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By Norman L. Johnson

This publication presents a accomplished survey of the latest methodology--both theoretical and applied--on the statistical research and detection of defective/"non-conforming" goods in quite a few sorts of inspection for attributes, while the inspection itself is topic to errors.

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By Norman L. Johnson

This publication presents a accomplished survey of the latest methodology--both theoretical and applied--on the statistical research and detection of defective/"non-conforming" goods in quite a few sorts of inspection for attributes, while the inspection itself is topic to errors.

Show description

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17) in order to obtain E[Z;lZj]' we only need to evaluate E[YjIZj]. - N Pj where pj=DN- 1 pj+(1-DN- 1 )pj, as above. Also Pr [item is NCI item classified as C] = D (1 - p). ] p. )--) )) )1 - . (p. ] )) , D = niPi + ni(Pi - Pi)N I( N -n j 1- 1- ~_ }Pj - Pj) - ) _ (Zj - njpj) (N - nj)pi1 - Pj) i :j: j. 16). e. ni = 1 for i = 1, ... , k, each one of the Y's and Z's is either 0 or 1. 11b) then THE CASE WITH UNEQUAL ERROR PROBABILITIES 41 becomes pr[z=z]=(N)-l I D Yl ... I ( N~k Yk k X fI {y,pf;(1 - ,; 1 D- L,;lY, ) py -Z; + (1 - y,)p;z;(1- p;)l-Z;} (z, = 0, l;y, = 0,1).

Distributions Let Y == (Y 1 , ... , Yk ), where Yj is the (unknown) number of truly NC items in the jth sample, and y == (Yl"",Yk), a realized value of Y. We use the symbol (:) == (bl"~" bJ = (a - L~; ::)! f1~; b) to denote a multinomial coefficient. 1a) with the following constraints on Y=(YI,Yz, ... 1 b) Y ~ Mult Hypg(n;D,N). Let Z =: (ZI"'" Zk)' where Zj is the number of items in the jth sample classified as NC. 3) ZIY ~ Bin(Y, p)*Bin(n - Y,p'). where Bin(Y,p)*Bin(n- Y,p')=: ( Bin(Yl,p) * Bin(nl - Yl'P')) ::: Bin(YbP)*Bin(nk - Yk,p') .

However the computation results provide quite a clear picture. 01. Second, (or double sampling schemes, when the sample size is large, the effects of changes in p and p' are more significant, but the lot size has little effect on the probabilities of acceptance for given DIN. Finally, for link sampling procedures, the probabilities of acceptance are naturally sensitive to differences between D; and the average of D; _ 1 and Di+ l' All of the above features of these schemes are intuitively reasonable, but they serve as reminders of the delicate relationships among the parameters and sensitivity to values of the error probabilities.

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