974 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1953 



allowances for the process average to vary a reasonable amount around 

 this nominal. The methods developed and included in the general speci- 

 fication allow the process average to vary within a band of dbj^cr around 

 the nominal which results in limits for individual units of product, desig- 

 nated as "A^' limits in the specification, equal to nominal (A^) =b 33^ a. 

 The value chosen represents a balance between the needs of the operat- 

 ing requirements of the product and the difficulties of maintaining closer 

 controls in the factory. 



In Fig. 3 the permissible variation of individual units of product is 

 represented by a Normal distribution curve displaced zbj^o- from the 

 nominal N . Since the specification limits are represented by ±A, the 

 allowable variation in the process average is ±0.1A. 



This is a severe requirement, for in spite of the care employed in col- 

 lecting data during the preproduction period for computing the "natural 

 tolerance" of a manufacturing process, there is always the danger that 

 all the variations which are an unavoidable part of regular production do 

 not occur during the time data are collected. There could be periods 

 after manufacture has started when the factory could not determine 

 whether the out-of -control condition was one which should be promptly 

 ehminated or whether some important characteristic of the process 

 which had not occurred earlier had made its appearance. At this stage 

 it is important to have available some method for sorting product al- 

 ready manufactured which will meet the desired distribution pattern 



LIMITS SPECIFIED FOR INDIVIDUAL PRODUCTS 

 MINIMUM MAXIMUM 



Fig. 3 — The relations between a frequency distribution of individual units of 

 product and specified maximum and minimum limits when the average or nominal 

 is allowed to vary ±^^o. 



