Optimal design of an improved (Formula presented.) and R control chart for joint monitoring of process location and dispersion

Abstract

Enhancing the detection power of control charts for detecting small to moderate process changes is always the focus of attention in academia. To improve the detection ability of conventional (Formula presented.) and R control charts, an improved joint (Formula presented.) and R chart, which combines the ordinary (Formula presented.) and R charts with runs rules of the type ‘r out of m’, is proposed to monitor the process location and dispersion simultaneously. A finite Markov chain imbedding approach is employed to develop the resulting control scheme. A comparative study is conducted to investigate the performance of the proposed chart in terms of the out-of-control average run length. The statistical performance of the suggested chart when the process parameters are estimated is also evaluated. The numerical results indicate that (1) the proposed chart improves the detection ability of traditional (Formula presented.) and R charts in detecting small to moderate process shifts; (2) the suggested scheme performs better than the EWMA and CUSUM schemes in detecting large process fluctuations. Furthermore, when specific values of r and m are selected, the statistical performance of the proposed chart for detecting small shifts is close to or even better than that of its competitors; (3) the run length performance of the proposed chart is greatly affected by parameter estimation, especially for small process shifts.