Adaptive multivariate double sampling and variable sampling interval Hotelling's T 2 charts

In the world of business, quality improvement is of high importance for the manufacturing industries. Statistical process control via control charts provides an online monitoring of the product's characteristic. The adaptive feature is being widely used in the design parameters of a control chart, which allows at least one of them to change during the process monitoring. Specifically, a control chart is considered adaptive if at least one of the chart's parameters (sample size, sampling interval, or control limit coefficient) is allowed to change in real time on the basis of the actual values of the sample statistics.In this paper, recent developments in the design of multivariate adaptive control schemes are presented and discussed.

Section: Adaptive Hotelling's T2 and Generalized Variance Control Chartsmentioning

confidence: 99%

Section: Adaptive Hotelling's T2 and Generalized Variance Control Chartsmentioning

confidence: 99%

Section: General Conclusionmentioning

confidence: 99%

Section: General Conclusionmentioning

confidence: 99%

See 2 more Smart Citations

A survey on multivariate adaptive control charts: Recent developments and extensions

Perdikis

Psarakis

2019

“…Leoni and Costa 18 suggested a Shewhart control chart to monitor bivariate and trivariate mean vectors. An adaptive Hotelling T 2 control chart based on double sampling plan is introduced in other study 19 …”

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.

The effectiveness of Max‐half‐Mchart over Max‐Mchart in simultaneously monitoring process mean and variability of individual observations

Kruba

Mashuri

Prastyo

2021

Control charts are widely used in industrial environments for the simultaneous or separate monitoring of the process mean and process variability. The Max-Mchart is a multivariate Shewhart-type simultaneous control chart that is used when monitoring subgroups. While this sampling design allows the computation of the generalized variance (GV) used to calculate the process variability, a GV chart cannot be plotted for individual observations. Hence, we cannot compute the single statistic in the Max-Mchart. This study aims to overcome the aforementioned issue. To this end, first, we develop a new Max-Mchart for individual observations by utilizing the statistic in the dispersion control chart. Second, instead of the standard normal distribution, we propose a new transformation using a half-normal distribution to calculate the statistic for the process mean and process variability. Thus, the proposed chart is called the Max-Half-Mchart, whose control limit is calculated using the bootstrap approach. An evaluation based on the average run length values shows the robustness of the Max-Half-Mchart for the simultaneous monitoring of the process mean and process variability. The single statistic in the Max-Half-Mchart is more consistent with the statistic in Hotelling's 2 and the dispersion chart than that of the Max-Mchart.