Determining the Reference Sample Size Needed to Control the Accuracy of the Conditional in-control ARL of a Normal-theory CUSUM

The question considered in this paper is how large does an in‐control reference sample need to be in order to control the effects of using estimated parameters when using a normal‐theory cumulative sum (CUSUM) tracking statistic? Previous research has demonstrated the effect of estimation errors on the conditional in‐control average run length of the CUSUM. The contributions of this paper are simple analytical tools that determine the required reference sample size needed to ensure probabilistic control of the relative error of the conditional in‐control average run length. The availability of these tools rounds out the design phase of the CUSUM by enabling a practical procedure for determining the needed size of the reference sample.