y法结果的TSS统计X法Y法NXs22[(XXs−)/]2s22[(YYs−)/]2iR"(X)1/[sR"(X)]Xi/[sR"(X)]iRX"()YiR"(Y)1/[sR"(Y)]Xi/[sR"(Y)]iRY"()110.450.0251627.917011.32757.710.270.046465.54780.5936.0210.440.0251632.217040.42807.710.230.046469.54803.2998.1310.450.0251627.917011.32757.710.180.046474.74831.91079.4410.410.0251645.417128.22961.310.240.046468.54797.5982.358.900.0202584.623002.821016.28.820.039654.15769.25380.4610.460.0251623.616982.42708.310.250.046467.54791.8966.7710.470.0251619.216953.52659.410.250.046467.54791.8966.7810.410.0251645.417128.22961.310.300.047462.54763.6891.0910.280.0241704.217518.73690.310.040.045489.54914.21329.41012.590.032986.012413.3693.112.340.057311.13838.4132.21112.630.032977.812350.2754.612.240.056316.63875.396.51210.440.0251632.217040.42807.710.360.047456.64730.1805.21312.520.0321000.412525.4590.812.180.056320.03897.877.51412.630.032977.812350.2754.612.430.057306.23805.7168.61512.500.0321004.612557.7562.812.300.057313.33853.1117.31612.650.032973.812318.8786.112.370.057309.43827.4143.91714.090.037738.510406.14038.613.780.064244.93374.81071.81812.540.032996.312493.2619.312.200.056318.93890.383.61914.040.037745.210462.73902.713.720.064247.23391.91020.82015.360.041595.29142.87750.515.010.070203.83058.92248.92115.740.042560.48821.08915.015.360.072194.02979.52615.52215.700.042563.98853.88791.915.230.071197.53008.52478.22315.760.042558.78804.68976.515.270.071196.42999.52520.32415.800.042555.28772.29099.715.390.072193.22972.92647.32515.750.042559.58812.88945.715.400.072192.92970.72657.92615.800.042555.28772.29099.715.450.072191.62959.72711.22715.780.042556.98788.49038.115.520.073189.72944.52785.9TSS计算30248.1355462.4130446.99122.4106622.937912.8XY或11.7511.69式（1）的计算有：2Xi1Xi−XX=∑∑()22/()=（355462.4）/（30248.1）=11.75，TSS=(∑)=130446.9iissRR""()XX()XisR"()X式（2）的计算有：2Yi1YYi−Y=∑∑()22/()=（106622.9）/（9122.4）=11.69，TSSY=(∑s)=37912.8iissRR""()YY()iR"()YB.3.2F检验TSSTSS基于表A.1，因为F=X=5017.2＞＞F0.95(27,26)=1.93，F=Y=1458.2＞＞F0.95(27,26)=1.93，XN−1YN−1表明共用样品N之间存在显著性差异，即X法和Y法足以辨别QC样品间的变异。14 GB/T27408-2010B.4CSS的计算B.4.1CSS和CSS01a根据4.3，表B.3分别给出了CSS和CSS的CSS计算结果。01a表B.3CSS0与CSS1aXY-Xw2wXwY2NYiiiiiwi(Yi-Xi)iiiiwi(Yi-Xi-a)110.2710.45-0.18364.8311.823812.483746.811.448210.2310.44-0.21364.8316.093808.833732.210.397310.1810.45-0.27364.8326.603812.483713.970.266410.2410.41-0.17364.8310.543797.883735.861.94458.828.90-0.08520.563.334633.004591.3613.831610.2510.46-0.21364.8316.093816.133739.510.397710.2510.47-0.22352.8617.083694.423616.800.187810.3010.41-0.11352.864.273673.253634.446.242910.0410.28-0.24384.4722.153952.333860