Monitoring the Coefficient of Variation Using a Variable Sampling Interval Control Chart

Abstract

The coefficient of variation (CV) is a quality characteristic that has several applications in applied statistics and is receiving increasing attention in quality control. Few papers have proposed control charts that monitor this normalized measure of dispersion. In this paper, an adaptive Shewhart control chart implementing a variable sampling interval (VSI) strategy is proposed to monitor the CV. Tables are provided for the statistical properties of the VSI CV chart, and a comparison is performed with a Fixed Sampling Rate Shewhart chart for the CV. An example illustrates the use of these charts on real data gathered from a casting process.Castagliola et al. 5 suggested a new method to monitor the CV by means of two one-sided EWMA charts of the CV squared. The performance investigation requires for this chart an extensive computational analysis based on a Markov chain approach (whereas the Hong et al. 4 approach is only based on simulation). A numerical analysis demonstrated that the control chart proposed by Castagliola et al. 5 almost always yielded smaller ARL values than the control chart proposed by Hong et al., 4 even if this statistical outperformance is often rather small.Very recently, Calzada and Scariano 6 suggested a synthetic control chart (denoted SynCV) for monitoring the CV. The results showed (see Table 8 in Calzada and Scariano 6 ) that the out-of-control ARLs obtained for the SynCV chart are obviously smaller than the ones for the CV chart of Kang et al., 3 but the former are generally larger than the out-of-control ARLs obtained for the EWMA-CV 2 chart of Castagliola et al. 5 as long as the increasing shift in the CV is not too large. Contrary to Castagliola et al., 5 in which the authors investigated both the CV increasing and decreasing cases, Calzada and Scariano 6 only provided results concerning the CV increasing case.Shewhart-type control charts have been extensively adopted with the advantage of their easy implementation. They provide good performance in detecting large changes in the process mean. However, they may take a longer time to detect small and moderate shifts. Classical alternatives to overcome this problem are using more advanced-type control charts such as the supplementary run rules chart, the synthetic chart, the cumulative sum (CUSUM) control chart, or the EWMA control chart and/or using adaptative strategies such as the variable sampling interval (VSI) charts and the variable sample size (VSS) charts. A very comprehensive survey about the design of adaptive charts was presented by Tagaras. 7 It covers all kinds of adaptive charts that use variable sample sizes, variable sampling intervals, and variable control limit coefficients, as well as different combinations of adaptive design parameters.In the sampling interval control charts, the sampling interval h is allowed to vary as a function of the prior sample position. The sampling interval chart uses control and warning limits, which divide the chart into three regions: the safe region, the warning region, and the out...

A new exponentially weighted moving average control chart for monitoring the coefficient of variation

“…The results showed that the synthetic chart performed better than that of Kang et al (2007), but worse than Castagliola et al (2011) as long as the increasing shift in the CV is not too large. In addition, Castagliola et al (2013a) evaluated an adaptive Shewhart control chart implementing variable sampling interval strategy to monitor the process CV. Castagliola et al (2013b) proposed a Shewhart chart with supplementary run rules to monitor the CV.…”

Monitoring the coefficient of variation using a variable sample size control chart in short production runs

“…The following example has been introduced in Castagliola et al [5] for the implementation of a VSI control chart monitoring the CV in a long production run context and will be adapted, in this paper, for a short production run context. For more information concerning this example, refer to Castagliola et al [5].…”

“…For more information concerning this example, refer to Castagliola et al [5]. This example considers actual data from a die casting hot chamber process kindly provided by a Tunisian company manufacturing zinc alloy (ZAMAK) parts for the sanitary sector.…”

“…More recently, Castagliola et al [3] suggested a new method to monitor the CV by means of two one-sided EWMA charts of the CV squared. Calzada and Scariano [4] suggested a synthetic control chart (denoted SynCV) for monitoring the CV, and Castagliola et al [5][6][7] proposed alternative approaches to monitor the CV based on Run Rules, Variable Sampling Interval (VSI), and Variable Sample Size (VSS) strategies, respectively.…”

On the performance of coefficient of variation charts in the presence of measurement errors

“…In the SPC literature, Shewhart‐type control chart for monitoring the coefficient of variation (CV), which is defined as the ratio of the population standard deviation to the population mean, has already been investigated by Kang et al; subsequently, several control charts have been developed in the literature for monitoring the CV. For further details, see, for instance, Castagliola et al, Calzada and Scariano, Castagliola et al, Castagliola et al, Zhang et al, Castagliola et al, Castagliola et al, Amdouni et al, You et al, and Tran and Tran among others. For example, in textile manufacturing industry, the variation among tensile strength measurements from thin thread is significantly smaller than measurements taken from heavy thread because of the inherent physical properties of fiber.…”