On the multivariate progressive control chart for effective monitoring of covariance matrix

Abstract

With the development of modern acquisition techniques, data with several correlated quality characteristics are increasingly accessible. Thus, multivariate control charts can be employed to detect changes in the process. This study proposes two multivariate control charts for monitoring process variability (MPVC) using a progressive approach. First, when the process parameters are known, the performance of the MPVC charts is compared with some multivariate dispersion schemes. The results showed that the proposed MPVC charts outperform their counterparts irrespective of the shifts in the process dispersion. The effects of the Phase I estimated covariance matrix on the efficiency of the MPVC charts were also evaluated. The performances of the proposed methods and their counterparts are evaluated by calculating some useful run length properties. An application of the proposed chart is also considered for the monitoring of a carbon fiber tubing process. K E Y W O R D Sdispersion monitoring, estimation effects, multivariate control chart, phase I, progressive setup INTRODUCTIONMany manufacturing processes have multiple correlated quality characteristics; multivariate control chart is very effective in monitoring such processes. 1 For example, monitoring multivariate quality variables like the diameter and length of the manufacturing process of a dowel pin. Hotelling 2 introduced a 2 -control chart; this chart is very efficient at detecting large shifts in the process mean vector, which is also mentioned by Mahmood et al. 3 Two multivariate cumulative sum (MCUSUM) charts were proposed by Healy, 4 where the first chart monitors the process mean vector, and the other monitors the covariance matrix. Crosier 5 also proposed a multivariate CUSUM chart. Pignatiello Jr and Runger 6 introduced another multivariate CUSUM control charts for detecting shifts in the process mean vector. Lowry et al 7 provided a Multivariate exponentially weighted moving average (EWMA) chart for detecting small and intermediate shifts in the process parameter. This chart is a direct extension of the univariate EWMA control chart by Roberts. 8 The multivariate CUSUM and EWMA control charts are very efficient in detecting small and moderate shifts in the process parameters. Ajadi and Riaz 9 proposed two multivariate charts which combine the effects of MEWMA and MCUSUM charts. Their proposed charts are more effective in detecting only small shifts in the proposed than the MEWMA and MCUSUM charts. Next, multivariate dispersion charts are employed to detecting changes in the covariance matrices. For example, Alt 10 proposed generalized variance chart (GVC), |S|. The determinant of the sample covariance matrix was employed as the summary statistics. Chen et al 11 worked on a Max-MEWMA chart in monitoring the mean vector and covariance matrix 2724

Triple Homogeneously Weighted Moving Average Charts for Monitoring Process Dispersion

“…Finally, several issues are recommended for future studies of the THWMAV charts. For example, the concepts of the THWMAV charts can be used with the idea of neutrosophic statistics [32,33], in the high-yield processes [34], in multivariate process cases [35], etc.…”

Improved Nonparametric Control Chart Based on Ranked Set Sampling with Application of Chemical Data Modelling

“…is study is carried out where the process variable follows the univariate distributions. However, the proposed NPDHWMA RSS charting scheme can be used to enhance the monitoring of high-quality processes [29,30], time-between-events [31], multivariate processes [32], and neutrosophic statistics [33,34] scenarios. Data Availability e data used in the real-life application can be obtained from the corresponding author upon request.…”

Progressive mean as a special case of exponentially weighted moving average: Discussion

“…Some recent modifications/extensions of PM chart can be seen in Abbasi et al 5 . Ajadi et al., 6 Alevizakos and Koukouvinos, 7 Mahmood et al 8 . and references therein.…”

“…respectively. Some recent modifications/extensions of PM chart can be seen in Abbasi et al 5 Ajadi et al, 6 Alevizakos and Koukouvinos, 7 Mahmood et al 8 and references therein. Through some mathematical manipulations, Abbas 1 showed that the PM statistic in (2) can be rewritten as:…”