A METHOD OF RATING MANUFACTURED PRODUCT 367 



can be neglected,^ which gives -yjpN. Considering the practical case, 

 if the ratio of the number of defects is small compared with the possible 

 number of defects, then the standard deviation of the expected number, 

 d, is equal to ^Id. For many telephone products certain types of de- 

 fects may occur several times on a single unit of product; for example, 

 when inspection is made for the tension requirement of springs on a 

 relay or for character of soldered connections on a switchboard, then 

 N refers to the number of springs or the number of soldered connections, 

 respectively, inspected during the month. Likewise p refers to the 

 probability of occurrence of a defective spring or of a defective soldered 

 connection. Fortunately, in the determination of the standard devia- 

 tion it is not necessary to know exactly what p is nor what A^^ is, so 

 long as it is known that p is small (less than .10 for ordinary engineering 

 purposes). This condition is usually satisfied in practice, hence the 

 above result can be used. 

 Equation (4) then becomes 



To simplify routine computations, this can be changed in form by 

 removing the factor — from each term (this is merely the Expected 



Demerits per Unit ( — j for a given type of defect) which gives 



and the ( — 1 factors may be computed directly from the totality of 



data available for establishing the Expected Demerits per unit. 

 In shorter notation, equation (6) can be expressed as 



0"/^ = ^ 



n\ n I e_ 



(7> 



If the number of units inspected is the same for all types of defects,, 

 i.e. Wi = W2 = etc. = n, equation (7) becomes 



'"■ = *\IV^ ['"(§), 



(8)' 



* This follows directly from the Law of Small Numbers. Theoretically this result 

 is obtained if p is small, N infinite and pN finite. See any standard text on the 

 subject. Practically this law can be used as an approximation if p is less than .10- 

 and N is greater than 16. 



