SAMPLING INSPECTION TABLES 29 



E_ffect of Rounding — The use of rounded values of n, «i and «2 gives values 

 of Consumer's Risk other than exactly 0.10. However each sampling plan lists 

 sample sizes based on the largest lot size in the corresponding lot size range. 

 As a result, the Consumer's Risk associated with the pt value designated at the 

 top of the Lot Tolerance tables does not exceed 0.10 except in a few isolated cases, 

 where the risk may be as high as 0.12 for the largest lot size. Likewise, the 

 AOQL value for any sampling plan in the AOQL tables does not exceed the value 

 designated at the top of each table except in a few isolated cases, where the error 

 due to rounding may be as much as 10% of the designated value for the largest 

 lot size. 



The Consumer's Risk value of 0.10 and the AOQL values listed in the tables, 

 are therefore with few exceptions, upper bounds that will not be exceeded in the 

 application of the tables. 



NOMENCLATURE 



N Number of pieces in lot. 



n Number of pieces in sample. 



«i Number of pieces in first sample. 



fi2 Number of pieces in second sample. 



c Allowable defect number. 



c\ Allowable defect number for first sample, Wi. 



C2 Allowable defect number for first and second samples combined, «i + fPi. 



pt Lot tolerance fraction defective. 



p Fraction defective; also used specifically to denote fraction defective in 



submitted product. 

 p Process average (expected) fraction defective in submitted product. 

 Pa Average fraction defective in product after inspection — Average Outgoing 



Quality (AOQ). 

 pL Maximum value of average fraction defective in product after inspection — 



Average Outgoing Quality Limit (AOQL). 

 pi Specific value of p in submitted product, for which pA = pL- 

 Pc Consumer's Risk. 

 Pa Probability of acceptance. 

 Pp Producer's Risk. 

 / Average number of pieces inspected per lot for submitted product of p 



quality. 

 / Specific value of / when p in submitted product = p. 

 Imin Minimum value of /. 



M = ptN Number of defects in lot of tolerance {pt) quality. 

 M = pN Number of defects in a lot of process average {p) quality. 



P 

 k = — Ratio of process average fraction defective to lot tolerance fraction 



pt 

 defective. 



- P 



k = — Ratio of process average fraction defective to AOQL. 



pL 

 m Number of defects found in sample. 



C„ = rri — — ; Number of combinations of N things taken n at a time. 



{N — n)l nl 



