Sec. 5.6 



CONTROL CHARTS 



149 



in the procedure described above. As more samples accumulate a 

 better estimate of p can be computed and used. 



It may be that the quality of a manufactured item is judged by 

 means of a measurement such as length, diameter, weight, or a volume 

 which is likely to be a member of a near-normal population rather than 

 a binomial population. The principles involved are the same but now 

 x and s £ (see Chapter 6 for definitions) must be used instead of esti- 

 mates of p and its standard deviation. In such situations the upper 

 and lower control limits are given, respectively, by: 



X rtr 



sV{^x 2 )/n(n - 1) 



Aside from this change, the control charts are constructed and inter- 

 preted as before. Of course, sample means, X{, are plotted against 

 order of draw. 



In view of the fact that the s% is somewhat tedious to compute, it has 

 been found to be both satisfactory and economical to use control limits 

 which employ the range as the measure of variation instead of the 

 standard deviation. This procedure and the necessary tables are given 

 and discussed in publications on quality control or on industrial statis- 

 tics, and will not be given here. 



PROBLEMS 



1. Another group of samples taken under conditions described for Table 5.61 

 gave the following results. Make a control chart similar to Figure 5.61 and 

 draw appropriate conclusions. 



