CONTROL CHARTS APPLYING A SEQUENTIAL TEST AT FIXED SAMPLING INTERVALS 39 quadrature.as follows g(udu≈∑ru,g(u, in equation (B3).Using the rom (B ASN and OC from (B7)and (B8)in equation (B4) for integrating over and w produces an approximation Ano(uo)to ANOS(u) are the corresponding weights.Since (B1)and (B2) Finally,for the SPRT chart. the fixed length of o the scond quadrature.To apply Gaussian quadrature to th (and in particular,after the control statis integrals in (B1) time from the the d(let f the shift t ution),and th grating o n qu and l e the corresponding weights.Applying Gaussian ibuited over d.The efore,the (82)thu hart ism S of the Sp equa ASN(u)=1+∑o(u,)ASN(u,f(4,-W）(B5) SSATS =0.5d+(ABL(O)-1d =0.5d+（10c0 (B9 0C(u)=(g-u-6+ +∑ra,oCuf-.（Bo) SSATS. The det en,evall (B5 mhihhteoesofnihrqlaias2。a nd employing double precisionthroughout all co veexcellent approximations 0ms.m=12,24.40.64 ure points were also considered,in order to establish he ay of the computat ons.Considering up to aied for any of the computation ture points were used.The results are.thus,highl T the r the tation of th and CUSUM schemes will be nted in future Q=[. 以6r=m.A papers on computational algorithms and computer qu=gi(ull. Acknowledgments where q=(uj)f(u-u).for j=1.m.Then ASN(w)=1+qu)1-Q)-1, (B7) where I is the m x m identity matrix and 1 is the ment Research Grant. m x 1 vector of I's.Further.define the m x 1 vector References p=pil. wherep=+),for i=1.m.Then 0C=(g-u-8+)+q()1-Q)'p.(B8) Vol.29.No.1.January 1997 Journal of Quality Technology Reproduced with permission of the copyright owner.Further reproduction prohibited without permission.Reproduced with permission of the copyright owner. Further reproduction prohibited without permission