Abstract
An approximation to the average run length for cumulative sum control charts is derived using the analogy between this procedure and the sequential probability ratio test for normal observations. This approximation is also derived by using a Brownian motion approximation to the cumulative sum. The Brownian motion approximation does not require the normality assumption. The analytical expression for the average run length obtained from the approximation is then used to determine the optimal choice of parameters to minimize the average run length at a specified deviation flom control, subject to a fixed average run length when in control.
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