ECONOMIC QUALITY CONTROL OF PRODUCT 375 



that the causes of variabiHty should be left to chance. Such criteria 

 are basic to any method of securing control within limits. Let us, 

 therefore, consider them critically. It is too much to expect that the 

 criteria will be infallible. We are amply rewarded if they appear to 

 to work in the majority of cases. 



Generally speaking, the criteria are' of the nature of limits derived 

 from past experience showing within what range the fluctuations in 

 quality should remain, provided they are to be left to chance. For 

 example, when such limits are placed on the fluctuations in the qualities 

 shown in Fig. 3, we find (see Fig. 4) that in one case two points fall out- 

 side the limits and in the other case no point falls outside the limits. 

 Upon the basis of the use of such limits, we look for trouble in the form 



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 H 

 _J 

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a 



O 



z 

 o 



I- 

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D 



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Ul 



1 



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• • • 



ONLY SUCH VARIATIONS •SHOULD BE « LEFT* TO , CHANCE 



AS TIME GOES ON 



Fig. 5 — Art plus modern statistical machinery makes possible the establishment of 



such limits. 



of assignable causes in one case but not in the other. However, to be 

 of really practical interest, we should be able to answer the following 

 question: Can we expect to be able to find and eliminate causes of 

 variability only when deviations fall outside the limits? First, let us 

 see what statistical theory has to say in answer to this question. 



Upon the basis of postulate 3, it follows that we can find and remove 

 causes of variability until the remaining system of causes is constant 

 or until we reach that state where the probability that the deviations in 

 quality remain within any two fixed limits (Fig. 5) is constant. How- 

 ever, this assumption alone does not tell us that there are certain limits 

 within which all observed values of quality should remain provided the 

 causes cannot be found and eliminated. In fact so long as the limits 

 are set so that the probability of falling within the limits is less than 



