The run sum t control chart for monitoring process mean changes in manufacturing

Abstract

The \( \overline{X} \) type charts are not robust against estimation errors or changes in process standard deviation. Thus, the t type charts, like the t and exponentially weighted moving average (EWMA) t charts, are introduced to overcome this weakness. In this paper, a run sum t chart is proposed, and its optimal scores and parameters are determined. The Markov chain method is used to characterize the run length distribution of the run sum t chart. The statistical design for minimizing the out-of-control average run length (ARL1) and the economic statistical design for minimizing the cost function are studied. Numerical results show that the t type charts are more robust than the \( \overline{X} \) type charts for small shifts, in terms of ARL and cost criteria, with respect to changes in the standard deviation. Among the t type charts, the run sum t chart outperforms the EWMA t chart for medium to large shifts by having smaller ARL1 and lower minimum cost. The run sum t chart surpasses the \( \overline{X} \) type charts by having lower ARL1 when the charts are optimally designed for large shifts but the run sum \( \overline{X} \) and EWMA \( \overline{X} \) prevail for small shifts. In terms of minimum cost, the \( \overline{X} \) type charts are superior to the t type charts. As occurrence of estimation errors is unpredictable in real process monitoring situations, the run sum t chart is an important and useful tool for practitioners to handle such situations.