386 BELL SYSTEM TECHNICAL JOURNAL 



part of each bakery. The important thing for us to note, however, is 

 that the bakery having the h^west percentage return, 1.99 per cent, also 

 shows better control than the other bakeries as judged by the number 

 of points falling outside the control limits in the period of 36 weeks. 



3. Attainment of Maximum Benefits from Quantity Production 

 The quality of the finished product depends upon the qualities of raw 

 materials, piece parts and the assembling process. It follows from 

 simple theory that so long as such quality characteristics are controlled, 

 the quality of the finished unit will be controlled, and will therefore 

 exhibit minimum variability. Other advantages also result. For 

 example, by gaining control, it is as we have already seen, possible to 

 establish standard statistical distributions for the many quality char- 

 acteristics involved in design. Very briefly, let us see just how these 

 statistical distributions, representing states of control, become useful 

 in securing an economic design and production scheme. 



Suppose we consider a simple problem in which we assume that the 

 quality characteristic Y in the finished product is a function / of m 

 different quality characteristics, Xi, X^, • • • , X^, representable 

 symbolically by Equation (3). 



Y =f{X„ X,, ■■■, XJ. (3) 



For example, one of the X's might be a modulus of rupture, another a 

 diameter of cross section, and Y a breaking load. Engineering re- 

 quirements generally place certain tolerances on the variability in the 

 resultant quality characteristic F, which variability is in turn a func- 

 tion of the variabilities in each of the m different quality characteristics. 

 As already stated, the quality characteristic Y will be controlled 

 provided the m independent characteristics are controlled. Knowing 

 the distribution functions for each of the m different independent 

 variables, it is possible to approximate very closely the per cent of the 

 finished product which may be expected to have a quality characteristic 

 Y within the specified tolerances. If it is desirable to minimize the 

 variability in the resultant quality Y by proper choice of materials, for 

 example, and, if standard distribution functions for the given quality 

 characteristics are available for each of several materials, it is possible 

 to choose that particular material which will minimize the variability 

 of the resultant quality at a minimum of cost. 



4. Attainment of Uniform Quality Even TJiough Inspection Test Is 



Destructive 

 So often the quality of a material of the greatest importance to the 

 individual is one which cannot be measured directly without destroying 



