The optimal CUSUM control chart with a dynamic non-random control limit and a given sampling strategy for small samples sequence.

This article proposes a performance measure to evaluate the detection performance of a control chart with a given sampling strategy for finite or small samples sequence and prove that the CUSUM control chart with dynamic non-random control limit and a given sampling strategy can be optimal under the measure. Numerical simulations and real data for an earthquake are provided to illustrate that for different sampling strategies, the CUSUM chart will have different monitoring performance in change-point detection. Among the six sampling strategies that take only a part of samples, the numerical comparing results illustrate that the uniform sampling strategy (uniformly dispersed sampling strategy) has the best monitoring effect.

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