Efficient CV Control Charts Based on Ranked Set Sampling

Abstract

Monitoring process variability is essential for establishing efficient process-control schemes. In practice, when the mean levels of a parameter are constant, and the process variance (or standard deviation) is independent of the mean, then, the process variability is typically monitored using conventional Shewhart R or S charts. However, in some practical situations, the mean levels are not constant, and the variance is not independent of the mean. In such cases, the coefficient of variation (CV) is often constant, and thus, CV control charts are generally used to address the issue of the variability in the process. In this paper, new CV charts based on ranked sampling schemes are proposed to enhance the monitoring power of the traditional CV chart. The charts are established based on ranked set sampling (RSS), median RSS (MRSS), and extreme RSS (ERSS), and are examined in terms of their run length performance. The efficiency of the proposed charts is compared with the existing classical CV chart under simple random sampling (SRS) scheme. The results, based on a simulation study, indicate that the newly developed rank-based CV charts show better detection of monitoring signals in process CV than the classical CV chart. In particular, the CV chart based on the ERSS technique performs notably better. A real-life example concerning the monitoring of outlet temperature is also provided to illustrate the application of the proposed charts.

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