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BELL SYSTEM TECHNICAL JOURNAL 



fluctuation in product which is no greater than that which could have 

 resulted from the non-assignable causes as it would be to try to find 

 the exact manner in which each of the causes contributed to missing 

 the bull's-eye in the analogous case of target practice just considered. 

 Here then is the practical commercial problem — When do the ob- 

 served differences between the product for one period and that for an- 

 other indicate lack of control due to assignable causes, and when, on 

 the other hand, do the differences in quality of manufactured product 

 observed from one period to another indicate only fortuitous, chance 

 or random effects which we cannot reasonably hope to control without 

 radically changing the whole manufacturing process? We shall out- 

 line a typical example of the way this question arises, outline the basis 

 for its solution and present the results in the form of a control chart. 



Typical Example 



Fig. 1 shows the frequency polygon for 15,050 instruments inspected 

 for quality X. These instruments were selected at random throughout 

 the year from a product manufactured in quantities of approximately 



One year's Product- 



5 1600 



Quality Defined by Characteristic X 



Fig. 1- — Polygon showing distribution in quality for 15,050 units of product. Do these 

 data present anj' evidence of lack of control? 



2,000,000 per year. Is there any indication from these data that the 

 product had not been uniform or controlled throughout the twelve 

 month period in which the instruments had been selected? 



Oftentimes we must decide from a study of a single frequency poly- 

 gon of data such as given in Fig. 1, whether or not the product has been 



