Quality Control Charts for Monitoring Process Mean Using Varied L Ranked Set Sampling

Abstract

In the statistical process control literature, there exist several improved quality control charts based on cost-e ective sampling schemes, including the ranked set sampling (RSS) and median RSS (MRSS). A generalized cost-e ective RSS scheme has been recently introduced for e ciently estimating the population mean, namely varied L RSS (VLRSS). In this thesis, we construct new quality control charts for monitoring the process mean using VLRSS scheme, including the cumulative sum (CUSUM), the exponentially weighted moving average (EWMA), the Shewhart- EWMA and Shewhart-CUSUM charts, with perfect and imperfect rankings. Extensive Monte Carlo simulations are used to compute the run length characteristics of the proposed control charts. These control charts are then compared with their existing counterparts based on simple random sampling, RSS and MRSS schemes. It is found that, with either perfect or imperfect rankings, the proposed control charts perform better than the existing control charts in detecting small to moderate shifts in the process mean. A real life dataset is also used to elucidate the implementation and working of the proposed control charts. An algorithm to generate a varied L ranked set sample is given in the Appendix.