Advanced multivariate cumulative sum control charts based on principal component method with application

Riaz, Muhammad; Zaman, Babar; Mehmood, Rashid; Abbas, Nasir; Abujiya, Mu’azu Ramat

doi:10.1002/qre.2889

Cited by 9 publications

(15 citation statements)

References 39 publications

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“…This section provides a comprehensive assessment of the proposed AEWMA 1 PCA control chart against the MCE (1) and MCE (2) control charts designed by [12], the MCUSUM control chart offered by [7], MC 1 control chart proposed by [8], MC PCA 1 and MCUSUM PCA control charts suggested by [23], PC-chart recommended by [21], Hotelling's T 2 presented by [5], MEC (1) and MEC (2) initiated by [56], and EWMA-PC by [14]. (1) and MCE (2) Control Charts…”

Section: Resultsmentioning

confidence: 99%

“…This section presents the background of existing methodologies which comprise the process characteristics, Mahalanobis distance (see [10]), Hotelling's T 2 [5] control chart, MC 1 control chart by [8], control chart based on PC proposed by [21], MC PCA 1 control chart designed by [23], the relation between PCM and MD statistics, and directional invariance property.…”

Section: Existing Methodsmentioning

confidence: 99%

“…Reference [23] recommended the MC PCA 1 control chart to identify the shift in the process mean vector. The MC PCA 1 control chart structure depends on the MC 1 control chart and PCA 2 i statistic.…”

Section: Pca Control Chartmentioning

confidence: 99%

“…Moreover, instructions on how to use PCA in control charts can be found in studies [19][20][21][22], and comprehensive details are given in these references. However, the latest development of PCA techniques in control charts can be observed in the studies of [12,23].…”

Section: Introductionmentioning

confidence: 99%

“…To accomplish the stated objective, this study offers two AEWMA control charts based on the PCA method, symbolized as AEWMA PCA , to identify the different sizes of a shift in the mean vector. The proposed AEWMA PCA control charts accept the plotting statistic of the MC PCA 1 control chart as an input, whereas as the MC PCA 1 control chart (see [23]) is the modified form of the MC 1 control chart based on PCA statistics instead of the variable's vector. For adaptive features, two score functions such as Huber and Bi-square are used.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector

et al. 2022

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The special causes of variations, which is also known as a shift, can occur in a single or more than one related process characteristics. Statistical process control tools such as control charts are useful to monitor shifts in the process parameters (location and/or dispersion). In real-life situation, the shift is emerging in different sizes, and it is hard to identify it with classical control charts. Moreover, more than one process of characteristics required special attention because they must monitor jointly due to the association among them. This study offers two adaptive control charts to monitor the different sizes of a shift in the process mean vector. The novelty behind this study is to use dimensionally reduction techniques such as principal component analysis (PCA) and an adaptive method such as Huber and Bi-square functions. In brief, the multivariate cumulative sum control chart based on PCA is designed, and its plotting statistic is utilized as an input in the classical exponentially weighted moving average (EWMA) control chart. The run length (RL) properties of the proposed and other control charts are obtained by designing algorithms in MATLAB through a Monte Carlo simulation. For a single shift, the performance of the control charts is assessed through an average of RL, standard deviation of RL, and standard error of RL. Likewise, overall performance measures such as extra quadratic loss, relative ARL, and the performance comparison index are also used. The comparison reveals the superiority over other control charts. Furthermore, to emphasize the application process and benefits of the proposed control charts, a real-life example of the wind turbine process is included.

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Section: Resultsmentioning

confidence: 99%

Section: Existing Methodsmentioning

confidence: 99%

Section: Pca Control Chartmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector

et al. 2022

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A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

Ajadi

Wong

Mahmood

et al. 2021

Quality & Reliability Eng

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Multivariate charts for process dispersion detect changes in the variancecovariance matrix of a process. Most of the existing multivariate charts for monitoring the dispersion of individual observations were designed based on exponentially weighted moving average (EWMA) charting schemes. However, an alternative to the EWMA scheme is the cumulative sum (CUSUM) control chart, which has proven to be better in some cases. In the last decades, few studies have been conducted on methods based on multivariate CUSUM (MCUSUM) schemes to monitor the covariance matrix of individual observations. Consequently, we propose a new MCUSUM dispersion chart. Besides, most of the existing methods have been developed by assuming that the process parameters are known and that the process distribution is normal; these assumptions are not always true in practice. Hence, we compare the performance of the proposed chart and its counterparts based on the estimation effects under normal and nonnormal distributions. The results show that the proposed chart outperforms the other charts in terms of minor shifts in the process. Similarly, the proposed chart is the most robust to the normality assumption among the compared charts. The average value of the conditional average run length was used as the performance measure. Finally, the proposed method was also implemented with a simulated dataset to support the stated proposal findings.

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Sensitivity and reliability comparisons of EWMA mean control chart based on robust scale estimators under non‐normal process: COVID data application

Saeed,

Bataineh,

Abu‐Shawiesh

et al. 2024

Quality & Reliability Eng

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Robust control charts are getting vital importance in statistical process control theory as they are insensitive to the departure from normality. Therefore, the main objective of current work is to determine the effects of non‐normal process on the Exponentially Weighted Moving Average (EWMA) control chart. To achieve this goal, the sensitivity and reliability comparisons are made under the non‐normal process by comparing five robust M‐scale estimators, suggested in literature to modify the EWMA control limits for monitoring process mean and on the basis of percentile bootstrap estimator. The paper addresses the run length (RL) distribution of a robust EWMA control chart under the non‐normal process for which the exponential distribution is used as non‐normal process. The standard deviation of RL, out‐of‐control average run length (ARL), and shift detection probabilities are examined to assess the sensitivity and reliability of robust EWMA control charts for mean of monitoring process. The results of this research indicate that the classical EWMA control chart's performance is substantially impacted by the non‐normal distribution and the proposed EWMA control charts show higher sensitivity than classical one in terms of having smaller values of out‐of‐control ARLs. A real‐life example from the medical sciences field is provided the practical usage of the proposed control charts. The simulation analysis and practical example have shown that the suggested control charts are effective in quickly monitoring the out‐of‐control process.

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Advanced multivariate cumulative sum control charts based on principal component method with application

Cited by 9 publications

References 39 publications

An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector

An Adaptive EWMA Control Chart Based on Principal Component Method to Monitor Process Mean Vector

A new multivariate CUSUM chart for monitoring of covariance matrix with individual observations under estimated parameter

Sensitivity and reliability comparisons of EWMA mean control chart based on robust scale estimators under non‐normal process: COVID data application

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