Within Batch Variabilities the Control Chart for Range

Consider the data used previously in Table 7.1, Chapter VII (b). We wish now to test the hypothesis that the variabilities within each column (batch) are drawn from a homogeneous population in other words, that batches do not differ in their internd variability. 

For this purpose we obtain the range w for each batch and plot these consecutively on a chart as in figure 6. We then calculate the mean range , here equal to 2.50, and plot on the chart an inner control line at D o- ts w = 2.17 X 2.50 = 5.4 and an outer control line at D ( . w = 2.98 X 2.50 = 7.5. These D factors are obtained from Table V in the Appendix for sample size 3. If the batches are similar in their internal variability, then on the averse not more than 1 out of 40 points will lie outside the inner control line, and only 1 

In the present instance it is clear from figure 6 that there are not points outside either of the control lines, so there is no reason to suppose that the batches differ in their internal variability. 

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