The effects of constructed bivariate copulas on multivariate control charts effectiveness

Sukparungsee, Saowanit; Sasiwannapong, Sirasak; Busababodhin, Piyapatr; Areepong, Yupaporn

doi:10.1002/qre.2850

Cited by 5 publications

(4 citation statements)

References 15 publications

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“…Koutras and Sofikitou 34 and Triantafyllou and Panayiotou 35 used control charts based on the order statistic to monitor the bivariate vector‐based data. A two‐level multivariate Bayesian control chart based on the Marshall‐Olkin bivariate exponential (MOBE) distributed data was proposed by Duan et al 36 For bivariate vector‐based event data, copula based MEWMA, multivariate double EWMA and MCUSUM charts were proposed by Kuvattana and Sukparungsee, 37 Sasiwannapong et al, 38 and Sukparungsee et al, 39 and the Hotelling's

{T}^2

chart based on the different type of copulas was discussed by Sukparungsee et al 40 For the multivariate vector‐based event data, copula based MCUSUM chart was proposed by Sukparungsee et al 41 and the MEWMA charts based on transformed exponential data and asymmetric gamma distributions were discussed by Khan et al 42 and Flury and Quaglino, 7 respectively.…”

Section: Comparative Analysismentioning

confidence: 99%

A real‐time monitoring approach for bivariate event data

Zwetsloot

Mahmood

Taiwo

et al. 2023

Appl Stoch Models Bus & Ind

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Early detection of changes in the frequency of events is an important task in many fields, such as disease surveillance, monitoring of high‐quality processes, reliability monitoring, and public health. This article focuses on detecting changes in multivariate event data by monitoring the time‐between‐events (TBE). Existing multivariate TBE charts are limited because they only signal after an event occurred for each of the individual processes. This results in delays (i.e., long time‐to‐signal), especially when we are interested in detecting a change in one or a few processes with different rates. We propose a bivariate TBE chart, which can signal in real‐time. We derive analytical expressions for the control limits and average time‐to‐signal performance, conduct a performance evaluation and compare our chart to an existing method. Our findings showed that our method is an effective approach for monitoring bivariate TBE data and has better detection ability than the existing method under transient shifts and is more generally applicable. A significant benefit of our method is that it signals in real‐time and that the control limits are based on analytical expressions. The proposed method is implemented on two real‐life datasets from reliability and health surveillance.

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{T}^2

Section: Comparative Analysismentioning

confidence: 99%

A real‐time monitoring approach for bivariate event data

Zwetsloot

Mahmood

Taiwo

et al. 2023

Appl Stoch Models Bus & Ind

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“…   I p×p (18) respectively. Equation (11) through equation (18) are solved in Mathematica version 12.2 package [37].…”

Section: Robustness To Non-normality Of the Proposed Chartsmentioning

confidence: 99%

“…[15]- [17] proposed adaptive versions of MCUSUM and MEWMA charts for the process mean based on fixed and variable sampling intervals. We refer interested to [18]- [22] for some recent enhancements of the MEWMA, MCUSUM and MHWMA charts.…”

Section: Introductionmentioning

confidence: 99%

One-Sided and Two One-Sided Multivariate Homogeneously Weighted Moving Charts for Monitoring Process Mean

Adegoke

Riaz

Ganiyu³

2021

IEEE Access

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Multivariate memory-type control charts that use information from both the current and previous process observations have been proposed. They are designed to detect shifts in both upper and downward directions with equal precision when monitoring the process mean vector. The absence of directional sensitivity can limit the charts' application, particularly when users are interested in detecting variations in one direction than the other. This article proposes one-sided and two one-sided multivariate control charts for monitoring shifts in the process mean vector. The proposed charts are presented in the form of the multivariate homogeneously weighted moving average approach that yields efficient detection of shifts in the mean vector. We provide simulation studies under different shift sizes in the process mean vector and evaluate the performance of the proposed charts in terms of their run length properties. We compare the average run length (ARL) results of the charts with the conventional charts as well as the onesided and two one-sided multivariate exponentially weighted moving average (MEWMA) and multivariate cumulative sum (MCUSUM) charts. Our simulation results show that the proposed charts outperform the existing charts used for the same purpose, particularly when interest lies in detecting small shifts in the mean vector. We show how the charts can be designed to be robust to non-normal distributions and give a step-by-step implementation efficient application of the charts when their parameters are unknown and need to be estimated. Finally, an illustrative example is provided to show the application of the proposed charts.INDEX TERMS Average run length; multivariate homogeneously weighted moving average; one-sided control charts; two one-sided control charts, robustness, estimation.

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“…A two-level multivariate Bayesian control chart based on the Marshall-Olkin bivariate exponential (MOBE) distributed data was proposed by Duan et al (2020). For bivariate vector-based event data, copula based MEWMA, multivariate double EWMA and multivariate CUSUM charts were proposed by Kuvattana and Sukparungsee (2015), Sasiwannapong et al (2019), and Sukparungsee et al (2021), and the Hotelling's T 2 chart based on the different type of copulas was discussed by Sukparungsee et al (2018). For the multivariate vector-based event data, copula based MCUSUM chart was proposed by Sukparungsee et al (2017) and the MEWMA charts based on transformed exponential data and asymmetric gamma distributions were discussed by Khan et al (2018) and Flury and Quaglino (2018), respectively.…”

Section: Comparative Analysismentioning

confidence: 99%

A Real Time Monitoring Approach for Bivariate Event Data

Zwetsloot¹,

Mahmood²,

Taiwo³

et al. 2021

Preprint

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Early detection of changes in the frequency of events is an important task, in, for example, disease surveillance, monitoring of high-quality processes, reliability monitoring and public health. In this article, we focus on detecting changes in multivariate event data, by monitoring the time-between-events (TBE). Existing multivariate TBE charts are limited in the sense that, they only signal after an event occurred for each of the individual processes. This results in delays (i.e., long time to signal), especially if it is of interest to detect a change in one or a few of the processes. We propose a bivariate TBE (BTBE) chart which is able to signal in real time. We derive analytical expressions for the control limits and average time-to-signal performance, conduct a performance evaluation and compare our chart to an existing method. The findings showed that our method is a realistic approach to monitor bivariate time-betweenevent data, and has better detection ability than existing methods. A large benefit of our method is that it signals in real-time and that due to the analytical expressions no simulation is needed. The proposed method is implemented on a real-life dataset related to AIDS.

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The effects of constructed bivariate copulas on multivariate control charts effectiveness

Cited by 5 publications

References 15 publications

A real‐time monitoring approach for bivariate event data

A real‐time monitoring approach for bivariate event data

One-Sided and Two One-Sided Multivariate Homogeneously Weighted Moving Charts for Monitoring Process Mean

A Real Time Monitoring Approach for Bivariate Event Data

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