618 BELL SYSTEM TECHNICAL JOURNAL 



Protection and Economy Features of the Method 



The adoption of sampling inspection at any stage of manufacture 

 carries with it the premise that the product emerging from this point 

 does not have to conform 100 per cent with specification requirements. 

 It is often more economical, all things considered, to allow a small 

 percentage of defective pieces to pass on to subsequent assembly- 

 stages or inspections for later rejection than to bear the expense of a 

 100 per cent inspection. Under these conditions, the status of the 

 inspection can be clarified by establishing a definite tolerance for 

 defects for the lots submitted to the inspector for acceptance. This 

 may be specified as an allowable percentage defective, a figure which 

 may be considered as the border line of distinction between a satis- 

 factory lot and an unsatisfactory one. Thus, if the percentage 

 defective is greater than this "tolerance per cent defective," the lot 

 is unsatisfactory and should be rejected. We say "should be" 

 rejected but this cannot be accomplished with absolute certainty if 

 only a sample is examined. Sampling inspection involves taking 

 chances since the exact quality of a lot is not known when only a part 

 is inspected. According to the laws of chance, a sample will occasion- 

 ally give favorable indications for bad lots which will result in passing 

 them for delivery to consumers. 



The first requirement for the method will therefore be in the form 

 of a definite insurance against passing any unsatisfactory lot that is 

 submitted for inspection. 



The second requirement that will be imposed is that the inspection 

 expense be a minimum, subject to the degree of protection afforded 

 by the first requirement. 



For the first requirement, there must be specified at the outset a 

 value for the tolerance per cent defective as well as a limit to the 

 chance of accepting any submitted lot of unsatisfactory quality. The 

 latter has, for convenience, been termed the Consumer's Risk and is 

 defined, numerically, as the probability of passing any lot submitted 

 for inspection which contains the tolerance number of defects. 



As will be shown further on, the first requirement can be satisfied 

 with a large number of different combinations of sample sizes and 

 acceptance criteria. To satisfy the second requirement, it is necessary 

 then to determine the expected amount of inspection for a variety of 

 inspection plans, determine the cost of examining or testing, add the 

 costs other than those incurred in the simple process of examining 

 samples, and choose among these plans that which involves a minimum 

 of inspection expense. 



There are, of course, a number of possible general methods of 



