Multivariate Total Quality Control: Foundation and Recent by Carlo Lauro, Jaromir Antoch, Vincenzo Esposito Vinzi,

By Carlo Lauro, Jaromir Antoch, Vincenzo Esposito Vinzi, Gilbert Saporta

The significant concentration of the publication is on utilizing the equipment appropriate for an online and off-line strategy keep an eye on either within the univariate and multivariate case. The authors don't purely be aware of the traditional scenario while the error accompanying the saw strategy are quite often disbursed, but in addition describe intimately the extra basic events that decision for using the powerful and non-parametric techniques. inside those methods, using contemporary tools of the multivariate research within the overall qc is more desirable with specific connection with the client delight sector, the tracking of period facts and the comparability of styles generated from multioccasion observations. The authors disguise either pratical computational points of the matter and the required mathematical heritage, bearing in mind standards of overall caliber control.

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Ll) apply, however, different standardization is needed. Namely, a 2 has to be replaced by a~ =a 2 (fwjf. 9) has to be replaced by a 2 /(1 - p) or by its estimator. , by O:~,n(L) = R(O) + where for k R(k) = ~ ~ 2f; (1-~) L R(k), L < n, 0 {I: t=l (Yt - Yiii) (YtH - Yiii) + ~ t=m+l (Yt - Y';) (YtH - Y';)} . If we have more information about the type of dependency, it is advisable to use the estimator specific for the particular model since the above mentioned estimator O:6,n(L) behaves quite poorly for small and moderate sample sizes.

68) with Xi = i/n, i = 1, ... 69). 71), while p( L,8nJ:'O:~Lft-,8)nJ {I Ukl} > X) ~ ~2(1-cI>(x))+2x¢(x) 1 1-,8 ,8 For deatils see Kim and Siegmund (1989). 73) 1 ()( ( ))dt. 3. Change in both intercept and slope - random design We test the null hypothesis H against the alternative A in the form H : Yi = a + bXi + ei, A : :3 m E {2, ... , n - 2} i = 1, ... i where a =1= aD and/or b =1= bD. Let us denote (1 . ~1) , 1 and X2 (k) (1. 74) such that Yi = a + bXi + ei, Xk = ,n, X~ = Xk = 1, ... ~~+1) 1 Xn :2 (a - aD,b - bD)((X~Xk)-l + (Xk'X~r1) -1 (a - aD,b - bD)' = = ~ (nkCY,o - Vn)2 + Q;y(k) + Q~~(k) _ Q;y(n)) , n- k 0- 2 Qxx(k) Qxx(n) Q~x(k) where a, aD, band bDare the least squares estimators of corresponding quantities under A and k k Qxx(k) L = (Xi - Xk) (Xi - Xk), Qxy(k) = i=l n L (Xi - Xk)(Yi - Yk), i=l n The maximum-type test statistics are of the form max 2Sk::;n-2 {X2} k and max LBnJ::;k::;L(1-,B)nJ {X~}.

51) becomes Off -line statistical process control 27 REMARK: There were developed also U-test statistics and Kolmogorov-Smirnov type test statistics for our problem. For more information we refer to the book Csorgo and Horvath (1997). 3. MOSUM type test statistics Now, we introduce two different classes of test statistics for our problem. g. 31) and Gin small. 10. 54) corresponds to the second order difference (the second order derivative) of Sk'S. g. e. P ( max { G x G) + bn '~l-exp {-2eX } ,x E R an,G 1, and p( max G x + bn,G -log ~) ~ { v2G (In an,G ~l-exp{ -2e- X where an,G = Vr::::::n: 2 log G and bn,G n 1 n }, XERl, 1 = 2 log G + 2" log log G - 2" log 7f.

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