The use of the auxiliary information (AI) method in control charts is gaining increasing attention. Many studies have shown that auxiliary information-based charts can boost the charts’ performances in the detection of out-of-control signals. In this study, a run sum chart for the mean based on auxiliary characteristics (abbreviated as the RS-AI chart) is proposed. The optimization designs of the RS-AI chart in minimizing the steady-state out-of-control average run length (ARL) and expected average run length (EARL) are developed. The formulae to compute the steady-state ARL and EARL of the RS-AI chart are derived using the Markov chain approach. The RS-AI chart is compared with the Shewhart AI, synthetic AI, and exponentially weighted moving average AI charts. The results show that the RS-AI chart outperforms the competing charts for all shift sizes when the correlation between the auxiliary and the study variable is large. A numerical example is given to demonstrate the implementation of the RS-AI chart.
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