Comparison of independent process analytical measurements a variographic study

Transcription

1 WSC 7, Raivola, Ruia, February, 010 Comparion of independent proce analytical meaurement a variographic tudy Atmopheric emiion Watewater Solid wate Pentti Minkkinen 1) Lappeenranta Univerity of Technology ) Aalborg Univerity Campu Ebjerg Pentti.Minkkinen@lut.fi Pentti Minkkinen

2 Outline Proce analytical chemitry meaurement ytem Why comparion are needed Calibration Performance tet of meaurement ytem Comparion of proce mean Data analyi method Incorrect Correct

3 Proce Analytical Chemitry Off-line analyi At-line analyi On-line analyi In-line analyi Non-invaive analyi

4 Student t-tet Mot widely ued tatitical tet in teting the equality of the mean value of two meaurement et Baic aumption: Set independent Normal ditribution (enitive to nonnormality) Aumption eldom met in proce analyi

5 t-tet for comparing mean Two meaurement et: x1, x1, 1, n1, 1 x, x n i n i,,, n i = number of meaurement 1 d x x 1 = degree of freedom = difference of the two mean QUESTION: I d ignificantly different from zero?

6 1 F , A) Standard deviation of both et can be aumed to be equal 1, confirmed with F-tet If thi i not ignificant the tandard deviation can be pooled. (1) ()

7 The tandard deviation of the difference with freedom, i degree of d n 1 n Two way to detect if d i different from zero (3) a) If the confidence interval, ci, doe not include zero ci d t, b) t-tet d (4) t d d 0 (5)

8 B) Standard deviation not equal The tandard deviation of the difference d i calculated a * d 1 The degree of freedom have to be etimated by uing Satterthwaite formula * 1 n 1 n 4 d n 1 1 n (F-tet ignificant) Significance etimated either by uing Eq. 4 or 5 (6) (7)

9 C) Parallel determination on ame ample d x1 x, d,, n, n d 1 ci d or on t-tet t, d n SD of the difference Concluion on ignificance can be baed on confidence interval (8) t d d 0 n (9)

10 Pitfall Tet A) and B) cannot be ued to tet difference of analytical method, if tet are carried out on different ample (betweenample variance will mak the analytical variance) Tet C) eliminate the between-ample variance. However, if the analytical variance i dependent on concentration d i are not normally ditributed All tet fail, or are inefficient in multivariate cae, if correlated variable are teted one-attime Autocorrelation i a problem in all

11 Etimation of the variance (uncertainty) of the mean of a data et from a dynamic (elongated) 1-D data et Data et are autocorrelated, i.e., ample taken within hort interval have value which differ le than ample taken far apart aumption on normality doe not hold

12 Error made in etimating the mean of a continuou object from dicrete ample i called Point Selection Error, PSE. PSE i the error of the mean of a continuou lot etimated by uing dicrete ample. PSE depend on ample election trategy, if conecutive value are autocorrelated. Selection option: random tratified random tratified ytematic. Point election error ha two component: PSE = PSE 1 + PSE PSE 1... error component caued by random drift PSE... error component caued by cyclic drift Statitic of correlated erie i needed to evaluate the ampling variance of mean of the reult.

13 CONCENTRATION CONCENTRATION CONCENTRATION Random election TIME TIME Stratified election Sytematic election TIME Sample election mode

14 When ampling autocorrelated erie the ame number of ample give different uncertaintie for the mean depending on election trategy Random ampling: Stratified ampling: Sytematic ampling: Normally p > tr > y, x x x tr n y except in periodic procee, where y may be the larget p n n p i the proce tandard deviation tr and y are tandard deviation etimate where the autocorrelation ha been taken into account.

