SAMPLING INSPECTION TABLES 23 



The use oi P = 0.06 for determining «i + n^ corresponding to c^ as well as 

 for determining n\ corresponding to ci results in a Consumer's Risk of approxi- 

 mately 0.10, as may be checked by writing the Consumer's Risk equation (3) 

 as follows: 



Pc = / , Pm,ni,N,M + ^ j Pm,ni + ni,N,M ~ I Po,ni,lV,M / , Pm,ni,N-~n\,M 

 m=0 m=0 \ 7n=0 



m=C2 — 1 

 + Pl,ni,W,M 2_, Pm,ni,N—nx,M—l + " ' " 

 m=0 



OT=C2— ci \ 



■\- Pci,ni,N,M 2__i Pm,ni,N—ni,M—ci\. (11) 



m=0 / 



The sum of the first two terms is 0.12 and the sum of the terms in parentheses 

 is of the order of 0.02. 



Average Quality Protection 

 General Relations 



When the fraction defective in submitted product is p, the average quality 

 after inspection {Pa) is given by 



N - I 

 pA=p~Y~ (^2) 



when all defective pieces found are replaced. If defective pieces found are re- 

 moved but not replaced, 



N - I 

 Pa=P — =- , (120 



the factor pi representing the average number of defective pieces removed. In 

 deriving the tables, equation (12) has been used. The error in pA resulting from 



the use of (12) rather than (12') is — , which is generally small. 



The average outgoing quality limit (pi) is the maximum value of pA that will 

 result under any sampling plan, considering all possible values of p in the sub- 

 mitted product. The value of p for which this maximum value of pA occurs is 

 designated as pi, hence 



pL = pi -^ . (13) 



The value of pi for which pA = Pl may be determined by differentiating equation 

 (12) with respect to p, equating to 0, and solving for p, that is 



dp.^N^_pdl^ 



dp N N dp ^ ^ 



Single Sampling 



Given: Lot size (N), AOQL (Pl), process average fraction defective Q). 

 To find: Values of n and c that will minimize /. 



