IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACH

In statistical process control and monitoring (SPCM), traditional (or classical) X control schemes are designed under the assumption of normally distributed data. However, in real-life applications, the normality assumption could easily fail to hold, and the results would no longer be realistic. The...

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Main Authors: Jean -Claude Malela - Majika, Busanga Jerome Kanyama, Maria Rapoo
Format: Article
Language:English
Published: Center for Quality, Faculty of Engineering, University of Kragujevac, Serbia 2018-03-01
Series:International Journal for Quality Research
Subjects:
Online Access:http://www.ijqr.net/journal/v12-n1/2.pdf
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spelling doaj-d8a672bdef374240b25d7388826dcfb12021-03-02T01:54:11ZengCenter for Quality, Faculty of Engineering, University of Kragujevac, SerbiaInternational Journal for Quality Research1800-64501800-74732018-03-01121174210.18421/IJQR12.01-02IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACHJean -Claude Malela - Majika0Busanga Jerome Kanyama 1Maria Rapoo2University of South Africa , College of Science, Engineering and Technology Department of Statistics P O Box 392 UNISA 0003, Florida 1709 South AfricaUniversity of South Africa , College of Science, Engineering and Technology Department of Statistics P O Box 392 UNISA 0003, Florida 1709 South AfricaUniversity of South Africa , College of Science, Engineering and Technology Department of Statistics P O Box 392 UNISA 0003, Florida 1709 South AfricaIn statistical process control and monitoring (SPCM), traditional (or classical) X control schemes are designed under the assumption of normally distributed data. However, in real-life applications, the normality assumption could easily fail to hold, and the results would no longer be realistic. Therefore, X control schemes designed under flexible probability distributions are needed. In this paper, we consider to improve the Shewhart-type X control scheme using supplementary 2-of-(h+1) and 1-of-1 or 2-of-(h+1) runs-rules (where ?? 1) for non-normal data. The proposed control schemes are designed using the Burr type XII probability distribution function (pdf) because of its properties and suitability for general industrial applications. The performance of the proposed control schemes is investigated using the Markov chain approach. It was found that the proposed schemes outperform the existing standard and improved X control schemes in many cases. An illustrative real-life example is used to demonstrate the implementation of the proposed schemes.http://www.ijqr.net/journal/v12-n1/2.pdfurr type XII X control scheme2-of-(h+1) schemeimproved 2-of-(h+1) schemeMarkov of chain approachzero-state modesteady-state mode
collection DOAJ
language English
format Article
sources DOAJ
author Jean -Claude Malela - Majika
Busanga Jerome Kanyama
Maria Rapoo
spellingShingle Jean -Claude Malela - Majika
Busanga Jerome Kanyama
Maria Rapoo
IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACH
International Journal for Quality Research
urr type XII X control scheme
2-of-(h+1) scheme
improved 2-of-(h+1) scheme
Markov of chain approach
zero-state mode
steady-state mode
author_facet Jean -Claude Malela - Majika
Busanga Jerome Kanyama
Maria Rapoo
author_sort Jean -Claude Malela - Majika
title IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACH
title_short IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACH
title_full IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACH
title_fullStr IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACH
title_full_unstemmed IMPROVED SHEWHART-TYPE X CONTROL SCHEMES UNDER NON-NORMALITY ASSUMPTION: A MARKOV CHAIN APPROACH
title_sort improved shewhart-type x control schemes under non-normality assumption: a markov chain approach
publisher Center for Quality, Faculty of Engineering, University of Kragujevac, Serbia
series International Journal for Quality Research
issn 1800-6450
1800-7473
publishDate 2018-03-01
description In statistical process control and monitoring (SPCM), traditional (or classical) X control schemes are designed under the assumption of normally distributed data. However, in real-life applications, the normality assumption could easily fail to hold, and the results would no longer be realistic. Therefore, X control schemes designed under flexible probability distributions are needed. In this paper, we consider to improve the Shewhart-type X control scheme using supplementary 2-of-(h+1) and 1-of-1 or 2-of-(h+1) runs-rules (where ?? 1) for non-normal data. The proposed control schemes are designed using the Burr type XII probability distribution function (pdf) because of its properties and suitability for general industrial applications. The performance of the proposed control schemes is investigated using the Markov chain approach. It was found that the proposed schemes outperform the existing standard and improved X control schemes in many cases. An illustrative real-life example is used to demonstrate the implementation of the proposed schemes.
topic urr type XII X control scheme
2-of-(h+1) scheme
improved 2-of-(h+1) scheme
Markov of chain approach
zero-state mode
steady-state mode
url http://www.ijqr.net/journal/v12-n1/2.pdf
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AT busangajeromekanyama improvedshewharttypexcontrolschemesundernonnormalityassumptionamarkovchainapproach
AT mariarapoo improvedshewharttypexcontrolschemesundernonnormalityassumptionamarkovchainapproach
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