52 BELL SYSTEM TECHNICAL JOURNAL 



variations from instrument to instrument in the quantity A'. After 

 the manufacturing methods ha\e been estabhshed, the first problem 

 is to obtain answers to tin- lullowing (|uestions: 



1. What is the most probaijlc value of A'? 



2. What is the percentage of instrumeiUs iiaxiiig \-.iIuos of X 

 between any two limits? 



3. Arc the causes controlliiii; \\\v product random, or arc ilu'v 

 correlated ? ^ 



In this practical case we mu?-l decide to choose a certain number 

 of instruments in order to obtain the answers to these questions; 

 that is, to obtain the most probable frequency distribution. We 

 must, however, go one step further. We must choose a certain 

 number of instruments at stated periods in order to determine whether 

 or not the product is changing. How big a sample shall we choose 

 in the first place, and how large shall the periodic samples be? Obvi- 

 ously it is of great economic importance to keep the sample number 

 in any case at a minimum required to establish within the reejuircd 

 degree of precision the answers to the questions raised. 



The close similarity between the physical and engineering problems 

 must be obvious. Naturally, then, we need not confine ourselves 

 in the present discussion to a consideration of only the problems 

 arising in connection with the study of those microphonic properties 

 of carbon which gave rise to the present investigation. Several 

 examples are therefore chosen from fields other than carbon stud\-. 

 However only those points which have been found of practical ad- 

 vantage in connection with the analysis of more than "iDD.OOO obsi-rwi- 

 tions will be considered. 



The type of inspection priil)lcin ma\ lie illll^^raIl■d liy thr data 

 given in Table H. 



The symbol X refers to the efficicnc\' of transmitters as determined 

 in the process of inspection : N represents the number of instruments 

 measured in order to obtain the average value A'. The first four 

 rows of data represent the results obtained by four inspection groiijjs 

 G\, Gz, Gi and 6V The results given are for the same period of time. 

 The next three rows are those for different machines Mu M-i and .\fj. 

 The last row gives the results of single tests on 08,502 transmitters, a 

 part of which was measured on each of the three machines. The third 

 column in the table gives the standard di-\ iatinns. It \\ ill be obser\ed 



"The slKnificincc of this quistioti will liccumc iiuire evident in the cnurse of 

 the paper. VVc shall liiul that, if the causes are such as to he technically temied 

 random, we can answer all practical questions with a far greater degree of 

 precision than we can if the causes are not random. 



