Question

Is the average run length performance of a control chart more meaningful measure of performance than the type 1 and type 2 error probabilities? what information does arl convey that the statistical error probabilities do not?

Answer 1

In response to the first question, about the performance of the average duration of a control chart, the performance is not so much. When the Type I and Type II errors are determined and the costs related to both errors are higher than the ARL. The ARL provides an inference of the ability to detect a certain change but does nothing else.