.050.0031012.3412.59-0.25234.0314.632946.412887.900.0111112.2412.63-0.39240.3836.563036.062942.315.1941210.3610.44-0.08352.862.263683.843655.619.3751312.1812.52-0.34240.3827.793009.622927.882.2621412.4312.63-0.2234.039.362955.772908.960.4331512.3012.50-0.2234.039.362925.352878.540.4331612.3712.65-0.28234.0318.352960.452894.920.3201713.7814.09-0.31182.9817.582578.232521.500.8211812.2012.54-0.34240.3827.793014.422932.692.2621913.7214.04-0.32182.9818.742569.082510.521.0852015.0115.36-0.35151.9518.612333.992280.811.7402115.3615.74-0.38143.9320.782265.402210.712.7012215.2315.70-0.47146.9532.462307.132238.067.5722315.2715.76-0.49146.9535.282315.942243.948.9652415.3915.80-0.41143.9324.192274.042215.034.0142515.4015.75-0.35143.9317.632266.842216.471.6482615.4515.80-0.35143.9317.632274.042223.661.6482715.5215.78-0.26140.989.532224.732188.070.041CSS计算6973.5486.5182942.181248.675.24X或Y11.89411.651式（3）的计算有：12∑wi==226973.5，CSS0=−∑wXiii()Y=486.51。issRR""()YX+()i式（4）的计算有：∑∑wYiiwXii2iiCSS=−wY⎡⎤X+a=75.24a=−=−=11.65111.894−0.243，1a∑ii⎣⎦()i。∑∑wwiiiiiB.4.2CSS2根据4.3，因为CSS假定不合适，故进入CSS的计算。1b215 GB/T27408-2010B.4.2.1第1次迭代表B.4给出了CSS的第1次迭代。2表B.4CSS2拟合的第1次迭代2NYXwwXwYxywxy2⎡⎤ws()ybx−iiiiiiiiiiiiwixi⎣⎦iiRX"()i110.2710.45364.833812.53746.8-1.4-1.4727.46760.560.329210.2310.44364.833808.83732.2-1.5-1.4753.71771.140.090310.1810.45364.833812.53714.0-1.4-1.5774.87760.560.061410.2410.41364.833797.93735.9-1.5-1.4763.85803.290.44158.828.9520.564633.04591.4-3.0-2.84412.084665.872.875610.2510.46364.833816.13739.5-1.4-1.4732.88750.060.090710.2510.47352.863694.43616.8-1.4-1.4703.89715.370.041810.310.41352.863673.33634.4-1.5-1.4707.37776.931.373910.0410.28384.473952.33860.1-1.6-1.6999.581001.350.0011012.3412.59234.032946.42887.90.70.7112.25113.420.0031112.2412.63240.383036.12942.30.70.6104.23130.271.2811210.3610.44352.863683.83655.6-1.5-1.3662.29745.832.0641312.1812.52240.383009.62927.90.60.579.6294.250.5581412.4312.63234.032955.82909.00.70.8134.21126.820.1031512.312.5234.032925.32878.50.60.692.0685.990.1031612.3712.65234.032960.42894.90.80.7127.23133.810.0771713.7814.09182.982578.22521.52.22.1855.55882.540.2071812.212.54240.383014.42932.70.60.585.27100.360.5581913.7214.04182.982569.12510.52.12.1812.51842.810.2732015.0115.36151.952334.02280.83.53.41769.151825.590.4462115.3615.74143.932265.42210.73.83.72053.162129.080.6872215.2315.7146.952307.12238.13.83.62001.792128.841.9662315.2715.76146.952315.92243.93.93.62056.072196.492.3272415.3915.8143.932274.02215.03.93.72102.062196.031.0212515.415.75143.932266.82216.53.93.72080.702140.170.4202615.4515.8143.932274.02223.73.93.82135.792196.030.4202715.5215.78140.982224.72188.13.93.92119.772129.160.010求和6973.582942.181248.629959.431202.617.82XY或11.8911.65b00.9607根据式（7）~式（11），CSS的第1次迭代计算有：2∑wXii∑wYiii，Y==i11.65，wxy=29959.4，wx2=31202.6，X==11.89∑iii∑ii∑wi∑wiii222∑wxyiii∑wsiiR"()X(ybx−=i)17.82，b0==22220.9607。