Some aspects of statistical quality control using ranked set sampling

Abstract

Quality control charts for sample mean and range have been constructed using some modifications of ranked set sampling (RSS) namely: median ranked set sampling (MRSS), extreme ranked set sampling (ERSS), double ranked set sampling (DRSS), as well as our suggested modifications of DRSS—median double ranked set sampling (MDRSS), double median ranked set sampling (DMRSS) and extreme double ranked set sampling (EDRSS). Using computer simulation and assuming that the underlying distribution is normal, the average run length (ARL) of the new charts were computed and compared to the control charts based on traditional simple random sampling (SRS) and regular RSS at various shift values. All the new charts are found to be performing better than the SRS and RSS charts. Controls charts for mean based on MRSS, ERSS, DRSS, MDRSS, DMRSS, and EDRSS as well as for R chart using ERSS and EDRSS were also developed using real data.