8 BELL SYSTEM TECHNICAL JOURNAL 



Protection is defined by specifying values of, 



(a) Lot Tolerance Per Cent Defective, the allowable per cent defective 

 in a lot. 



(b) Consumer's Risk, the probability of accepting a lot of tolerance 

 quality. 



If the allowable defect number is c, then the Consumer's Risk is the 

 probability of finding c or less defects in a random sample of n pieces drawn 

 from a lot of N pieces in which the per cent defective is equal to 

 the lot tolerance per cent defective. The tables presented are based on a 

 Consumer's Risk of 0.10, a value found most useful in practice. For this 

 choice, the chances of accepting a lot of worse than tolerance quality are 

 less than 1 in 10. 



TABLE 1 



Solution for a Particular Case — Single Sampling, Lot Quality Protection 



Plan involving minimum amount of inspection. 



For each value of c, such as 0, 1, 2, etc., there is a unique value of sample 

 size w, such that the probability of finding c or less defects is 0.10. Any 

 of these combinations of n and c will thus provide the desired consumer 

 protection. 



Now, for a given value of process average per cent defective, one of 

 these combinations involves a smaller total amount of inspection than any 

 of the others, as illustrated in Table 1. This combination of n and c, 

 which provides the desired solution, gives the most efficient adjustment be- 

 tween the Consumer's Risk and Producer's Risk from the standpoint of 

 minimizing inspection effort. Fig. 2 shows the relationship between these 

 two risks for the conditions given in Table 1. 



Curves providing a basis for solutions, such as that given in Table 1, 

 have been published* for a Consumer's Risk of 0.10. The appended SL 

 tables (Single Sampling Lot Quality Protection) provide for practical 



