SAMPLING INSPECTION TABLES 13 



For this plan, protection is defined by specifying a definite value of 

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

 value of sample size that will give the specified value of AOQL. This is 

 illustrated in Fig. 4. Any of these combinations of n and c provide the 

 desired protection, and as for the lot quality protection plans, we choose 

 that combination of n and c that gives a minimum amount of inspection 

 for uniform product of process average quality. 



In the Appendix it is shown that the allowable defect number satisfying 

 the condition of minimum inspection is dependent on two factors (1) 

 the number of defects per lot for process average quality, and (2) the ratio 

 of the process average per cent defective to the AOQL value. Fig. 9 of 

 the Appendix defines zones of allowable defect numbers for which the 

 average amount of inspection is a minimum. 



The appended SA tables (Single Sampling Average Quality Protection) 

 provide a complete set of minimum inspection solutions for AOQL values 

 from 0.1% to 10%. The choice of n and c for each solution in the tables is 

 based on the procedure of Fig. 3 (using c zones given by Fig. 9), to insure 

 that the AOQL value over the area in question will not exceed the specified 

 value and to give on the average for this area the most economical plan. 



On each table are given values of lot tolerance per cent defective for a 

 Consumer's Risk of 10%. These values are found useful in practice since 

 it is often desirable to know the degree of protection afforded to individual 

 lots. 



Double Sampling — Average Quality Protection 



The solution for double sampling differs from that for single sampling 

 in that no simple relation has been found that gives directly the sample 

 sizes that will result in a specified value of AOQL for a given lot size. 

 This, together with the lack of simple relations for determining the choice 

 of allowable defect numbers (ci and c^ that provide a minimum solution, 

 has necessitated an empirical choice, the consequence of which is much the 

 same as for the similar action taken in the solution of the problem of double 

 sampling for lot quality protection.* Specifically, the interrelationship 

 between wi, W2, Ci and C2 used in the latter case for a 10% Consumer's 

 Risk is used again here and the solutions given are consequently minima that 

 are contingent on this choice. An extensive trial and error investigation, 

 using the underlying theoretical relations, leads to the conclusion that the 

 degree to which the solutions given in these tables approach the true min- 

 ima, is of the same order of magnitude as for the double sampling tables 

 for lot quality protection. 



The method of solution is essentially that illustrated by example in the 



* See footnote page 11. 



