Performance of the MEWMA‐CoDa control chart in the presence of measurement errors

Zaidi, Fatima; Castagliola, Philippe; Tran, Kim Phuc; Khoo, Michael B. C.

doi:10.1002/qre.2705

Cited by 33 publications

(26 citation statements)

References 44 publications

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“…But if we use n > p, then it is also possible to monitor variability using the statistic defined in Gnanadesikan and Gupta (1970). (see, for instance, Zaidi et al (2020)).…”

Section: Linearly Covariate Measurement Errors Model For Codamentioning

confidence: 99%

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Effect of Measurement Errors on the Multivariate CUSUM CoDa Control Chart for the Manufacturing Process

Imran¹,

Sun²,

Zaidi³

et al. 2022

Preprint

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Control charts, one of the main tools in Statistical Process Control (SPC), have been widely adopted in manufacturing sectors as an effective strategy for malfunction detection throughout the previous decades. Measurement errors (M.E's) are involved in the quality characteristic of interest. The authors explored the impact of a linear covariate error model on the multivariate cumulative sum (CUSUM) control charts for a specific kind of data known as compositional data(CoDa). The average run length (ARL) is used to assess the performance of the proposed chart. The results indicate that M.E's significantly affects the multivariate CUSUM-CoDa control charts. The authors have used the Markov chain method to study the impact of different involved parameters using four different cases for the variance-covariance matrix (i.e. uncorrelated with equal variances, negatively correlated with equal variances, uncorrelated with unequal variances, positively correlated with unequal variances). The authors concluded that the ARL of the multivariate CUSUM-CoDa chart increase with an increase in the value of error variance-covariance matrix, while the ARL decreases with an increase in the subgroup size m or the constant powering b. For the implementation of the proposal, two illustrated examples have been reported for multivariate CUSUM-CoDa control charts in the presence of M.E's. One deals with the manufacturing process of uncoated aspirin tablets, and the other is based on monitoring machines in the muesli manufacturing process.

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“…But if we use n > p, then it is also possible to monitor variability using the statistic defined in Gnanadesikan and Gupta (1970). (see, for instance, Zaidi et al (2020)).…”

Section: Linearly Covariate Measurement Errors Model For Codamentioning

confidence: 99%

“…Similar to Zaidi et al (2020), the following four cases for the CoDa variance-covariance matrix Σ * are considered,…”

Section: Performance Of the Mcusum-coda Control Chart In The Presence...mentioning

confidence: 99%

Effect of Measurement Errors on the Multivariate CUSUM CoDa Control Chart for the Manufacturing Process

Imran¹,

Sun²,

Zaidi³

et al. 2022

Preprint

Self Cite

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“…Note that the effect of measurement errors on the performance of HWMA scheme to monitor the process mean is discussed in Thanwane et al 18,19 for Cases K and U, respectively. For some early discussions on measurement errors in SPM context, see Linna and Woodall, 27 Maravelakis et al, 28 and Maravelakis 29 ; however, for some recent contributions, see Riaz et al, 30 Sabanho et al, 31,32 Zaidi et al, 33,34 Nguyen et al, 35 and Noor-ul-Amin et al 36 The objective of this paper is to incorporate FIR features in the time-varying control limits of the HWMA scheme to monitor the mean of processes with and without measurement errors so that its sensitivity in detecting start-up problems can be improved. In the review papers by Jensen et al, 37 Psarakis et al, 38 and Does et al, 4 it is stated that the estimation of the process parameters significantly degrades the performance of a monitoring scheme; thus, the investigation of the effect of parameter estimation on the performance of the HWMĀscheme for both a constant and linearly increasing measurement system error variances is conducted.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The use of fast initial response features on the homogeneously weighted moving average chart with estimated parameters under the effect of measurement errors

Thanwane

Malela‐Majika

Aslam

et al. 2021

Quality & Reliability Eng

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Fast initial response (FIR) features are generally used to improve the sensitivity of memory-type control charts by shrinking time-varying control limits in the earlier stage of the monitoring regime. This paper incorporates FIR features to increase the sensitivity of the homogeneously weighted moving average (HWMA) monitoring schemes with and without measurement errors under constant as well as linearly increasing variance scenarios. The robustness and the performance of the HWMA monitoring schemes are investigated in terms of numerous run-length properties assuming that the underlying process parameters are known and unknown. It is found that the FIR features improves the performance of the HWMA monitoring scheme as compared to the standard no FIR feature HWMA scheme, and at the same time, it is observed that the simultaneous use of a recently proposed FIR feature and multiple measurements significantly reduces the negative effect of measurement errors. An illustrative example on the volume of milk in bottles is used to demonstrate a real-life application.

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“…Next, Maravelakis et al (2004) and Maravelakis (2012) investigated the effect of measurement errors on the EWMA and CUSUM schemes, respectively; with the effect of a two-component measurement error on the EWMA scheme investigated in Abbasi (2016). For some recent discussions on measurement errors published after the review paper of Maleki et al (2017), see for instance Asif et al (2020), Cheng and Wang (2018), Nguyen et al (2019), Noor-ul-Amin et al (2020), Riaz et al (2019), Sabahno et al (2019, 2020), Salmasnia et al (2018), Shongwe et al (2020a, b, c), Tang et al (2019), Tran et al (2019a, b, c, 2020), Yeong et al (2017), Zaidi et al (2019, 2020).…”

Section: Introductionmentioning

confidence: 99%

The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme

Thanwane

Malela‐Majika

Castagliola

et al. 2020

Transactions of the Institute of Measurement and Control

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Monitoring schemes are typically designed under the assumption of perfect measurements. However, in real-life applications, data tend to be subjected to measurement errors, that is, a difference between the real quantities and the measured ones mostly exist even with highly sophisticated advanced measuring instruments. Thus, in this paper, the negative effect of measurement errors on the performance of the homogenously weighted moving average (HWMA) scheme is studied using the linear covariate error model for constant and linearly increasing variance. Monte Carlo simulations are used to evaluate the performance of the proposed HWMA scheme in terms of the run-length characteristics. It is observed that as the smoothing parameter increases, measurement errors have a higher negative effect on the performance of the HWMA [Formula: see text] scheme. More importantly, it is shown that the negative effect of measurement errors is reduced by using multiple measurements and/or by increasing the slope coefficient of the covariate error model. Moreover, the performance of the HWMA [Formula: see text] scheme is compared with the corresponding exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) [Formula: see text] schemes. An illustrative example is provided to help in implementing this monitoring scheme in a real-life situation.

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Performance of the MEWMA‐CoDa control chart in the presence of measurement errors

Cited by 33 publications

References 44 publications

Effect of Measurement Errors on the Multivariate CUSUM CoDa Control Chart for the Manufacturing Process

Effect of Measurement Errors on the Multivariate CUSUM CoDa Control Chart for the Manufacturing Process

The use of fast initial response features on the homogeneously weighted moving average chart with estimated parameters under the effect of measurement errors

The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme

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