Hassen A. Muttlak
Different quality control charts for the sample mean are developed using ranked set sampling (RSS) and median ranked set sampling (MRSS). These new charts are compared to the usual control charts based on simple random sampling (SRS) data. The charts based on RSS and MRSS are shown to have smaller average run length (ARL) than the classical chart especially if the process starts to get out of control. The MRSS is compared with RSS and SRS data, it turns out that MRSS dominates all other methods in terms of the ARL if the process starts to get out of control. Real data are collected using the SRS, RSS and MRSS. These data sets are used to construct the corresponding control charts. These charts are compared to usual SRS chart. It turns out that the newly developed charts are more efficient in estimating the population mean and the process is more stable. Through this study we are assuming that the underlying distribution is normal. A check of the normality for our data set indicated that the normality assumption is reasonable.
Key Words: Average run length, lower confidence limit, median ranked set sampling, simple random sampling and upper confidence limit.