∑∑wxii−−wsiR"()X()yibxi因为|b-b0|=0.0393＞0.001b，需再次迭代。B.4.2.2第2次迭代表B.5给出了CSS的第2次迭代。216 GB/T27408-2010表B.5CSS2拟合的第2次迭代222NYiXiwiwiXiwiYixiyiwixiyiwixi⎡⎤⎣⎦wsiiRX"()()ybx−iwi(yi-bxi)110.2710.45371.363880.73813.8-1.4-1.4742.77776.570.0030.029210.2310.44371.363876.93799.0-1.5-1.4769.53787.350.0510.173310.1810.45371.363880.73780.4-1.4-1.5791.10776.570.6062.449410.2410.41371.363865.83802.7-1.5-1.4779.87820.130.0180.11158.828.9529.054708.64666.2-3.0-2.84490.784749.070.2291.362610.2510.46371.363884.43806.4-1.4-1.4748.30765.870.0480.161710.2510.47358.963758.33679.3-1.4-1.4718.28730.030.0880.333810.310.41358.963736.83697.3-1.5-1.4721.83792.750.4482.145910.0410.28391.144020.93927.1-1.6-1.61019.701021.570.3231.2961012.3412.59238.433001.82942.20.70.7113.64114.810.0240.0861112.2412.63245.033094.82999.20.70.6105.53131.980.8593.5031210.3610.44358.963747.53718.8-1.5-1.3675.90761.070.9004.2201312.1812.52245.033067.82984.50.60.580.5495.380.3231.3301412.4312.63238.433011.42963.70.70.8135.94128.420.3001.1831512.312.5238.432980.42932.70.60.693.1486.960.2591.0251612.3712.65238.433016.12949.40.80.7128.86135.520.0030.0191713.7814.09186.582629.02571.12.22.1870.62898.070.0180.0431812.212.54245.033072.72989.40.60.586.28101.590.3161.3031913.7214.04186.582619.62559.92.12.1826.78857.600.0020.0022015.0115.36155.002380.92326.63.53.41802.351859.830.0340.0802115.3615.74146.802310.62254.83.83.72091.702169.030.0070.0072215.2315.7149.952354.12283.73.83.62040.172169.670.2391.0732315.2715.76149.952363.12289.73.93.62095.522238.660.3591.5712415.3915.8146.802319.42259.23.93.72141.542237.270.0070.0642515.415.75146.802312.12260.73.93.72119.772180.330.0750.2042615.4515.8146.802319.42268.03.93.82175.932237.270.0820.2252715.5215.78143.742268.22230.83.93.92158.742168.260.6702.370求和7101.7844828275730525.131791.66.2926.37XY或11.9011.65b00.9604根据式（7）~式（11），CSS的第2次迭代计算有：22222∑wxyiii=30525.1，∑wxii=31791.6，∑wsiiR"()X()ybx−=i6.29，∑wxyiii30525.1。b===0.960402222∑∑wxii−−wsiR"()X(yibxi)31791.6−6.29因为|b-b0|=0.0003＜0.001b，停止迭代，用b0=0.9604，带入CSS2中，有：2CSS2=−∑wyii()bxi=26.37，aYbX=−=11.65−0.960411.90×=0.2212。iB.5CSS的统计检验根据4.4的式（14）~式（17），F和t检验如下：()TSSXY+−TSSCSS2/NFF==5926.7＞＞(27,25)1.94=，表明方法间显著相关。