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Cumulative Sequential Control Charts with Sample Size Bound

This paper proposes sequential control charts with an upper bound on sample size. Existing sequential control charts have no restriction on the number of observations at a sampling point. For situations where sampling and testing an item is time-consuming or expensive, sequential control charts may not be directly applied. When the number of observations in a sampling point reaches the upper bound and there is no out-of-control signal, the proposed cumulative sequential control chart defers the decision to the next sampling point of which starting value is the value of the current statistic. Two Markov chains, inner and outer chains, are used to derive the formulas for evaluating the performance of the proposed chart. It is compared with $\bar{X}$ and cumulative sum control charts with fixed and variable sample sizes. The fast initial response (FIR) feature is studied. Guidelines for the design of the proposed charts are also given.