Cumulative sum statistical control charts using ranked set sampling data

Different cumulative sum (CUSUM) control charts for the sample mean based on ranked set sampling (RSS) data and median ranked set sampling (MRSS) data are developed and compared to the usual CUSUM based on simple random sampling (SRS) data using computer simulation. All the charts based on ranked set sampling data are shown to have smaller average run length (ARL) than the classical CUSUM charts based on SRS if the process starts to get out of control, and have approximately the same ARL if the process is in control. Real data using the RSS and MRSS are used to illustrate the new developed methods and construct the corresponding control charts. These charts are compared to usual SRS chart, it turns out that the newly developed charts are more efficient i.e. having smaller ARL In this study we are assuming the underling distribution is normal.