A multivariate CUSUM control chart for monitoring Gumbel's bivariate exponential data

Xie, FuPeng; Sun, Jian; Castagliola, Philippe; Hu, Xuelong; Tang, Anan

doi:10.1002/qre.2717

Cited by 16 publications

(7 citation statements)

References 34 publications

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“…Step 2: Generate an out-of-control GBE vector M OC t = (X t , Y t ) of the GBE (θ 1 , θ 2 , δ) model at sampling point t using the following equations (see Xie et al [43]),…”

Section: Zero-state Casementioning

confidence: 99%

A Variable Sampling Interval Multivariate Exponentially Weighted Moving Average Control Chart for Monitoring the Gumbel’s Bivariate Exponential Data

Xie

Qiao

et al. 2022

Scientia Iranica

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The general assumption in designing a multivariate control chart is that the multiple variables are independent and normally distributed. This assumption may not be tenable in many practical situations, because multiple variables with dependency often need to be monitored simultaneously to ensure the process is in control. The Gumbel's bivariate exponential (GBE) distribution is considered to be a better model for skewed data with dependency in reliability analysis. In this paper, a multivariate exponentially weighted moving average (MEWMA) scheme with variable sampling interval (VSI) feature is developed to monitor the mean vector of GBE model. The Monte Carlo simulation is used to evaluate the average time to signal (ATS) performance of the proposed VSI MEWMA GBE scheme for three different types of shifts. Some tables are presented to show the ATS performance of the proposed scheme with different designed parameters. Additionally, both the zero-state and the steady-state ATS performance of the proposed scheme is compared with that of the conventional MEWMA chart with FSI (Fix Sampling Interval) feature. Comparative results show that the suggested scheme works better than its FSI counterpart in monitoring GBE data. Finally, a simulation example is provided to show that the VSI MEWMA GBE scheme performs well in monitoring GBE data.

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“…Step 2: Generate an out-of-control GBE vector M OC t = (X t , Y t ) of the GBE (θ 1 , θ 2 , δ) model at sampling point t using the following equations (see Xie et al [43]),…”

Section: Zero-state Casementioning

confidence: 99%

A Variable Sampling Interval Multivariate Exponentially Weighted Moving Average Control Chart for Monitoring the Gumbel’s Bivariate Exponential Data

Xie

Qiao

et al. 2022

Scientia Iranica

Self Cite

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“…Possible comparative methods to select from are the initial MBTE chart by Xie et al (2011). Or more recently, the method by Xie et al (2021) who extended the idea of Xie et al (2011) by using the multivariate cumulative sum (CUSUM) control chart. Koutras and Sofikitou (2017) and Triantafyllou and Panayiotou (2020) used control charts based on the order statistic to monitor the bivariate vector-based data.…”

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 design is then applied to Shewhart, EWMA, and CUSUM control charts for the process mean monitoring. Xie et al 26 studied a multivariate CUSUM (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GRE) data. They also compared the proposed MCUSUM GRE chart with MEWMA chart and individual CUSUM chart.…”

Section: Introductionmentioning

confidence: 99%

“…The design is then applied to Shewhart, EWMA, and CUSUM control charts for the process mean monitoring. Xie et al 26 Generally, the maximum likelihood or least squares estimators are used for regression parameter estimation, however, they can produce biased estimate for data containing outliers. [27][28][29] Mandel 29 discussed the regression control chart thoroughly and provided instructions for setting up these charts.…”

Section: Introductionmentioning

confidence: 99%

Robust proportional hazard‐based monitoring schemes for reliability data

Nabeel

Ali

Shah

2021

Quality & Reliability Eng

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Reliability of products is a key factor for successful businesses. In general, the existing monitoring schemes have poor performance as reliability data are often censored. Also, the products are manufactured in multistage processes where the outgoing quality gets affected by the previous stage quality. Besides this cascade property, historical data with outliers make the analysis even more complicated. This paper discusses exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts for monitoring a two‐stage dependent process. In particular, the proportional hazard (PH) model is assumed for modeling the relationship of quality characteristics. Furthermore, to remove the detrimental effects of outliers on the results, robust regression method known as the M‐estimation is used. Besides a real case study, the performance of the proposed monitoring approach is assessed through a comprehensive simulation study. The results suggested that the EWMA chart outperforms the CUSUM chart.

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A multivariate CUSUM control chart for monitoring Gumbel's bivariate exponential data

Cited by 16 publications

References 34 publications

A Variable Sampling Interval Multivariate Exponentially Weighted Moving Average Control Chart for Monitoring the Gumbel’s Bivariate Exponential Data

A Variable Sampling Interval Multivariate Exponentially Weighted Moving Average Control Chart for Monitoring the Gumbel’s Bivariate Exponential Data

A Real Time Monitoring Approach for Bivariate Event Data

Robust proportional hazard‐based monitoring schemes for reliability data

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