A proposed variable parameter control chart for monitoring the multivariate coefficient of variation

Self Cite

The coefficient of variation (CV) is used in process monitoring when the process mean and standard deviation are proportional to each other. In this work, a side‐sensitive modified group runs CV (SSMGR CV) chart is proposed for monitoring the process CV. The run length performance of the SSMGR CV chart is compared to those of the existing CV charts in terms of the average and standard deviation of the run length criteria. The SSMGR CV chart is found to outperform the existing CV charts. In addition, the run length performance of the SSMGR CV chart is also evaluated in the presence of measurement errors, as these errors are not only unavoidable in practice but they also affect the sensitivity of a control chart in detecting an out‐of‐control situation. The results obtained show that the accuracy and precision errors affect the performance of the SSMGR CV chart in detecting an out‐of‐control situation.

Section: Introductionmentioning

confidence: 99%

Side‐sensitive modified group runs charts with and without measurement errors for monitoring the coefficient of variation

Saha

Khoo

Castagliola

et al. 2020

Self Cite

“…An adaptive EWMA chart has been designed by Haq and Khoo 2 for monitoring the process MCV. Nguyen et al 9 suggested two one‐sided synthetic charts, while Chew et al 10 presented the variable parameters scheme, for monitoring the MCV. Additionally, Nguyen et al 11 proposed the VSI‐based Shewhart‐MCV chart.…”

Section: Introductionmentioning

confidence: 99%

Monitoring multivariate coefficient of variation with upward Shewhart and EWMA charts in the presence of measurement errors using the linear covariate error model

Ayyoub

Khoo

Lee

et al. 2020

Self Cite

In practice, measurement errors exist and ignoring their presence may lead to erroneous conclusions in the actual performance of control charts. The implementation of the existing multivariate coefficient of variation (MCV) charts ignores the presence of measurement errors. To address this concern, the performances of the upward Shewhart‐MCV and exponentially weighted moving average MCV charts for detecting increasing MCV shifts, using a linear covariate error model, are investigated. Explicit mathematical expressions are derived to compute the limits and average run lengths of the charts in the presence of measurement errors. Finally, an illustrative example using a real‐life dataset is presented to demonstrate the charts’ implementation.

“…19 Shepherd et al 20 proposed a Hotelling T 2 control chart based on shrunken covariance estimator. Many researchers have studied the aspects of Hotelling T 2 control chart including Chew et al, 21 Chong et al, 22 Dargopatil and Ghute, 23 and Sabahno et al 24 These estimators have some weaknesses. One is their high sensitivity to the presence of outliers, which leads to malfunction of the Hotelling T 2 control chart.…”

Section: Introductionmentioning

confidence: 99%

Robust T² control chart using median‐based estimators

Maleki

Mehri

Aghaie

et al. 2020

One of the most widely used multivariate control charts is the Hotelling T 2. In order to construct a Hotelling T 2 control chart, the mean vector (μ) and the variance-covariance matrix (Σ) must be first estimated. The classical estimators of μ and Σ are usually used to design Hotelling T 2 control chart. The classical estimators are sensitive to the presence of outliers. One way to deal with outliers is to use robust estimators. In this study, a robust T 2 control chart is proposed. The mean vector is obtained from the sample median. The median absolute deviation and the comedian are used as the estimates of the elements of the variance-covariance matrix. The proposed robust estimators of the mean vector and the variance-covariance matrix are compared with the sample mean vector and the sample variance-covariance matrix, and the M estimator of these parameters, through efficiency and robustness measures. The performances of the proposed robust T 2 control chart and the classical and the M estimators are also compared by means of average run length. Simulation results reveal that the proposed robust T 2 control chart has much better performance than the traditional Hotelling T 2 and similar performance to the M estimator in detecting shifts in process mean vector. Use of other robust estimators to estimate the process parameters is an area for further research.