The Investigation of Multi-Stage Processes

We can thus see that the larger proportion of the total variability in the above process is arising at stage A, and only a minor part at stage B. Thus in any attempt to standardise the process, to reduce the total variability in the find product, almost all the attention should be directed towards stage A. 

Suppose we directed our eflforts at standardising stage B, and were completely successful, and reduced to zero. The total variance would now be o = 5.22, i.e. the standard deviation would be 2.29 and the 95% spread 1.96 X 2.29 = 4.5, or the total spread of 9.0. The total spread originally was 10.6, so the improvement has been comparatively slight. 

on the other hand, we had directed our efforts at standardising stage A and were completely successful in reducing to zero, the total variance would now be Ob = 2.17 or the standard deviation 1.47. The 95% spread would then be 1.96 X 1.47 == 2.9 and the total spread 5.8. 

The analysis of variance proceeds by concentrating initially upon the structure of the process, and only subsequently investigating individual variables. 

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