# Cite Article

### The Monitoring of Dirichlet Compositional Data

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@article{IJASEIT13429, author = {Reham W. Elshaer and Aya A. Aly}, title = {The Monitoring of Dirichlet Compositional Data}, journal = {International Journal on Advanced Science, Engineering and Information Technology}, volume = {11}, number = {5}, year = {2021}, pages = {1868--1875}, keywords = {Compositional data; Dirichlet distribution; phase II monitoring; quality control; MEWMA chart.}, abstract = {Compositional data are used in many applications such as Cement, Asphalt, and many other Chemical industries. Such data represent random variables whose values must sum up to a certain constant. Quality engineers and technicians require monitoring compositional data and detecting the source of the irregularity in the process as soon as it happens. Throughout the literature, complicated methods were introduced to monitor compositional data. Such methods are computationally complex and can lead to difficulties in interpreting the results. The Dirichlet distribution is commonly used in the literature to model compositional data. In this study, we propose three simple methods to monitor the mean vector of the Dirichlet distribution. The first method is based on a MEWMA control chart. The second method is based on transforming the Dirichlet random variables into beta random variables and then monitoring them using multiple EWMA control charts, while the third method uses multiple EWMA control charts for transformed independent random variables. Using a simulation technique, the performance of the three methods is investigated, and the three methods performed very well under different sample sizes, many random variables, and values of the distribution parameters. When the process is out-of-control, the source of the out-of-control signal can be detected using Method 2 and Method 3. Method 2 maintained its good performance with a probability 0.99 of correctly detecting the source of the signal. Method 3 performed well except for the case of Dirichlet parameter values less than one. However, it maintained almost a probability of correct detection of at least 90% in most cases. The three proposed methods are simple, do not need complicated calculations, and can easily be applied and used by practitioners.

}, issn = {2088-5334}, publisher = {INSIGHT - Indonesian Society for Knowledge and Human Development}, url = {http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=13429}, doi = {10.18517/ijaseit.11.5.13429} }

## EndNote

%A Elshaer, Reham W. %A Aly, Aya A. %D 2021 %T The Monitoring of Dirichlet Compositional Data %B 2021 %9 Compositional data; Dirichlet distribution; phase II monitoring; quality control; MEWMA chart. %! The Monitoring of Dirichlet Compositional Data %K Compositional data; Dirichlet distribution; phase II monitoring; quality control; MEWMA chart. %XCompositional data are used in many applications such as Cement, Asphalt, and many other Chemical industries. Such data represent random variables whose values must sum up to a certain constant. Quality engineers and technicians require monitoring compositional data and detecting the source of the irregularity in the process as soon as it happens. Throughout the literature, complicated methods were introduced to monitor compositional data. Such methods are computationally complex and can lead to difficulties in interpreting the results. The Dirichlet distribution is commonly used in the literature to model compositional data. In this study, we propose three simple methods to monitor the mean vector of the Dirichlet distribution. The first method is based on a MEWMA control chart. The second method is based on transforming the Dirichlet random variables into beta random variables and then monitoring them using multiple EWMA control charts, while the third method uses multiple EWMA control charts for transformed independent random variables. Using a simulation technique, the performance of the three methods is investigated, and the three methods performed very well under different sample sizes, many random variables, and values of the distribution parameters. When the process is out-of-control, the source of the out-of-control signal can be detected using Method 2 and Method 3. Method 2 maintained its good performance with a probability 0.99 of correctly detecting the source of the signal. Method 3 performed well except for the case of Dirichlet parameter values less than one. However, it maintained almost a probability of correct detection of at least 90% in most cases. The three proposed methods are simple, do not need complicated calculations, and can easily be applied and used by practitioners.

%U http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=13429 %R doi:10.18517/ijaseit.11.5.13429 %J International Journal on Advanced Science, Engineering and Information Technology %V 11 %N 5 %@ 2088-5334

## IEEE

Reham W. Elshaer and Aya A. Aly,"The Monitoring of Dirichlet Compositional Data,"International Journal on Advanced Science, Engineering and Information Technology, vol. 11, no. 5, pp. 1868-1875, 2021. [Online]. Available: http://dx.doi.org/10.18517/ijaseit.11.5.13429.

## RefMan/ProCite (RIS)

TY - JOUR AU - Elshaer, Reham W. AU - Aly, Aya A. PY - 2021 TI - The Monitoring of Dirichlet Compositional Data JF - International Journal on Advanced Science, Engineering and Information Technology; Vol. 11 (2021) No. 5 Y2 - 2021 SP - 1868 EP - 1875 SN - 2088-5334 PB - INSIGHT - Indonesian Society for Knowledge and Human Development KW - Compositional data; Dirichlet distribution; phase II monitoring; quality control; MEWMA chart. N2 -Compositional data are used in many applications such as Cement, Asphalt, and many other Chemical industries. Such data represent random variables whose values must sum up to a certain constant. Quality engineers and technicians require monitoring compositional data and detecting the source of the irregularity in the process as soon as it happens. Throughout the literature, complicated methods were introduced to monitor compositional data. Such methods are computationally complex and can lead to difficulties in interpreting the results. The Dirichlet distribution is commonly used in the literature to model compositional data. In this study, we propose three simple methods to monitor the mean vector of the Dirichlet distribution. The first method is based on a MEWMA control chart. The second method is based on transforming the Dirichlet random variables into beta random variables and then monitoring them using multiple EWMA control charts, while the third method uses multiple EWMA control charts for transformed independent random variables. Using a simulation technique, the performance of the three methods is investigated, and the three methods performed very well under different sample sizes, many random variables, and values of the distribution parameters. When the process is out-of-control, the source of the out-of-control signal can be detected using Method 2 and Method 3. Method 2 maintained its good performance with a probability 0.99 of correctly detecting the source of the signal. Method 3 performed well except for the case of Dirichlet parameter values less than one. However, it maintained almost a probability of correct detection of at least 90% in most cases. The three proposed methods are simple, do not need complicated calculations, and can easily be applied and used by practitioners.

UR - http://ijaseit.insightsociety.org/index.php?option=com_content&view=article&id=9&Itemid=1&article_id=13429 DO - 10.18517/ijaseit.11.5.13429

## RefWorks

RT Journal Article ID 13429 A1 Elshaer, Reham W. A1 Aly, Aya A. T1 The Monitoring of Dirichlet Compositional Data JF International Journal on Advanced Science, Engineering and Information Technology VO 11 IS 5 YR 2021 SP 1868 OP 1875 SN 2088-5334 PB INSIGHT - Indonesian Society for Knowledge and Human Development K1 Compositional data; Dirichlet distribution; phase II monitoring; quality control; MEWMA chart. AB