Between Batch Variabilities The Control Chart for Means

We wish to test whether the batches differ significantly in their means, having regard to the observed amount of variability of the individuals. 

This is in complete agreement with the conclusion reached using the analysis of variance in Chapter VII (b). With the control chart the arithmetical labour is much less, but ibe analysis of variance has the advantage of giving numerical estimates of the relative importance of the Between Batch and Within Batch variabilities, and of the exact significance of the existence of the Between Batch variability. For detailed and exact work, therefore, the analym of variance is to be preferred, but for preliminary and exploratory investigations the control chart is very useful. 

An important proviso in the use of control charts is that the control lines should be based upon at least 10 and, preferably, 20 batches otherwise the estimate of the mean range w is not very accurate. 

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