614 BELL SYSTEM TECHNICAL JOURNAL 



of receiving a lot of unsatisfactory quality shall not exceed some 

 definite figure." This risk involves two probabilities: 



(a) that an unsatisfactory lot will be submitted for inspection. 

 (h) that the inspector will pass as satisfactory, an unsatisfactory 

 lot submitted for inspection. 



Without definite information regarding probable variations in the 

 producer's performance and without an absolute assurance that this 

 performance will remain consistently the same, the use of probability 

 (a) in stating the risk to the consumer might be misleading. This 

 probability will therefore receive no further consideration in this paper 

 so far as the definition of the risk to the consumer is involved. 



For probability {b) a reasonably low value for an upper limit can 

 be given without any knowledge of the producer's performance. 

 This upper limit (as defined below) has been taken as the starting 

 point for the inspection method presented in this paper. The concept 

 of risk which has been adopted gives the consumer unconditional 

 assurance that his "chance of getting any unsatisfactory lot submitted 

 for inspection shall not exceed some definite magnitude." This 

 magnitude is the Consumer's Risk used. 



Our problem may hence be stated as follows: 



Given a product of a specified type of apparatus or material 

 coming from a producer in discrete lots, what inspection plan 

 will involve a minimum of inspection expense, and at the same 

 time insure that under no conditions will more than a specified 

 proportion of the unsatisfactory lots submitted for inspection be 

 passed for delivery to consumers? 



This problem is economic in character and its solution involves the 

 use of probability theory for establishing the height of the barrier 

 to be placed in the path of unsatisfactory material. 



Our attention will be directed particularly to the inspection of 

 material which is produced more or less continuously on a quantity 

 basis as distinguished from intermittent production in relatively 

 small amounts. Under these conditions the producer is able to 

 secure a continuing record of performance and to set up an inspection 

 program which takes advantage of current quality trends. 



General Considerations in Setting Up an Inspection Method 



The broad purpose of inspection is to control quality by critical 

 examinations at strategic points in the production process. Raw 

 materials must be inspected. Some of the rough and finished parts 

 must be inspected. In the manufacture of even the simpler kinds of 

 merchandise, inspections dot the chart of progress from raw materials 



