6 BELL SYSTEM TECHNICAL JOURNAL 



a submitted lot that has a per cent defective equal to the Lot Tolerance 

 Per Cent Defective. This probability is termed the Consumer's Risk. 



{h) Average Quality Protection — in which there is prescribed some chosen 

 value of average per cent defective in the product after inspection (Average 

 Outgoing Quality Limit, AOQL), that shall not be exceeded no matter what 

 may be the level of per cent defective in the product submitted to the 

 inspector. 



Single sampling plans employing the first of these two types of protection 

 were developed in an earlier paper .^ An extension of the underlying theory 

 as applied to double sampling will be given here. Sampling plans em- 

 ploying the second type of protection will likewise be covered for both the 

 single sampling and double sampling procedures.* 



The development of the second concept (AOQL) in 1927 was the result 

 of a practical need in certain types of manufacturing process inspections, 

 following considerable experience in the application of inspection pro- 

 cedures based on the first concept (Lot Tolerance and Consumer's Risk) 

 which had been developed in 1924. Both have since been used extensively. 



Minimum Amount of Inspection 



For all of the four inspection plans covered, certain general principles, 

 given in the earlier paper ,^ are used. 



For each plan two requirements are imposed — first, that the plan shall 

 provide a specified degree of protection (as covered by (a) or (b) above), 

 and second, that the amount of inspection shall be a minimum for product 

 of expected quality, subject to the degree of protection imposed by the first 

 requirement. 



The first requirement can be satisfied by a large number of different 

 combinations of sample sizes and allowable defect numbers. The second 

 requirement dictates which one of these combinations shall be chosen, 

 and requires a determination of the value of per cent defective to be nor- 

 mally expected in product submitted to the inspector. This expected 

 value is referred to as the "process average" per cent defective. 



For the inspection procedures here adopted, the amount of inspection 

 that will be done in the long run is made up of two parts: (1) the number of 

 pieces inspected in the samples and (2) the number of pieces inspected in 

 the remainder of those lots that fail to be accepted by sample. We are 



* An adaptation of these concepts to inspection by the method of variables, using 

 the arithmetic mean as an acceptance criterion, is given in a doctorate thesis (Columbia 

 University) by H. G. Romig, "Allowable Average in Sampling Inspection," March 1939, 

 for the case of a normally distributed characteristic that is statistically controlled with 

 respect to the standard deviation. 



