A Double Generally Weighted Moving Average Chart for Monitoring the COM-Poisson Processes

Chen, Jen‐Hsiang

doi:10.3390/sym12061014

Cited by 8 publications

(7 citation statements)

References 22 publications

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“…Since data dispersion cannot be identified beforehand, an expanded Poisson distribution called the Conway and Maxwell Poisson (denoted as COM‐Poisson) takes into account both location and dispersion parameters. Hence, Chen 60 proposed the GWMA COM‐Poisson scheme, which is shown to yield a better small shifts performance than the EWMA COM‐Poisson scheme. The latter conclusion holds in many situations when monitoring location parameter only or simultaneously monitoring location and dispersion parameters, but over the entire range of shifts when monitoring dispersion only (except in very few instances with a large dispersion parameter).…”

Section: Gwma Schemesmentioning

confidence: 99%

“…Next, Huang et al 75 proposed a DGWMA SoS scheme and showed that it has a better ARL and SDRL detection ability than the corresponding DEWMA and GWMA SoS schemes in many situations. More recently, Chen 60 showed that the DGWMA COM‐Poisson scheme has better small shifts detection ability (in monitoring location, dispersion, and the latter two simultaneously) than the EWMA, DEWMA, and GWMA COM‐Poisson schemes.…”

Section: Dgwma Schemesmentioning

confidence: 99%

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Generally weighted moving average monitoring schemes: Overview and perspectives

Mabude

Malela‐Majika

Castagliola

et al. 2020

Quality & Reliability Eng

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An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution‐free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (ie, double GWMA, composite Shewhart‐GWMA, mixed GWMA‐CUSUM, and mixed CUSUM‐GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA‐related schemes (ie, 66 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.

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Section: Gwma Schemesmentioning

confidence: 99%

Section: Dgwma Schemesmentioning

confidence: 99%

Generally weighted moving average monitoring schemes: Overview and perspectives

Mabude

Malela‐Majika

Castagliola

et al. 2020

Quality & Reliability Eng

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“…11 The PEWMA chart using a ranked set sampling scheme has been suggested by Abujiya et al 12 The extended work on PGWMA has been developed by Chiu and Lu, 13 Chiu and Sheu, 14 and Chen. 15 Abbasi 16 developed Poisson progressive mean (PPM) charts under the zero and steady-state situations. The interested readers are referred to Rakitzis et al, 17 Morais et al, 18 Cabral Morais and Knoth, 19 Abbas et al, 20 and Aly et al 21 for more literature on Poisson charting schemes.…”

Section: Introductionmentioning

confidence: 99%

An unbiased function‐based Poisson adaptive EWMA control chart for monitoring range of shifts

Abbas

Nazir

Riaz

et al. 2023

Quality & Reliability Eng

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For monitoring the number of nonconformities per unit in industrial processes during the inspection, Poisson control charts are most widely deployed. These charting structures are referred to as attribute control charts as the quality characteristic under study is based on a nominal scale other than a quantitative or measured scale. In this study, Poisson adaptive exponentially weighted moving average (PAEWMA) has been designed and the performance of the said chart under a steady‐state situation along with the zero‐state condition has been studied for detecting changes over an unknown range of shifts. The enactment of the proposed PAEWMA design with existing schemes has been evaluated and compared using run‐length (RL) profiles such as; average RL (ARL), the standard deviation of RL (SDRL), and some percentile points of the RL distribution. The extra quadratic loss and relative mean index measures have been used for comparing the range of shifts. The comparison reveals that the proposed PAEWMA chart under the steady‐state situations performs far better than the competitors. The effect of estimation of the process parameter is also a part of the study. The three applications of the proposal have been included; which are taken from the artificial dataset, from past study monitoring dataset, and the other from the aircraft accident monitoring data for the implementation of the proposal.

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“…However, the mentioned procedures require excellent expertise, high computational efforts, and time. The Conway-Maxwell (COM)-Poisson (COM-Poisson) model proposed by Guikema and Goffelt [45] is the better alternative, which is a flexible model and able to handle any type of disperse data [46]. Lord et al [47] and Lord et al [48] have successfully used COM-Poisson regression to model the traffic crash data.…”

Section: Introductionmentioning

confidence: 99%

GLM-Based Flexible Monitoring Methods: An Application to Real-Time Highway Safety Surveillance

et al. 2021

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Statistical modeling of historical crash data can provide essential insights to safety managers for proactive highway safety management. While numerous studies have contributed to the advancement from the statistical methodological front, minimal research efforts have been dedicated to real-time monitoring of highway safety situations. This study advocates the use of statistical monitoring methods for real-time highway safety surveillance using three years of crash data for rural highways in Saudi Arabia. First, three well-known count data models (Poisson, negative binomial, and Conway–Maxwell–Poisson) are applied to identify the best fit model for the number of crashes. Conway–Maxwell–Poisson was identified as the best fit model, which was used to find the significant explanatory variables for the number of crashes. The results revealed that the road type and road surface conditions significantly contribute to the number of crashes. From the perspective of real-time highway safety monitoring, generalized linear model (GLM)-based exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are proposed using the randomized quantile residuals and deviance residuals of Conway–Maxwell (COM)–Poisson regression. A detailed simulation-based study is designed for predictive performance evaluation of the proposed control charts with existing counterparts (i.e., Shewhart charts) in terms of the run-length properties. The study results showed that the EWMA type control charts have better detection ability compared with the CUSUM type and Shewhart control charts under small and/or moderate shift sizes. Finally, the proposed monitoring methods are successfully implemented on actual traffic crash data to highlight the efficacy of the proposed methods. The outcome of this study could provide the analysts with insights to plan sound policy recommendations for achieving desired safety goals.

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A Double Generally Weighted Moving Average Chart for Monitoring the COM-Poisson Processes

Cited by 8 publications

References 22 publications

Generally weighted moving average monitoring schemes: Overview and perspectives

Generally weighted moving average monitoring schemes: Overview and perspectives

An unbiased function‐based Poisson adaptive EWMA control chart for monitoring range of shifts

GLM-Based Flexible Monitoring Methods: An Application to Real-Time Highway Safety Surveillance

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