CORRECnON 01' J). 1 1. 1 1-()R M ILISLREM EKT 23 



Thus with the aid of the ahoxe theory we fiiul the most ecouoinical 

 method of inspection requires 2 observations on each of S() units. 



Application in Setting Limit Lines 



Over 99 per cent, of the averages of samples of size N drawn from 



a product whose law of distribution is friX) where friX) is either 



normal or second approximation may be expected to lie within the 



ax 



limits defined bv the true average X plus or minus 3 7^,. If an average 



V iV 



falls outside these limits, this fact is taken as probiibly indicating the 

 existence of a trend or cyclic fluctuation in product, the cause of 

 whirh should be sought. The presence of errors of measurement 

 increases the separation of these limits to Go-,, from 6(rr- Our pre- 

 cision of detecting trend or cyclic fluctuation is thereby decreased. 



Cases often happen in practice where a„ is from 15 per cent, to 

 25 per cent, greater than or- In some instances ao has been found 

 to be nearly 50 per cent, greater than or. 



PART III 



Error Correction of Data Taken to Relate Observed 



Deviations in Quality of Product to 



Some Particular Cause 



In many practical cases it is not possible to write down an equation 

 to show how the quality of a finished product depends upon the 

 factors controlled by different manufacturing steps. To cite one such 

 case, we may know that the quality of the finished article depends 

 upon the control of the temperature to which some of the piece parts 

 are heated in the process of manufacture. Thus the microphonic 

 properties of carbon depend upon the temperature to which the 

 carbon is heated. In cases where the relationship between quality 

 and some factor (such as temperature in the above illustration) can 

 only be determined through a study of the correlation existing between 

 the quality and the particular factor, use must be made of the correl- 

 ation coefficient r which is defined as 



r = 



Cxf^yN 



where x and y represent respectively deviations from the average 

 quality X and the average magnitude Y of some factor which is 



