QUALITY CONTROL 735 



temporary standards. In every case the choice of the fixed values calls 

 for the exercise of engineering judgment. The statistical problem 

 enters after these standards have been fixed. It is to determine 

 whether or not the observed fluctuations in the observed estimates of 

 the parameters are explainable upon the basis of chance. In general, 

 the method of fixing the limits closely corresponds to that whereby a 

 manufacturer sets up specifications for any kind of product. 



It should be noted that from a statistical standpoint the control 

 charts are based upon a priori reasoning. The type, of cause system 

 specified by the engineer is taken as a standard a priori system which 

 is accepted as an ideal which the manufacturer hopes to maintain. 

 The control chart thus makes it possible to differentiate between devia- 

 tions in quality which can reasonably be accounted for on the basis 

 of sampling and those deviations which cannot be so accounted for. 



It will have been noted that the limits are a function of the size of 

 the sample n. The question is therefore often raised: How large a 

 sample shall be chosen? 



So long as we are willing to risk our engineering judgment that the 

 system of causes is controlled, we need take no samples. If, however, 

 we have reason to believe that the quality has not been controlled or 

 at least wish to make sure that it is being controlled to the extent that 

 the deviation introduced by the assignable cause shall not escape 

 detection if greater than some chosen value, it is necessary for us to 

 take a sample of sufiticient size to reduce the limits of sampling fluctua- 

 tions in the particular parameter under study to just less than this same 

 value. 



In those cases where customary practice calls for the Inspection of a 

 certain number of units of product for reasons other than control, 

 these data may be used in the manner outlined above to indicate the 

 degree of control. In many instances the number of units of product 

 to be inspected is so fixed as to insure with a known degree of prob- 

 ability that the apparatus passing from one stage of the manufacturing 

 process to another meets a given tolerance for defects. This practice 

 serves to fix the number to be inspected in order to maintain a given 

 quality of apparatus as it passes through the stages of the manufactur- 

 ing process. The use of the data so obtained in the form of a control 

 chart serves to fix attention upon the assignable causes of variation in 

 the quality. The presence of these causes having been detected, it 

 generally becomes a comparatively simple matter to find and eliminate 

 them. In this way we can secure a controlled product usually requir- 

 ing less inspection and hence involving the lowest cost of manufacture. 



I am indebted to Mr. V. A. Nekrassoff for the construction of the 

 nomograms presented in this paper. 



