Evaluation of Shewhart time-between-events-and-amplitude control charts for several distributions

Rahali, Dorra; Castagliola, Philippe; Taleb, Hassen; Khoo, Michael B. C.

doi:10.1080/08982112.2018.1479036

Cited by 28 publications

(33 citation statements)

References 25 publications

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“…As in Rahali et al, 29 in order to simultaneously monitor the time between an event E and its amplitude, we investigate three different statistics Z = Z ( T ′ , X ′ ), denoted as Z 1 , Z 2 , and Z 3 , all functions of T ′ and X ′ , having the following properties: (i) Z↑ if either T ′ ↓ or X ′ ↑ , (ii) Z↓ if either T ′ ↑ or X ′ ↓ .…”

Section: Tbea Chartsmentioning

confidence: 75%

“…In this paper, we propose to extend the preliminary work in Rahali et al 29 and use three kinds of copulas in order to investigate the properties of one‐sided Shewhart TBEA charts for three different statistics Z 1 , Z 2 , and Z 3 , which all depend on T (time) and X (amplitude). The main limitations of this contribution are (i) the fact that a parametric distribution has to be chosen for X and T (without being exhaustive, this paper nevertheless investigates three distributions: gamma, normal, and Weibull), and (ii) the parameters of these distributions as well as the copulas dependence parameter have to be known or, at least, accurately estimated.…”

Section: Introductionmentioning

confidence: 99%

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Evaluation of Shewhart time‐between‐events‐and‐amplitude control charts for correlated data

Rahali

Castagliola

Taleb

et al. 2020

Quality & Reliability Eng

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In recent years, several techniques based on control charts have been developed for the simultaneous monitoring of the time interval T and the amplitude X of events, known as time‐between‐events‐and‐amplitude (TBEA) charts. However, the vast majority of the existing works have some limitations. First, they usually focus on statistics based on the ratio , and second, they only investigate a reduced number of potential distributions, that is, the exponential distribution for T and the normal distribution for X. Moreover, until now, very few research papers have considered the potential dependence between T and X. In this paper, we investigate three different statistics, denoted as Z1, Z2, and Z3, for monitoring TBEA data in the case of three potential distributions (gamma, normal, and Weibull), for both T and X, using copulas as a mechanism to model the dependence. An illustrative example considering times between machine breakdowns and associated maintenance illustrates the use of TBEA control charts.

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Section: Tbea Chartsmentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Evaluation of Shewhart time‐between‐events‐and‐amplitude control charts for correlated data

Rahali

Castagliola

Taleb

et al. 2020

Quality & Reliability Eng

Self Cite

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“…"The EQL can be defined as the weighted average of ARL over a process shifts range θ min < θ < θ max using the weight θ 2 , where θ is a general notation that may denote the shift in either the shape, the rate or in both parameters. (6) In this study, Equation-6 considered the uniform distribution for shifts, however, to reflect reality, this distribution can be any other distribution. The general equation for EQL can be written as:…”

Section: Eql and Rarlmentioning

confidence: 99%

A Comparison of Shewhart-Type Time-Between-Events Control Charts Based on the Renewal Process

et al. 2020

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To study the high quality processes, Time-between-events (TBE) control charts have several advantages over the ordinary control charts. However, the existing TBE charts are based on the exponential distribution, which limit the application of these charts to monitor rare events. Therefore, to generalize existing exponential TBE charts, recently two new TBE charts assuming Weibull and generalized exponential distributions for the inter-arrival times of the renewal process, have been proposed in the literature. The main aim of this study is to present a detailed comparison of these charts. We use the expected quadratic loss (EQL), relative average run length (RARL), continuous rank probability score (CRPS) and closeness measure to assess the performance of the Weibull and the generalized exponential charts. We also discuss four real data examples in this article. INDEX TERMS Average run length, continuous rank probability score, Expected quadratic loss, Generalized exponential distribution, High quality process, Relative average run length, Weibull distribution.

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“…In addition, TBE‐type charts for monitoring the gamma, the lognormal, or the Weibull distributions are also common, and readers can refer for instance to other works. 6‐9 …”

Section: Introductionmentioning

confidence: 99%

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

Xie

Sun

Castagliola

et al. 2020

Quality & Reliability Eng

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Exponentially distributed data are commonly encountered in high‐quality processes. Control charts dedicated to the univariate exponential distribution have been extensively studied by many researchers. In this paper, we investigate a multivariate cumulative sum (MCUSUM) control chart for monitoring Gumbel's bivariate exponential (GBE) data. Some tables are provided to determine the optimal design parameters of the proposed MCUSUM GBE chart. Furthermore, both zero‐state and steady‐state properties of the proposed MCUSUM GBE chart for the raw and the transformed GBE data are compared with the multivariate exponentially weighted moving average (MEWMA) chart and the paired individual cumulative sum (CUSUM) chart. The results show that the proposed MCUSUM GBE chart outperforms the other two types of control charts for most shift domains. In addition, an extension to Gumbel's multivariate exponential (GME) distribution is also investigated. Finally, an illustrative example is provided in order to explain how the proposed MCUSUM GBE chart can be implemented in practice.

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Evaluation of Shewhart time-between-events-and-amplitude control charts for several distributions

Cited by 28 publications

References 25 publications

Evaluation of Shewhart time‐between‐events‐and‐amplitude control charts for correlated data

Evaluation of Shewhart time‐between‐events‐and‐amplitude control charts for correlated data

A Comparison of Shewhart-Type Time-Between-Events Control Charts Based on the Renewal Process

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

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