14 BELL SYSTEM TECHNICAL JOURNAL 



Appendix. The pairs of values of Ci and Ci used in the solution are confined 

 to those given in Fig. 7 of the Appendix. For each of these pairs of Ci and 

 C2, sample sizes are determined, using the above mentioned relationship to a 

 10% Consumer's Risk, that will give the desired AOQL value. Of these 

 several sets of Ci, c^, «i and n2, that one is selected which involves the least 

 amount of inspection. 



The appended DA tables (Double Sampling Average Quality Protection) 

 provide a complete set of such minimum inspection solutions for AOQL 

 values from 0.1% to 10%. The choice of ui, no, C\ and c<i for each solution 

 in the tables is based on the general procedure of Fig. 3 (using the zones 

 given in Fig. 7) to insure that the AOQL value over the area in question 

 will not exceed the specified value and to give on the average for this area 

 the most economical plan. 



As for the single sampling AOQL tables there are listed values of lot 

 tolerance per cent defective for a Consumer's Risk of 10%. In this case, 

 these values have entered directly into the solution as explained above. 



Application of Sampling Tables 



In the above description of the sampling tables, attention has been con- 

 fined to the inspection of a single characteristic. The tables are, however, 

 equally applicable to a group of characteristics considered collectively pro- 

 vided defects with respect to these characteristics are of essentially the same 

 seriousness and may, therefore, be considered additive. When such appli- 

 cation is made, the per cent defective values given in the tables embrace 

 all such defects collectively, and since more than one defect may occur on 

 a single piece of product, any allowable defect number listed in the tables 

 should, by agreement, be considered either as a "number of defective pieces" 

 or as a "number of defects." 



The sampling tables based on lot quality protection (Tables SL and DL) 

 are perhaps best adapted to conditions where interest centers on each lot 

 separately — for example, where the individual lot tends to retain its identity 

 either from a shipment or a service standpoint. They have been found par- 

 ticularly useful in inspections made by the ultimate consumer or his pur- 

 chasing agent for lots or shipments purchased more or less intermittently. 



The sampling tables based on average quality protection (Tables SA 

 and DA) are especially adapted for use where interest centers on the 

 average quality of product after inspection rather than on the quality of each 

 individual lot and where inspection is, therefore, intended to serve, if 

 necessary, as a partial screen for defective pieces. The latter point of view 

 has been found particularly helpful, for example, in consumer inspections of 

 continuing purchases of large quantities of a product, and in manufacturing 



