Run Sum Chart for the Mean with Auxiliary Information

<jats:title>Abstract</jats:title>
<jats:p>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.</jats:p>