UNIVARIATE COEFFICIENT OF VARIATION CONTROL CHARTS BASED ON RANKED SET SAMPLING SCHEMES IN PHASE I

Abstract

Control chart is a very important tool used in Statistical Process Control. Monitoring variability is a vital part of modern statistical process control. In a situation where the in-control process has a constant mean and variance, the conventional Shewhart R and S charts are usually used to monitor the variation of the process. In cases where the mean and standard deviation are not constant, the coefficient of variation (CV) is often constant and is used to monitor variability. Improvement on the efficiency of these charts is often desirable especially with relatively small sample sizes. Moreover, the need of an efficient sampling scheme becomes more pronounced when the exact measurement of unit is difficult and expensive, but the visual ordering of units is possible and realizable. Consequently, in this study, new CV charts based on ranked set sampling schemes are proposed to enhance the monitoring power of the classical CV chart. The charts are established based on ranked set sampling (RSS), median RSS (MRSS), extreme RSS (ERSS), systematic RSS (SRSS) and neoteric RSS (NRSS), and are evaluated in terms of their Probability to Signal. The efficiency of the proposed charts is compared with the existing classical CV chart under simple random sampling (SRS) scheme. The results, based on simulation study, indicated that the newly proposed rank-based CV charts showed better detection of monitoring signals in process CV than the classical CV chart. In particular, the CV charts based on the NRSS and SRSS techniques performed notably better. A real-life application, concerning the non-isothermal Continuous Stirred Tank chemical Reactor (CSTR), was also provided to show the implementation of the proposed charts in phase I.