On the performance of VSI Shewhart control chart for monitoring the coefficient of variation in the presence of measurement errors

Nguyen, Huu Du; Nguyen, Quang Thang; Tran, Kim Phuc; Ho, Dang Phuc

doi:10.1007/s00170-019-03352-7

Cited by 36 publications

(32 citation statements)

References 24 publications

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“…Therefore, to overcome these challenges in real-time activity recognition, Hong, Kang [31] used an alternative method named as multisensor data fusion (assembly reliability evaluation method-AReM). For a more detailed introduction on the AReM see [32]. In the AReM system, information is gathered from an inertial sensor embedded in a smartphone and wireless sensor system, which is plugged between the user and environment.…”

Section: Practical Applicationmentioning

confidence: 99%

Cumulative Sum Chart Modeled under the Presence of Outliers

et al. 2020

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Cumulative sum control charts that are based on the estimated control limits are extensively used in practice. Such control limits are often characterized by a Phase I estimation error. The presence of these errors can cause a change in the location and/or width of control limits resulting in a deprived performance of the control chart. In this study, we introduce a non-parametric Tukey's outlier detection model in the design structure of a two-sided cumulative sum (CUSUM) chart with estimated parameters for process monitoring. Using Monte Carlo simulations, we studied the estimation effect on the performance of the CUSUM chart in terms of the average run length and the standard deviation of the run length. We found the new design structure is more stable in the presence of outliers and requires fewer amounts of Phase I observations to stabilize the run-length performance. Finally, a numerical example and practical application of the proposed scheme are demonstrated using a dataset from healthcare surveillance where received signal strength of individuals' movement is the variable of interest. The implementation of classical CUSUM shows that a shift detection in Phase II that received signal strength data is indeed masked/delayed if there are outliers in Phase I data. On the contrary, the proposed chart omits the Phase I outliers and gives a timely signal in Phase II. of estimation error may occur when there exist some extreme values or outliers in the Phase I observations [4]. Outliers may occur by chance in the process data or could be due to some incorrect specifications of instruments or as a result of human reporting error. The presence of outliers in a process data can adversely affect parametric computations. Of course, dropping the outliers from the sampled observations is the simplest remedy often used to avoid such a problem. However, this may not be appropriate for small sample data. Thus, outlier detection is key to adequate monitoring of process parameters. Recently, some non-parametric and robust outlier detection procedures have been suggested to enhance the performance of control charts in the presence of outliers. For example, see Schoonhoven, Nazir [5], Nazir, Riaz [6], Amdouni, Castagliola [7], Abid, Nazir [8], Zhang, Li [9] and Mahmood, Nazir [10], and the references therein. Hawkins [11], Beckman and Cook [12] and Barnett and Lewis [13] have studied several outlier detectors. The common parametric outlier detectors are the Student-type and Grubbs-type detectors mostly used in the regression residuals and when the data is normally distributed (cf. Grubbs [14] and Tietjen and Moore [15]). For non-normal data, the Tukey's outlier detection model is more robust since its independence of the sample mean and standard deviation [16]. Teoh, Khoo [17] suggested the local outlier factor, a non-parametric outlier detector for detecting the outliers in the multivariate setup. Knorr, Ng [18] designed a detector based on classification methodology while a detector based on order statistics was studied by T...

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Section: Practical Applicationmentioning

confidence: 99%

Cumulative Sum Chart Modeled under the Presence of Outliers

et al. 2020

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“…with ( ) = 1 b−a for ∈ Ω and ATS is defined as in (18). The values of EATS 1 are presented in Table 7 for Ω = [0.5, 1) and Ω = (1,2], which are used for downward and upward charts, respectively.…”

Section: The Numerical Performance and Comparisonmentioning

confidence: 99%

“…Therefore, several control charts have been proposed to monitor the CV. The Shewhart CV control chart was first presented by Kang et al 1 Then, the synthetic control chart monitoring the CV was studied by Nguyen et al, 2 Tran et al 3 and Calzada and Scariano, 4 The exponentially weighted moving average CV control chart, the cumulative sum CV control chart, and the run sum CV control chart were developed. [5][6][7][8] When two or more variables are considered simultaneously, the CV is extended on the multivariate case.…”

Section: Introductionmentioning

confidence: 99%

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Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

Nguyen¹,

Tran

Heuchenne

et al. 2019

Appl Stoch Models Bus & Ind

Self Cite

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In many industrial manufacturing processes, the ratio of the variance to the mean of a quantity of interest is an important characteristic to ensure the quality of the processes. This ratio is called the coefficient of variation (CV). A lot of control charts have been designed for monitoring the CV of univariate quantity in the literature. However, the CV control charts for multivariate quantity have not received much attention yet. In this paper, we investigate a variable sampling interval (VSI) Shewhart control chart for monitoring multivariate CV. The time between two consecutive samples is allowed to vary according to the previous value of the multivariate CV, which will help the chart to detect the process shifts faster. The comparison with the fixed sampling interval Shewhart chart is implemented to highlight the advantage of the VSI method. Finally, an illustrative example is demonstrated on real data.

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“…The SPM literature of approximately 60 articles dealing with measurement errors are reviewed in Maleki et al For some more recent research works on measurement errors, see Yeong et al, Zaidi et al, Sabahno et al, Tang et al, Nguyen et al, and Tran et al A number of methods used as remedial approaches are outlined in Maleki et al, and the most used methodology to reduce measurement inaccuracy is by taking multiple measurements of each item, which was first proposed by Linna and Woodall . The multiple measurements approach keeps being investigated in research works to this day; hence, in this paper too, this remedial approach for measurement inaccuracy is implemented.…”

Section: Introductionmentioning

confidence: 99%

On monitoring the process mean of autocorrelated observations with measurement errors using the w‐of‐w runs‐rules scheme

Shongwe

Malela‐Majika

Castagliola

2020

Quality & Reliability Eng

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Runs‐rules have been widely used since the 1950s in industrial and nonindustrial process monitoring applications to improve the performance of basic and other traditional monitoring schemes. However, none of the studies on runs‐rules have accounted for a process with a combined effect of measurement errors and autocorrelation. Hence, in this paper, the use of the w‐of‐w runs‐rules to improve the performance of the Shewhart trueX¯ scheme using an additive model with a constant variance and a first‐order autoregressive model is proposed. To reduce the combined negative effect of measurement errors and autocorrelation, we implement a sampling strategy based on rational subgroups in which (a) multiple measurements per item are taken (instead of a standard single measurement) and (b) non‐neighboring observations are gathered. Moreover, the latter sampling strategy is incorporated into the values of probability elements of a Markov chain matrix which is used to derive some closed‐form expressions for the zero‐ and steady‐state run‐length distribution. The main finding of this study is that, with respect to some overall performance measures, the proposed scheme outperforms the existing Shewhart trueX¯ scheme by a significant margin. A real‐life example is used to illustrate the practical implementation of the proposed scheme.

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On the performance of VSI Shewhart control chart for monitoring the coefficient of variation in the presence of measurement errors

Cited by 36 publications

References 24 publications

Cumulative Sum Chart Modeled under the Presence of Outliers

Cumulative Sum Chart Modeled under the Presence of Outliers

Variable sampling interval Shewhart control charts for monitoring the multivariate coefficient of variation

On monitoring the process mean of autocorrelated observations with measurement errors using the w‐of‐w runs‐rules scheme

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