SAMPLING INSPECTION TABLES 



11 



case — for each of which sample sizes may be selected so as to give the de- 

 sired Consumer's Risk of 0.10, but we wish to choose the combinations of 

 «i, "12, Ci and C2 that will involve a minimum amount of inspection for product 

 of process average quality. Furthermore, there are an unlimited number 

 of ways of apportioning the Consumer's Risk between the first and second 

 samples for each process average value. This latter factor introduces 

 one more variable factor than will permit of a ready solution by other than 

 trial and error methods, and accordingly an empirical choice has been made 

 on the basis of a complete investigation of the relative practical advantages 

 of several possible choices. Specifically, the solutions are based on an 

 apportionment such that the risk for the first sample is equal to the risk 

 for an independent sample equal in size to the first and second samples 



TABLE 2 

 Computation of Consumer's Risk- 



-DouBLE Sampling 



combined. The use of an 0.06 risk in determining Wi and «i + '>h. for given 

 values of Ci and c^ provides a Consumer's Risk of almost exactly 0.10 over 

 a considerable portion of the field covered by the tables, though in some 

 areas a value as low as 0.056 is necessary. The "minimum" solutions for 

 double sampling are, of course, conditioned by this choice.* 



As shown in the Appendix, paired values of Ci and c^ that satisfy the 

 condition of minimum inspection depend on (1) the tolerance number of 

 defects for a lot, and (2) the ratio of the process average to the lot tolerance 



* Study of the effect of different apportionments of the Consumer's Risk on the aver- 

 age amount of inspection for product of process average quality indicates that consider- 

 ably more than half of the 0.10 risk should be taken for small process average values and 

 that less than half should be taken for large process average values. The single choice 

 that was made provides a solution that closely approximates the true minimum over a 

 large portion of the tables, and was considered justified by the great saving in computa- 

 tion effort. With this choice, the average amount of inspection per lot does not in general 

 exceed the true minimum by more than 3 to 5% although for extremely low process aver- 

 age values the excess may be as much as 15%. 



