A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions

Liang, Wenjuan; Xiang, Dongdong; Pu, Xiaolong; Li, Yan; Jin, Lingzhu

doi:10.1080/16843703.2017.1372852

Cited by 20 publications

(12 citation statements)

References 28 publications

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“…In a real life scenario, this is not always possible to fulfil the normality assumption for the distributions of error during the process. A very few work in literature is about this situation including [12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

Zaka¹,

Akhter²,

Jabeen³

et al. 2021

Computer Modeling in Engineering &Amp; Sciences

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In practice, the control charts for monitoring of process mean are based on the normality assumption. But the performance of the control charts is seriously affected if the process of quality characteristics departs from normality. For such situations, we have modified the already existing control charts such as Shewhart control chart, exponentially weighted moving average (EWMA) control chart and hybrid exponentially weighted moving average (HEWMA) control chart by assuming that the distribution of underlying process follows Power function distribution (PFD). By considering the situation that the parameters of PFD are unknown, we estimate them by using three classical estimation methods, i.e., percentile estimator (P.E), maximum likelihood estimator (MLE) and modified maximum likelihood estimator (MMLE). We construct Shewhart, EWMA and HEWMA control charts based on P.E, MLE and MMLE. We have compared all these control charts using Monte Carlo simulation studies and concluded that HEWMA control chart under MLE is more sensitive to detect an early shift in the shape parameter when the distribution of the underlying process follows power function distribution.

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Section: Introductionmentioning

confidence: 99%

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

Zaka¹,

Akhter²,

Jabeen³

et al. 2021

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

show abstract

“…To deal with both above‐mentioned lacks in the literature, we have developed the control charts to monitor the shape of the parameter of underlying process distribution when the process is not assuming the normal distribution. A very few work in literature is about this situation of not normal process distribution including Noorossana et al, 13 Lin et al, 14 Erto et al, 15 Liang et al, 16 and Ahmed et al 17 . No work can be searched out to monitor the process shape parameter 15,18–20 ,.…”

Section: Introductionmentioning

confidence: 99%

“…To deal with both above-mentioned lacks in the literature, we have developed the control charts to monitor the shape of the parameter of underlying process distribution when the process is not assuming the normal distribution. A very few work in literature is about this situation of not normal process distribution including Noorossana et al, 13 Lin et al, 14 Erto et al, 15 Liang et al, 16 and Ahmed et al 17 No work can be searched out to monitor the process shape parameter. 15,18-20, To resolve these conditions, researchers focused on the construction of a control chart for nonnormal and proposed a variety of control charts other than the normal distribution (ND) like Chang and Bai 21 designed the control chart for positively skewed distribution and demonstrates the better results of false alarm rate when the distribution is symmetrical.…”

Section: Introductionmentioning

confidence: 99%

The modified control charts for monitoring the shape parameter of weighted power function distribution under classical estimator

Jabeen

Zaka

2021

Quality & Reliability Eng

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Zaka et al provided a new distribution called the Weighted Power function distribution (WPFD), which has application in reliability engineering and survival analysis. They used different estimation methods to estimate the unknown parameters of WPFD and proved that modified maximum likelihood estimator (MMLE) is best to consider for the estimation of parameters. We have constructed the memoryless and memory‐based control charts based on the assumption that the distribution of the underlying process does not follow the normal distribution. In this paper, we provide modified control charts using MMLE of the shape parameter for WPFD. We develop control charts to keep the process in control when the distribution of errors of underlying process follows WPFD. We propose the modified memoryless control chart, that is, Shewhart control chart and modified memory‐based control chart, that is, Exponentially weighted moving average (EWMA) and Hybrid exponentially weighted moving average (HEWMA) control charts. We have made the comparison of the proposed control charts using Monte Carlo simulation and the real‐life application for both and the memoryless control charts and memory‐based control charts. We see that HEWMA based on MMLE performs better as compared to other proposed control charts.

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“…A lot of existing studies on control charts rely on the assumption of normality, and some of these studies which must be recommended for having more detail include exponentially weighted moving average (EWMA) control charts first by Roberts, 2 and recently by Li et al 3 and Nguyen et al 4 ; cumulative-sum (CUSUM) control charts first introduced by Page 5 and recently by Sanusi et al, 6 Haq and Munir, 7 and Hossain et al 8 ; mixed EWMA-CUSUM control charts by Abbas et al, 9 Ajadi and Riaz 10 ; and hybrid exponentially weighted moving average (HEWMA) control charts due to Shamma and Shamma, 11 and Haq. 12 However, a few studies, for example, Noorossana et al, 13 Lin et al, 14 Erto et al, 15 Liang et al, 16 and Ahmed et al, 17 including many others, have discussed different control charts for the situations where normality assumptions are not met.…”

Section: Introductionmentioning

confidence: 99%

“…; mixed EWMA‐CUSUM control charts by Abbas et al., 9 Ajadi and Riaz 10 ; and hybrid exponentially weighted moving average (HEWMA) control charts due to Shamma and Shamma, 11 and Haq 12 . However, a few studies, for example, Noorossana et al., 13 Lin et al., 14 Erto et al., 15 Liang et al., 16 and Ahmed et al., 17 including many others, have discussed different control charts for the situations where normality assumptions are not met.…”

Section: Introductionmentioning

confidence: 99%

Control charts for the shape parameter of reflected power function distribution under classical estimators

Zaka

Akhter

Jabeen

et al. 2021

Quality & Reliability Eng

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The reflected power function distribution (RPFD) has applications in the fields of reliability engineering and survival analysis. To identify and remove the variation in different reliability processes and also to monitor the reliability of machines where the number of errors follows RPFD, we develop control charts to keep the process in control. A memory less control chart like a Shewhart control chart, and two memory-based control charts like an exponentially weighted moving average (EWMA) control chart and a hybrid exponentially weighted moving average (HEWMA) control chart are discussed and compared with each other. Proposal of these control charts is based on two different estimators, the percentile estimator (PE) and the modified maximum likelihood estimator (MMLE). This study shows that an HEWMA control chart based on PE performs better than PE-based Shewhart and EWMA control charts, as well as MMLE-based Shewhart, EWMA, and HEWMA control charts.

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A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions

Cited by 20 publications

References 28 publications

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

Control Charts for the Shape Parameter of Power Function Distribution under Different Classical Estimators

The modified control charts for monitoring the shape parameter of weighted power function distribution under classical estimator

Control charts for the shape parameter of reflected power function distribution under classical estimators

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