622 BELL SYSTEM TECHNICAL JOURNAL 



Fig. 4 gives curves which enable one to determine the minimum 

 average number of pieces inspected per lot for uniform product of 

 process average quality. For a given tolerance number of defects 

 and a given ratio of process average to tolerance, a value of tolerance 

 times minimum average number inspected per lot is determined. 

 This when divided by the tolerance gives the desired value of minimum 

 average number inspected per lot. 



Illustrative Example 



Suppose that lots of 1,000 pieces each are inspected for a charac- 

 teristic having a specified tolerance of 5 per cent defective and that 

 the process average quality of submitted lots is 1 per cent defective. 

 If it is desired to have a risk of 10 per cent of accepting a 5 per cent 

 defective lot, what single sampling plan should be followed by the 

 inspector to give a minimum amount of inspection, and how much 

 inspection per lot will be required on the average? 



Referring to Fig. 2, for "Tolerance Number of Defects" (.05 

 X 1,000) = 50 and "Ratio of Process Average to Tolerance" (.01/.05) 

 = .20, we find the acceptance number = 3. 



Referring to Fig. 3, for "Tolerance Number of Defects" = 50 and 

 "Acceptance Number" = 3, we find "Tolerance Times Sample Size" 

 = 6.5. Dividing by the tolerance (expressed as a fraction defective) 

 = .05, gives a sample size of 130. 



Referring to Fig. 4, for "Tolerance Number of Defects" = 50 and 

 "Ratio of Process Average to Tolerance" = .20, we find by inter- 

 polation that the "Tolerance Times Minimum Average Number 

 Inspected" = 8.2. Dividing by the tolerance, .05, gives an average 

 number inspected per lot of 164. 



This solution has thus been obtained by the initial specification of 

 first, the tolerance per cent defective for a single lot and a value for 

 the Consumer's Risk, these two factors being combined to give a 

 definite measure of protection against passing faulty material, and 

 second, a minimum amount of inspection for product of process 

 average quality. 



These two requirements control the exact details of inspection 

 procedure and must be initially chosen on the basis of practical 

 considerations and circumstances. The specification of these factors 

 lends definiteness to the problem of inspection and provides a rational- 

 ized basis of procedure which can be depended on to give the desired 

 degree of protection. Obviously, any value of Consumer's Risk may 

 be chosen according to circumstances. The value which is proper 

 in any case is dependent on the conditions associated with the product 



