A synthetic control chart for monitoring process dispersion with sample range

Abstract

A synthetic control chart for monitoring the changes in the standard deviation of a normally distributed process is proposed in this paper. The synthetic chart consists of the sample range (R) chart and the conforming run-length (CRL) chart. The R chart can be viewed as a special case of the synthetic chart. The operation, design and performance of this chart are described. Average run-length comparisons between other procedures and the synthetic chart are presented. It indicates that the synthetic chart is a good alternative for monitoring process dispersion. The variable sampling interval (VSI) schemes, as an enhancement to the synthetic chart, are discussed to further improve the chart performance. An example is presented to illustrate the application of synthetic chart and its VSI scheme.Keywords Control chart · Conforming run length · Process dispersion · Variable sampling interval Nomenclature n sample size R sample range W relative range CRL conforming run length k + coefficient of upper control limit of the R chart for δ > 1 k − coefficient of lower control limit of the R chart for δ < 1 L lower control limit of the CRL chart δ magnitude of the change in the process standard deviation δ d magnitude of the change in the process standard deviation that should be detected as soon as possible F(·) cumulative distribution function of W ARL R average number of R samples required to detect for the R chart

Optimal design of a synthetic chart for monitoring process dispersion with unknown in-control variance

“…So, the study of a chart which can detect both upward and downward shifts in the process dispersion becomes necessary and important. Along with these ideas, we extend the one-sided synthetic charts introduced by Chen and Huang (2005) and Huang and Chen (2005) and propose a two-sided synthetic S 2 chart to monitor the process dispersion.…”

“…Chen and Huang (2005) and Huang and Chen (2005) developed the synthetic charts for monitoring the process dispersion with the sample standard deviations and sample ranges, respectively. Khilare and Shirke (2012) proposed the nonparametric synthetic chart which is a combination of the sign sub-chart and the CRL sub-chart for detecting the increases in the process variation.…”

The synthetic control chart based on two sample variances for monitoring the covariance matrix

“…For the univariate case, many innovations have been proposed to improve the charts' performance, such as the CUSUM charts (see Page 1 and Reynolds and Stoumbos 2 ), the EWMA charts (see Lucas and Saccucci 3 and Costa and Rahim 4 ), the adaptive charts (see Costa 5,6 and De Magalhães et al 7 ), the double sampling charts (see Daudin 8 ) and the synthetic charts (see Wu and Spedding 9,10 , Wu et al 11 , Wu and Yeo 12 , Calzada and Scariano 13 , Davis and Woodall 14 , Scariano and Calzada 15 , Gadre and Rattihalli 16 , Chen and Huang 17 and Huang and Chen 18 ).…”

Some Group Runs Based Multivariate Control Charts for Monitoring the Process Mean Vector

“…It was shown that the synthetic X chart outperforms the Shewhart X chart over the entire range of shifts in the process mean. The development of the synthetic control chart for a univariate process has been also documented by Calzadaand Scariano [4], Davis and Woodall [5], Scariano and Calzada [6], Huang and Chen [7], and Costa and Rahim [8]. The development of the Multivariate synthetic control chart for monitoring process Mean vector (MV-Syn-M) has been proposed by Ghute and Shirke [9].…”