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.
