THE L3 SYSTEM — QUALITY CONTROL REQUIREMENTS 



949 



universe of true values for an element may be described by Curve A in 

 Fig. 1, having a spread of 2r. Let us also assume the distribution of 

 errors of measurement representing the precision of the measuring device 

 (assumed to be unbiased) is described by Curve B of Fig. 1, having a 

 spread of 2s. If, for the purposes of discussion, these distributions are 

 Normal, the resulting apparent distribution of the individual values 

 (the distribution of measured values) is a composite of the distribution 

 A and B, as shown by C urve C of Fig. 1. The spread of this distribution 

 will be 2g, where q = y/r^ + s^. If s = 3^r, as shown in Fig. 1, then 

 q = -s/r^ + 0.25r2 or g = l.llSr. Thus, the apparent distribution has a 

 spread which is about 12 per cent greater than the true distribution. 

 Similar computations for other values of measuring precision in relation 

 to the true distribution give the following: 



Measurements normally made to determine process capabilities include 

 the effect of random errors but not necessarily of systematic errors. 



The effect of systematic error or bias of the measurements is quite 

 different. Bias tends to cause unknown and unwanted displacement of 

 the process average from the aimed-at value. This, in turn, can be re- 



'Tv 



-B ERRORS OF 

 MEASUREMENT 



\ ^^ A TRUE VALUES 

 V 

 \ 



-SOS 



Fig. 1 — Effect of measuring errors. 



