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DETERMINE NDT LABORATORY INSPECTION UNCERTAINTY BY ROBUST ISOGUM METHOD P. Tong1, W. Su2 1 China Steel Corporation, Kaohsiung, Taiwan, 2Far-East College, Tainan, Taiwan Abstract: In order to fulfil the requirement of ISO 17025 laboratory accreditation requirement, NDT laboratory inspection uncertainty evaluation must be done for each NDT laboratory. This paper introduce a Robust ISOGUM model by adding Z_score and robust CV coefficient check to original ISO-GUM model, the advantage of this model is able to identify bad performance operator and improve laboratory uncertainty, and is also very easy to apply compare with ISO 5725 model. Both ISO 5725 and Robust ISO-GUM models use a UT weld inspection example to demonstrate the application results. Introduction: The purpose of determining NDT laboratory inspection uncertainty is to evaluate inspection capability and also to fulfil the requirement of ISO 17025 laboratory accreditation requirement of evaluating laboratory performance capability. Two evaluation models were proposed , they are ISO 5725 mode and ISO-GUM model. ISO 5725 model is sophisticated is calculation but has the advantage of finding poor inspection operators, while ISO-GUM is easy to apply but without the function of identifying bad inspection data. This paper introduce a new Robust ISO-GUM model to achieve the goal of good and easy operated laboratory inspection uncertainty evaluation.. Model 1 ISO 5725 Accuracy of measurement method: (1)Original Data Set ij n = Number of Inspections by operator i on defect j. ijk y = The kth data on defect j by operator i. j p= Number of operators on defect j inspections.ij y ij y ij n d ijd Average data on defect j by operator i. = ∑ = 1 n yj p = ∑ Average data of defect j. j y S ij ij n 1 d Sample variance of defect j by operator i. ij - = ∑ = () ()y ijd - y 2 ij n 1 (2)Outlier data check Single outlier observation Gc j S S = ∑ = ratio of maximum Sdj to total sum of Sdj () ( ) 1 P d dj max , = 1 dj S = Variance between NDT operators P dj b P Y = ∑ = j 1 j y - 2 - G - 1= max d p S y y
[]b j()= ij G - [] S y y () G,Grepresent contribution of max and minimum yij to deviation.1 p 2 p Dual outlier observation ()2 S o y y 2== - ∑p d dj j 1 S 2 o 2 p d 2=∑∑ - = 2 1 - dj y - p d - = 2 1 y () p 2 L dj j G = = Variance ratio of two smallest data. 2 L 3 p S S p p 2 S 2 o h p y y 2 2 =∑∑ == - - ()d dj dj j 3 3 d S 2 h 4 p S G = = Variance ratio of two largest data check. Compare with 1% and 5% critical value of Cochran's table and Grubb's table to determine the operator's data is accepted, suspected or rejected. Mandel's suspected data re-check [ ]b j ijij S y y H - = = average deviation ratio of suspected data ∑ = S a j p 1 d j a p = S 2 dj = variation deviation ratio of suspected data Compare with 1% and 5% critical value of Mandel's H and K Test to determine the operator's data is either accepted or rejected. Operator of rejected data is considered to be incompetent operator, data should be deleted from laboratory data set for uncertainty evaluation. (3)Laboratory inspection uncertainty evaluation () ( S K = ij S ij rj 2 1 n S 1 S )=repeatability variance() ()∑ - = p 1 i n 2 ij j p 1 i ij ∑ - j = ij S =Variance within operators ()() = dj p n y 2 - - = ∑∑ ∑ p i y n 2 2 y p y n p i ij ij j j - = - 1 p i 2 i ()ij ij ij j 1 = 1 == 1 1 j j p i p j S Lj p n n dj ij 2 1 ) = ∑S 2 - S 2 ( 2 rj ∑ ∑P i n - 2 - = 1 i = 1 = 1 ij ij j = Uj = 2 S + Rj S Lj rj S 2 = = Laboratory test uncertainty Model 2 Robust ISOGUM Method: (1)Outlier data check Median = middle data of yij Normalized interquartile-range(IQR) = Q3 (upper quartile) - Q1(lower quartile), by