Correction of Data for Errors of Measurement 



By W. A. SHEWHART 



Introduction 



EVERY mcasureinent is subject to error. This universally 

 accepted truth is the result of every-day experience. From 

 the simplest type of measurement, such as determining the length 

 of a board with an ordinary tape measure, to the most refined type 

 of measurement, such as determining the charge on an electron, 

 errors are bound to creep in. 



Now, a manufacturer must constantly make measurements of one 

 kind or another in an effort to control his production processes and 

 to measure the quality of his finished product in terms of certain of 

 its characteristics, but, before he can safely determine the significance 

 of observed differences in his production processes or in the quality 

 of his product as given by these measurements, he must make allow- 

 ance for his errors of measurement; i.e., for the fact that the observed 

 differences may be larger or smaller than the true differences. To 

 make such allowances for the errors of measurement of any character- 

 istic, to find out what the true magnitude of the characteristic most 

 probably is, to find out, as it were, what a thing most probably is 

 from what it appears to be, presents an endless chain of interesting 

 problems to be solved. 



Three important types of problems arising in engineering practice 

 are discussed in this paper. They are: 



1. Error correction of data taken to show the quality of a par- 

 ticular lot. 



2. Error correction of data taken periodically to detect significant 

 changes in quality of product. 



3. Error correction of data taken to relate observed deviations in 

 quality of product to some particular cause. 



The solution of the first one is presented here for the first time. 

 The solution of the second has been generalized to include cases not 

 previously solvable. All three types of problems are illustrated. 



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