QUALITY CONTROL 



733 



the limiting case of the limits set on x" for the case of two cells. We 

 see, however, when samples are actually drawn from a constant system 

 of causes, as was done as nearly as possible in obtaining the data for 

 Fig. 6 of the present paper, all of the estimates of the parameters re- 

 main well within the sampling limits at least the expected proportion 

 of the time. 



To show that the limits set by means of Specification Type V upon 

 the expected or average value of the data in Fig. 4 of the article on 

 control charts just referred to are much smaller than Could have been 

 set by means of either Specification Type III or Specification Type IV, 

 Fig. 8 is given. The limits based upon Specifications Type III and IV 



Fig. 8 



were obtained directly from the nomogram of Fig. 4. The magnitudes 

 of Ln stand in the order 19.3, 12.8 and 3.0. We see at a glance that 

 lack of control, not indicated at all upon the basis of either Types III 

 or IV, appears probable upon the basis of Type V. 



Of course the use of the nomogram of Fig. 5 involves certain as- 

 sumptions which now should be considered. The sampling limits are 

 based upon the assumption that the sample is drawn from a normal 

 universe. Even under these conditions the distributions of the values 

 of estimates of the four parameters considered above are skew with 

 the exception of that of the average, but approach normality as the 

 size of the sample is increased. Theoretical and practical considera- 



