12 



BELL SYSTEM TECHNICAL JOURNAL 



PART I 



Type 1 — Error Correction of Data Taken to Show the Quality 

 OF A Particular Lot 



Let us take a specific problem first. Assume that we have a lot 

 cc)nsistinjT of 15,000 transmitters ' and a machine with which to measure 

 the efficiency of each instrument. Suppose we make one observation 

 on each transmitter — a total of 15,000 measurements. Suppose we 

 find, as in the distribution illustrated in Fig. 1, that one measure- 

 ment is in the efficiency range —1.75 to —1.50, 17 within the range 



4000 

 36O0 

 3200 

 2600 

 84C0 

 2000 

 1600 

 1200 

 800 

 400 

 



■1.0 -.5 



EFFICIEN'CV 



Fig. 1 — Typical frequency distribution. Chart showing observed number of trans- 

 mitters versus efficiency 



— 1.50 to —1.25 units, and so on. The vertical height of a point 

 represents the number or frequency of occurrence of observations 

 falling within the corresponding inter\'al laid off on the horizontal 

 axis of the chart. 



So far so good, but suppose a customer wants to buy these trans- 

 mitters. We know that some transmitter which appeared to have an 

 efficiency within the range of 1.25 to 1.50 units say, maj' actually have 

 had an efficiency within some other interval. We know too that, 

 because of the errors of measurement, the transmitters appear to 

 differ more among themselves than they really do. We therefore 



^ Of course, the efficiency of a transmitter does not remain constant during a 

 series of tests but these inherent variations in the transmitter may be considered, 

 for our purpose, as forming a component part of the resultant error of measurement. 



