SAMPLING INSPECTION TABLES 5 



(c) If the number of defects found in the first sample exceeds c^, inspect all 

 the pieces in the remainder of the lot. 



(d) If the number of defects found in the first sample exceeds ci but does not 

 exceed cj, inspect a second sample of «2 pieces. 



(e) If the total number of defects found in the first and second samples 

 combined does not exceed C2, accept the lot. 



(f) If the total number of defects found in the first and second samples 

 combined exceeds C2, inspect all the pieces in the remainder of the lot. 



(g) Correct or replace all defective pieces found. 



The double sampling procedure can, perhaps, be visualized more easily 

 by reference to Fig. 1. 



The theoretical development assumes that the inspection operation itself 

 never overlooks a defect and that all defective pieces found, whether in 

 samples or in the remainders of those lots that are inspected completely, 

 will be corrected or replaced by conforming pieces.* Thus, lots that fail 

 to be accepted by sample are assumed to be completely cleared of defects. 



Protection and Economy Features 



When a consumerf adopts sampling inspection in place of 100 per cent 

 inspection, he forgoes the opportunity of assuring himself that each piece 

 of product will conform to requirements, and must choose a sampling plan 

 that will provide a degree of protection against defective material that is 

 consistent with his needs. This choice may be narrowed down by choosing 

 some value of allowable per cent defective, and by deciding whether this 

 allowable value should apply to a limited quantity of product such as a lot, 

 or to the general output comprising a more or less steady flow of lots. 



Two Kinds of Consumer Protection 



For both the single sampling and double sampling procedures outlined 

 above, tables are developed for each of the following two kinds of con- 

 sumer protection: 



(a) Lot Quality Protection — in which there is prescribed (1) some chosen 

 value of allowable per cent defective in a lot (Lot Tolerance Per Cent 

 Defective), and also (2) some chosen value for the probability of accepting 



* While the mathematical solution assumes correction or replacement of defective 

 pieces, it may be expedient practically to reject defective pieces and not replace them. 

 The effect of following this, rather than the assumed procedure, involves differences in 

 results too small to be of any practical consequence for the small values of per cent de- 

 fective covered by the tables. 



t The term "consumer" is used in the general sense of the recipient of the product 

 after the inspection has been completed. This maj', of course, be the ultimate consumer 

 or his agent. However, in a manufacturing unit, if one department produces parts for 

 use by a subsequent assembly department, the first department may be considered as 

 the producer and the second, the consumer. 



