The Bell System Technical Journal 



October, 1929 



A Method of Sampling Inspection 



By H. F. DODGE and H. G. ROMIG 



This paper outlines some of the general considerations which must be 

 taken into account in setting up any practical sampling inspection plan. 

 An economical method of inspection is developed in detail for the case 

 where the purpose of the inspection is to determine the acceptability of 

 discrete lots of a product submitted by a producer. By employing proba- 

 bility theory, the method places a definite barrier in the path of material 

 of defective quality and gives this protection to the consumer with a 

 minimum of inspection expense. 



ONE of the common questions in every day inspection work is, 

 How Much Inspection.'' The answer must always be arrived at 

 in the light of economy for only the least amount of inspection which 

 will accomplish the purpose can be justified. 



We wish here to consider the problem of setting up an economical 

 inspection plan whose immediate purpose is the elimination of indi- 

 vidual lots of product which are unsatisfactory in quality. By a lot 

 of unsatisfactory quality is meant one that contains more than a 

 specified proportion of defective pieces. This proportion is usually 

 small and is based on economic considerations. The interest in 

 inspections made for the elimination of such lots is shared by two 

 parties, — the producer and the consumer. The consumer establishes 

 certain requirements for the quality of delivered product. The 

 producer so arranges his manufacturing processes and provides such 

 an inspection routine as will insure the quality demanded. Our 

 problem recognizes that the consumer runs some risk of receiving 

 lots of unsatisfactory quality, if the quality of each lot is judged by 

 the results of inspecting only a sample. The method of attack 

 presumes the adoption of a risk whose magnitude is agreeable to the 

 consumer and the selection of a particular inspection procedure which 

 will involve a minimum of inspection expense on the part of the 

 producer while guaranteeing the protection agreed upon. 



Considering various possible concepts of a risk, the consumer would 

 prefer to have one adopted that was worded as follows: 



"Not more than a specified proportion of the delivered lots 

 shall be unsatisfactory in quality." 



In other words, he would like to have the assurance that "the risk 

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