ECONOMIC QUALITY CONTROL OF PRODUCT 387 



the material itself. So it is with the fuse that protects your home; with 

 the steering rod on your car; with the rails that hold the locomotive in 

 its course; with the propeller of an aeroplane, and so on indefinitely. 

 How are we to know that a product which cannot be tested in respect 

 to a given quality is satisfactory in respect to this same quality? How 

 are we to know that the fuse will blow at a given current; that the steer- 

 ing rod of your car will not break under maximum load placed upon it? 

 To answer such questions, we must rely upon previous experience. In 

 such a case, causes of variation in quality are unknown and yet we are 

 concerned in assuring ourselves that the quality is satisfactory. 



Enough has been said to show that here is one of the very important 

 applications of the theory of control. By weeding out assignable causes 

 of variability, the manufacturer goes to the feasible limit in assuring 

 uniform quality. 



5. Reduction in Tolerance Limits 



By securing control and by making use of modern statistical tools, 

 the manufacturer not only is able to assure quality, even though it 

 cannot be measured directly, but is also often able to reduce the 

 tolerance limits in that quality as one very simple illustration will serve 

 to indicate. 



Let us again consider tensile strength of material. Here the measure 

 of either hardness or density is often used to indicate tensile strength. 

 In such cases, it is customary practice to use calibration curves based 

 upon the concept of functional relationship between such characteris- 

 tics. If instead of basing our use of these tests upon the concept of 

 functional relationship, we base it upon the concept of statistical rela- 

 tionship, we can make use of planes and surfaces of regression as a 

 means of calibration, thus in general making possible a reduction in the 

 error of measurement of the tensile strength and hence the establish- 

 ment of closer tolerances. It follows that this is true because, when 

 quality can be measured directly and accurately, w^e can separate those 

 samples of a material for which the quality lies within given tolerance 

 limits from all others. Now, when the method of measurement is 

 indirect and also subject to error, this separation can only be carried 

 on in the probability sense assuming the errors of measurement are 

 controlled by a constant system of chance causes. It is obvious that, 

 corresponding to a given probability, the tolerance limits may be re- 

 duced as we reduce the error of measurement. 



Fig. 14 gives a simple illustration. Here the comparative magni- 

 tudes of the standard deviations of strength about the two lines of 

 regression and the plane ^ of regression are shown schematically by the 



^ For definition of these terms see any elementary text book on statistics. 



