620 BELL SYSTEM TECHNICAL JOURNAL 



inspection. Thus the amount of inspection is automatically increased 

 as quality degenerates. 



For every acceptance number, such as 0, 1, 2, etc., there is an unique 

 size of sample which will satisfy the specified values of tolerance 

 per cent defective and Consumer's Risk. We thus have many pairs 

 of values of sample size and acceptance number from which to choose. 



The second requirement dictates which pair shall be chosen. We 

 will select that pair which involves the least amount of inspection 

 for product of expected quality. In industry, the quality emerging 

 from any process tends to settle down to some level which may be 

 expected more or less regularly day by day. If this level could be 

 maintained quite constant, if the variations in quality were no larger 

 than the variations that could be attributed to chance, then inspection 

 could often be safely dispensed with. But practically, while such a 

 level may be adhered to most of the time, instances of man failure 

 or machine failure are bound to arise spasmodically and as a result 

 the quality of the output may gradually or suddenly become unsatis- 

 factory. The method of solution takes into consideration this usual 

 or expected quality and requires an estimate of the expected quality 

 under normal conditions. A satisfactory estimate of this can usually 

 be obtained by reviewing data for a past period during which normal 

 conditions existed and by utilizing such other pertinent information 

 as bears on manufacturing performance under present or anticipated 

 conditions. This expected value is defined as the process average to 

 be used in the solution. Thus the method under discussion will 

 assure the producer of a minimum of inspection expense so long as 

 he holds to his expected performance. If he gets into trouble and 

 the quality becomes poorer than normally expected, the method 

 automatically increases the inspection by an amount which varies 

 with the degree of quality degeneration. This reacts on the producer 

 directly by increasing his inspection expense and serves as an incentive 

 to the elimination of the causes of trouble. The producer's expected 

 performance is thus made use of in a way that affects the economy 

 of the producer's inspection work but is not used to color or affect 

 the magnitude of the Consumer's Risk. 



The amount of inspection, that will be done in the long run for 

 uniform product ^ of process average quality is made up of two parts: 



(1) The number of pieces inspected in the samples. 



(2) The number of pieces inspected in the remainder of those lots 



which fail to be accepted when a sample is examined. 



^ By "uniform product" is meant one produced under a constant system of 

 chance causes, giving rise to a quality which is a chance variable. In the present 

 paper, this chance variable is assumed to be the Point Binomial. 



