A CUSUM chart for detecting the intensity ratio of negative events

Qu, Liang; He, Shiwei; Khoo, Michael B. C.; Castagliola, Philippe

doi:10.1080/00207543.2017.1398423

Cited by 12 publications

(7 citation statements)

References 25 publications

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“…Wu et al [31] were the first to propose a combined T /X control chart based on a T chart to monitor the time interval and on a X chart to monitor the amplitude. From that moment, several other TBEA control charts have been developed, see Wu et al [32], Wu et al [33], Qu et al [21], Qu et al [23], Ali and Pievatolo [5], Rahali et al [24].…”

Section: Introductionmentioning

confidence: 99%

A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data

Castagliola

Celano

2020

Journal of Applied Statistics

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During the recent years, many control charts have been developed for the simultaneous monitoring of the time interval T between successive occurrences of an event E and its magnitude X. All these TBEA (Time Between Events and Amplitude) control charts assume a known distribution for the random variables T and X (like, for instance, the normal, lognormal, gamma or Weibull distributions). But, in practice, as it is rather difficult to know the actual distribution of the time T or the amplitude X, proposing a distribution-free approach could be a way to overcome this "distribution choice" dilemma. For this reason, we propose in this paper a distribution-free upper-sided EWMA (Exponentially Weighted Moving Average) type control chart, for simultaneously monitoring the time interval T and the magnitude X of an event. In order to investigate the performance of this control chart and obtain its run length properties, we also develop a specific method called "continuousify" which, coupled with a classical Markov chain technique, allows to obtain reliable and replicable results. A numerical comparison shows that our distributionfree EWMA TBEA chart performs as the parametric Shewhart TBEA chart, but without the need to pre-specify any distribution. An illustrative example obtained from a French forest fire database is also provided to show the implementation of the proposed distribution-free EWMA TBEA control chart.

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Section: Introductionmentioning

confidence: 99%

A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data

Castagliola

Celano

2020

Journal of Applied Statistics

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“…As the effect of an event E is not only quantified by its frequency T but also by its amplitude X, a combined scheme for monitoring the time interval using a T chart and the amplitude using a X chart have been introduced by Wu et al 17 The corresponding control chart is called a time-between-events-and-amplitude (TBEA) chart. After the paper of Wu et al, 17 several single TBEA charts have been developed (see previous works [18][19][20]. Very recently, Ali and Pievatolo 21 introduced a new control chart based on the assumption of a renewal process with rewards, where the reward represents the magnitude and a magnitude-over-threshold condition represents the occurrence of an event.…”

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

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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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“…The use of both current and past data makes CUSUM and EWMA strcutures more prominent as compared to the Shewhart chart in the process. The layout and improvements in the design structure of CUSUM charts can be found in literature 11–16 . Similarly, the works on enhancements of EWMA charts can be seen in the literature of previous studies 17–19 …”

Section: Introductionmentioning

confidence: 94%

IQR CUSUM charts: An efficient approach for monitoring variations in aquatic toxicity

Hussain

Sun

Mahmood

et al. 2021

Journal of Chemometrics

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Toxicant testing is a major component of the environmental solution testing program. This test system aims to evaluate the sensitivity of the test species, evaluate comparability between laboratory test results, and classify possible variability sources such as healthy organisms, organism batches, laboratory water, and food quality changes. For the continuous assessment of sensitivity and accuracy of laboratory toxicity tests, control charts are often used. The cumulative sum (CUSUM) charting structure is a popular monitoring tool that is often used due to its outstanding ability in recognizing small‐to‐moderate unusual changes in process parameters. The CUSUM control charts have now been widely accepted/applied for monitoring the process dispersion under the assumption that the process does not have outliers. In practice, most of the processes have outliers. Therefore, the use of the interquartile range (IQR) as a plotting statistic is an attractive choice for dispersion monitoring. Hence, in this study, the CUSUM control chart with auxiliary information‐based IQR estimators is proposed and employed to monitor dispersion or variation in the variable LC50 by using quantitative structure–activity relationship (QSAR) aquatic toxicity data set. The proposed IQR‐CUSUM charts are compared to its counterparts by using a variety of main output run‐length functions, such as average run length (ARL), standard deviation of run length (SDRL), and extra quadratic loss (EQL), derived from the distribution of run‐length. Further, results revealed that the proposed CUSUM charts have better detection ability as compared to existing counterpart charts, both in theoretical and practical considerations.

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A CUSUM chart for detecting the intensity ratio of negative events

Cited by 12 publications

References 25 publications

A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data

A distribution-free EWMA control chart for monitoring time-between-events-and-amplitude data

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

IQR CUSUM charts: An efficient approach for monitoring variations in aquatic toxicity

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