ELEMENTARY SAMPLING THEORY FOR ENGINEERING 2>i 



Charts A 



Charts A have been prepared by means of exact formula (3) to 

 show, for universes N = 300, 500, 700 and 900 from which samples, 

 n, of various indicated sizes are assumed to have been drawn, the 

 probability or "weight" W{c, X) as ordinate versus X as absicissa 

 for various values of c as indicated by the solid curves so designated. 

 The dotted curves crossing these solid curves show the weight indicated 

 by various values of the difference "J" between the percentage 

 observed defective and the percentage assumed defectives in the 

 universe. 



As examples illustrating the interpretation of Charts A consider 

 the following: 



Example 1: From a universe oi N = 700 items a random sample 

 n = 300 items has shown c = 3 or 1 per cent defectives. What is 

 the probability or weight to be associated with the hypothesis that 

 the universe contains not more than X = 14 or two per cent defectives? 

 From the A Chart corresponding to A'' = 700 and n = 300 we find 

 the c = 3 curve (shown heavy because it is an even per cent of the 

 sample n = 300). On this curve corresponding to an abscissa of 

 X = 14 we read our desired result as the ordinate W = .94. We 

 note that this is also a point on the d — \ per cent dotted curve 

 since \00{X jN — c/n) per cent — 1 per cent. 



Example 2: W^e are going to make a sample of « = 199 items out 

 of a universe of TV = 500 items and wish the weight or probability to 

 be .9 or better that the universe does not contain more than five 

 per cent defective items. What is the maximum number of defective 

 items that we may tolerate in our sample? Now five per cent of 

 N = 500 IS X = 25. Corresponding to an abscissa X = 2S and an 

 ordinate W = .9 we locate a point which lies between the c = 6 and 

 c = 7 curves. We could, therefore, accept the lot provided the 

 sample showed six or less defectives, or three per cent or less defectives. 



These Charts A are fundamental in nature, and involve the five 

 variables, N, n, X, c and W. The formula by means of which they 

 were computed is exact on the basis of the assumptions. Such errors 

 or irregularities as may appear to exist in them are of negligible 

 practical importance in view of the nature of the assumptions made, 

 and are mainly due to the difficulties in drafting such a family of 

 curves. 



Naturally a function involving several variables may be represented 



graphically in many different ways, some of which may be more 



convenient than others to use in connection with various practical 



problems. One of the restrictions often encountered in practical 



3 