align yij in increasing series. Deviation = yij - median Z_score = (yij - median)/ Normalized IQR |Z_score| ≤ 2 accepted, 2 < |Z_score| < 3 suspected, |Z_score| ≥ 3 rejected From Z_score data to decide the operator's data is acceptable or not, suspected or rejected. Operator of Z_score greater than 3 is considered to be incompetent operator, this data should be deleted from laboratory data set for uncertainty evaluation. (2) Robust CV coefficient Coefficient of variance of all operators(CVall) = Standard deviation of all yij / Average of all yij Coefficient of variance of good operators(CVgood) = Standard deviation of good yij / Average of j U ( ∑U d / j ) 2 d = 1 good yij Robust CV coefficient (R-CV)= |CVall -- CVgood|/ CVgood X 100% Inspection data is improved obviously if R-CV is greater than 50%. (3) Laboratory inspection uncertainty evaluation System modelling equation Mj = F(y1j,y2j,....ypj) = ( y1j +y2j +.... + ypj ) / pj =[( y1j +∆1j ) + (y2j+∆2j )+..... +(ypj+∆pj )]/ pj =[ y1j+y2j+..... +ypj] / pj + (∆1j +∆2j +..... +∆3j )] / pj = yj + ∆j σ( Mj)2 =(∂ Mj )/∂σ( yj)~σ( yj)2 +(∂ Mj )/∂σ( ∆j)~σ(∆j)2 =σ( yj)2 + σ(∆j)2 σ( yj) comes from reading error, by square distribution y σ mm σ(∆j) comes from covariance of data of yj σ(∆j) = j ( = ) = ) 3 / 1 ( . 0 577 S Uj = 2~σ(Mj) ) = ∑ ∑ ∑ n y y () ) 1 ( - - j = = Laboratory test uncertainty Results: The test sample is from inside company weld UT inspection by 16 operators following AWS D1.1 code. Table 1 is original data set. Table 2 is uncertainty calculation by ISO 5725 model, operator No.9 and No.12 are identified as incompetent operator form Grubb's test check and H and K test. After remove these two operator's data, laboratory uncertainty is 8.38. Table 3.1 and 3.2 is uncertainty calculation by Robusted ISO-GUM Model, operator No.9 and No.12 are identified as incompetent operator form Z_score test and re-confirmed by robust CV coefficient. After remove these two operator's data, laboratory uncertainty is 8.29. Discussion: Both Robust ISO-GUM model and ISO 5725 model get similar results in poor operator identification and laboratory uncertainty evaluation, but Robust ISO-GUM model is much easier to apply. The ISO-GUM model is modified by adding Z_score and robust CV coefficient to identify bad performance operator and keep the advantage of easy calculation of laboratory inspection uncertainty . The advantage of Robust ISO-GUM model to original ISO- GUM model is to kick off poor operators for further training and to improve laboratory uncertainty value at the same time. Conclusions: The robust ISOGUM model by adding Z_score and robust CV coefficient check to original ISOGUM mode has the advantage of identifying bad performance operators to improve laboratory uncertainty, and is also very easy to apply for calculating NDT laboratory uncertainty for fulfilling the requirement of ISO 17025 laboratory accreditation requirement. References: 1. ISO Guide to the Expression of Uncertainty in Measurement (ISO-GUM). 2. ISO 5725 Accuracy (trueness and precision) of measurement methods and results. 3. ISO 17025 Guide for laboratory Accreditation d d U ( ∑ = 2 j U / 1 Table 1 Original data set Operator #
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Table 2 Laboratory Inspection Uncertainty Evaluation by ISO 5725 model Def-1 Def-2 Def-3 Def-4 5% value 1% l value Table 3.1 Laboratory Inspection Uncertainty Evaluation by Robusted ISO-GUM model (Z_score for finding poor inspection data) Operator #
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Table 3.2 Laboratory Inspection Uncertainty Calculation Def-1 Def-2 Def-3 Def-4 |
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