Optimal design of a nonparametric Shewhart-Lepage control chart

One of the major issues of statistical process control for variables data is monitoring both the mean and the standard deviation. The traditional approach to monitor these parameters is to simultaneously use two seperate control charts. However there have been some works on developing a single chart using a single plotting statistic for joint monitoring, and it is claimed that they are simpler and may be more appealing than the traditonal one from a practical point of view. When using these control charts for variables data, estimating in-control parameters and checking the normality assumption are the very important step. Nonparametric Shewhart-Lepage chart, proposed by Mukherjee and Chakraborti (2012), is an attractive option, because this chart uses only a single control statistic, and does not require the in-control parameters and the underlying continuous distribution. In this paper, we introduce the Shewhart-Lepage chart, and propose the design procedure to find the optimal diagnosis limits when the location and the scale parameters change simultaneously. We also compare the efficiency of the proposed method with that of Mukherjee and Chakraborti (2012).