CX11 



Tables for Statisticians and Biometricians [XXI XXII 



The following rule is suggested: 



The foreman should report when 



(a) the sum of the breaking strength of the 20 articles in the sample is less 

 than 3395 Ibs.; 

 or when (6) the lowest breaking strength is less than 136 Ibs. 



This rule has the following basis: 



The standard error of the mean of samples of 20 is 12/V 20 = 2*6833 Ibs. The 

 table shows that the deviation to the 1 / point is 2*326 in samples of 1 and 3*289 

 in samples of 20. Hence the mean in a random sample of 20 should only once in a 

 hundred times be less than 176 - 2'326 x 2*6833 = 1G9'76 Ibs., and the sum of the 20 

 breaking strengths should not be less than 20 x 169'76 =3395*2 Ibs. Again the 

 lowest value in the sample should only be less than 176 3*289 x 12 = 136*53 Ibs. in 

 1 / of samples. Of course the strengths of the mean and of the weakest individual 

 are correlated, and a more exhaustive test might be applied, based on the mean and 

 standard deviation of the sample. But if one of the main purposes in controlling 

 variability is to prevent articles appearing below a certain level of strength, the 

 use of the lower limit seems to be suitable. The test is also much simpler in appli- 

 cation than one involving the calculation of the standard deviation of the sample. 



Diagram 2. 



