380 BELL SYSTEM TECHNICAL JOURNAL 



4. Role Played by Statistical Theory 

 It may appear thus far that mathematical statistics plays a relatively 

 minor role in laying a basis for economic control of quality. Such, 

 however, is not the case. In fact, a central concept in engineering work 

 of today is that almost every physical property is a statistical distribu- 

 tion. In other words, an observed set of data constitutes a sample of 

 the effects of unknown chance causes. 1 1 is at once apparent, therefore, 

 that sampling theory should prove a valuable tool in testing engineering 



60 r 



50 60 70 80 90 100 



MODULUS OF RUPTURE IN 100 POUNDS PER SQUARE INCH 



Fig. 9 — Variability in modulus of rupture of clear specimens of green sitka spruce 

 typical of the statistical nature of physical properties 



hypotheses. Here it is that much of the most recent mathematical 

 theory becomes of value particularly in analysis involving the use of 

 comparatively small numbers of observations. 



Let us consider, for example, some property such as the tensile 

 strength of a material. Provided our previous assumptions are justi- 

 fied, it follows that after we have done everything we can to eliminate 

 assignable causes of variation, there will still remain a certain amount 

 of variability exhibiting the state of control. Let us consider an ex- 

 tensive series of data recently published by a member of the Forest 

 Products Laboratories'- (Fig. 9). Here we have the results of tests for 

 tensile strength on L304 small test specimens of sitka spruce, the kind 



- Xewlin, J. A., Proceedings of the American Societv of Civil Engineers, September, 

 1926, pp. 1436-1443. 



