Run Sum Chart for the Mean with Auxiliary Information

Abstract

Abstract 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.