34 BELL SYSTEM TECHNICAL JOURNAL 



problems is that the weight W shall not be less than some specified 

 figure which may be considered to give us the desired degree of confi- 

 dence in the efficacy of our sampling procedure in weeding out defective 

 lots. Charts B and C are drawn up on the basis of three such specified 

 figures which are of practical interest, W = .75, W = .9, and W 

 = .99. Such restrictions enable us to show, without the large amount 

 of labor which would be required without them, the results of calcu- 

 lations for a wider range of the other variables. 



Chart B 



Chart B shows roughly for the proportion of observed defectives 

 cjn = .01, .04, and .07, the proportion of defectives in the universe 

 which we may expect not to exceed with weights W = .IS, .9 and .99 

 for various values of the sample n as abscissa and for N = 300, 500, 

 700, 900 and also the limit approached as N becomes infinite. This 

 form of presentation serves to relate the present material to the 

 earlier charts which accompanied the earlier article already mentioned 

 as having appeared in the Bell System Technical Journal for January, 

 1924, and shows how with a given size of sample n and a given pro- 

 portion of defectives observed, the larger the value of the universe TV, 

 the larger the variation which may be expected with any given degree 

 of probability. As would be expected, we also see that when the 

 size of the sample approaches the size of the universe, the range of 

 uncertainty approaches and our sample inspection becomes a 

 complete inspection. 



It will be noted that, up to the present point, we have not considered 

 cases for N > 1,000. The exact formulae become rather troublesome 

 to compute for these larger values of N. Fortunately, however, 

 various approximate methods outlined in the Appendix become suf- 

 ficiently accurate to be of service in these cases. 



Charts C 

 We have, therefore, by their aid when N > 1,000, prepared the 

 Charts C which we believe will cover a rather wide range of the 

 variables with sufficient precision to be of considerable practical 

 value. The points shown by dots are believed to be accurate to the 

 degree to which they are readable on the chart. For intermediate 

 values and for other values of the trouble limit the discrepancies are 

 indicated on the charts. One of these charts corresponds to each of 

 the three following weights, W = .75, W = .9, and W = .99. As 

 abscissa we show the per cent sample, 100 n/N. The ordinate scale 

 is proportional to the number of items n in the sample. The same 