15 Sytematic ampling from periodic proce a i TIME a L = 0 a ample = a i TIME a L = 0 a ample = If too low ampling frequency i ued in ampling periodic procee there i alway a danger that the mean i biaed

16 Etimation of PSE by variography Variogaphic experiment: N ample collected at equal ditance and analyzed, ai, M, M are analytical reult, i ample ize and mean ample ize, repectively. Mean of the proce: a L M i M a i i (10) Relative heterogeneity of the proce: h a a a M i L i, i L M i 1,,, N (11) Abolute heterogeneity of the proce: h i a i a L M M i, i 1,,, N (1)

17 Variogram of heterogeneity a function of ampling interval j : V j 1 N j N i 1 j h i j h i, j 1,,, N (13) To etimate variance the variogram ha to be integrated (numerically in Gy method). Analyi of variogram provide variance etimate for etimating the mean of the data et obtained by random, tratified or ytematic ample election mode var( a L ) ra, t, y n ( j) (14)

18 V V 1 0. V PROCESS VARIOGRAM a i Random a i a i Periodic Non-periodic drift Sample # Sample lag, j VARIOGRAMS FOR THREE DIFFERENT BASIC PROCESS TYPES

19 V ai Sample # Sample lag, j Data and variogram of a complex proce

20 Interpretation of the variogram V Range Sill V p V(cyclic) V(drift) V 0 Random effect (ampling, preparation, analyi) SAMPLE LAG, j

21 Example Simultaneou emiion meaurement by two different proce analyzer/team from a power plant NOx emiion O in tack

22 CONCENTRATION (ppm) NOx emiion: Control meaurement NOx1 Control x 1 = = 7.1 Routine x = 17.1 = TIME (h) d = 10.3 t-tet ignificant Reult of control v. routine meaurement, two proce analyzer

23 CONTROL 195 NOx ROUTINE Routine v. control meaurement of NOx emiion

24 VARIOGRAMS NOx1, Variogram Routine Control LAG (j) Variogram of the routine and control meaurement et

25 CONCENTRATION (% O) Oxygen Control Routine Control x 1 = = Routine x = 6.78 = 0.53 t=0.4 not ignificant TIME (h) Reult of control v. routine meaurement: parallel O meaurement uing two different proce analyzer

26 CONTROL (%O) 7.4 O ROUTINE (%O) Control v. routine meaurement, reult of linear regreion analyi: Intercept = (95 % ci = ) Slope = (95 % ci = )

27 CONTROL-ROUTINE (%O) d = d = 0.15 t=0.4 not ignificant SAMPLE # Difference of the control - routine meaurement

28 VARIOGRAMS 0.09 O, Variogram Control Routine LAG (h) Variogram of the routine and control meaurement et

29 (% O) 0. O, Standard Deviation Control Routine LAG (h) Standard deviation of ytematic ampling mode etimated from the variogram of the routine and control meaurement et

30 V(d) LAG (h) Variogram of the difference d, control-routine meaurement of O

31 Comparion of two different proce mean Doe proce change affect the reult (or behavior of the proce)?

32 80 CONC. mg/m TIME (h) Period 1 x 1 = = 15.4 Period x = 16.5 = 3. d =1.7 t = 1.68 Not ignificant NOx emiion from a power plant within two different time period, 745 and 738 data point

33 V (mg/m 3 ) LAG (h) Variogram of the of the data et from two different time pan

34 (mg/m 3 ) LAG (h) Standard deviation of ytematic ampling mode etimated from the variogram of the two time pan

35 t-tet taking the autocorrelation into account x 14.8, , 1 1 n x 16.5, 5.49, n t3 = 5.78 SIGNIFICANT

36 CONCLUSIONS Before electing the tatitical tool and drawing inference try to plot the data o that it how the deired phenomenon Variographic analyi of time erie i a powerful tool. It eparate random effect, non-periodic and periodic drift In multivariate cae variographic analyi can be carried out, e.g., on PCA core

37 THANK YOU, tack, kiito, danke, merci, obrigado,.. gracia, grazie, teekkur ederim, ukran, Спасибо.

38 Graduate coure at Lappeenranta Univerity of Technology (in Englih) Experimental Deign, 5-6 March, 010 Sampling for Chemical Analyi,7-9 April, 010