0.95CSS/(N−2)2()CSS−CSS/2FF==02219.0＞＞(2,25)=3.38，表明CSS偏倚修正能进一步改进X法整个0.95CSS/(N−2)2操作区间的预期一致性。∧CSS−CSStt==126.83＞=(25)=2.0595，其中，CSS1=CSS1a=75.38。选择YX=+0.22120.9604。20.975CSS/(N−2)217 GB/T27408-2010B.6R∧计算与结果报告XY2B.6.1χ检验22根据4.5.1，因CSS2=26.37，χχ==26.37＜0.95(25)37.7，则可使用式（18）来建立R∧。XYB.6.2R∧计算XY已知B.2.3中的估计有：R"=0.00914(X-2.939)；R"=0.01385(Y-1)，则式（18）的计算有：XY""222()Rb+()R22YXRY∧==[]0.0000959(−1)+[0.0000385(X−2.939)]XY2B.6.3正态性检验根据4.5.2，表B.6给出了式（19）~式（22）的A*统计汇总结果。表中的计算结果有A*=0.253＜A*=0.752，接受X法和Y法系列结果的正态性统计假定。B.6A*统计汇总NYiXiwiwiYi拟合值εivivi升序piA的第i项110.2710.45371.4219.27210.260.2430.13-1.850.0322-7.243210.2310.44371.4219.27210.25-0.343-0.46-1.60.0548-17.485310.1810.45371.4219.27210.26-1.491-1.60-1.180.1190-23.411410.2410.41371.4219.27210.220.4050.29-1.180.1190-28.99658.828.9529.1423.0038.771.1791.07-1.140.1271-36.113610.2510.46371.4219.27210.27-0.327-0.44-1.130.1292-43.269710.2510.47371.4219.27210.28-0.512-0.63-0.960.1685-39.189810.310.41359.0218.94810.221.5351.42-0.630.2643-37.945910.0410.28391.2119.77910.09-1.070-1.18-0.460.3228-36.4401012.3412.59238.4815.44312.310.4230.31-0.440.3300-39.5341112.2412.63245.0815.65512.35-1.739-1.85-0.180.4286-37.7881210.3610.44359.0218.94810.252.1262.01-0.120.4522-39.2541312.1812.52245.0815.65512.25-1.024-1.140.090.5359-36.0971412.4312.63238.4815.44312.351.2191.110.130.5517-37.7201512.312.5238.4815.44312.231.1401.030.150.5596-39.0971612.3712.65238.4815.44312.37-0.004-0.120.250.5987-34.5601713.7814.09186.6213.66113.750.3660.250.290.6141-34.5601812.212.54245.0815.65512.26-1.012-1.130.310.6217-30.6521913.7214.04186.6213.66113.710.2020.090.350.6368-31.1202015.0115.36155.0312.45114.970.4610.350.520.6985-25.9642115.3615.74146.8312.11715.340.2680.150.550.7088-21.6772215.2315.7149.9812.24615.30-0.851-0.961.030.8485-13.0132315.2715.76149.9812.24615.36-1.067-1.181.070.8577-13.0252415.3915.8146.8312.11715.40-0.067-0.181.110.8665-12.6902515.415.75146.8312.11715.350.6360.521.420.9222-10.1772615.4515.8146.8312.11715.400.6600.551.610.9463-5.6892715.5215.78143.7711.99015.381.7231.612.010.9778-2.925求和7115.4429.77336.92-735.63平均值0.114A=0.246标准偏差1.004A*=0.253表中：A的第i项——(2i-1)[ln(pi)+ln(1-pn+1-i)]。B.6.4结果报告结果报告如下：∧a）X法和Y法两者间所选的偏倚修正式为：YX=+0.22120.9604；22b）X法和Y法的方法间精密度（不确定度）为：RYX∧=−[]0.0000959(1)+−[0.0000385(2.939)]。XY18 GB/T27408-2010附录C（资料性附录）流程图与调查分析图C.1评价过程流程图表C.1评价结论调查与分析两种方法足以辨别两种方法之间偏倚修正能改进两种若存在偏倚，可否若不存在偏倚，存在样品偏倚？评价结果QC样品间的差异？呈显著相关？方法之间的一致性？处理为随机效应？残差随机发散？可辨别相关不能不存在—发散合格可辨别相关不能不存在—非发散不合格可辨别相关不能存在可以—合格可辨别相关不能存在不可以—不合格可辨别相关能不存在—发散合格可辨别相关能不存在—非发散不合格可辨别相关能存在可以—合格可辨别相关能存在不可以—不合格可辨别不相关————不合格无法辨别—————不合格19'