The demerit-based control chart for trinomial distribution

Purpose: The purpose of this paper is to investigate the properties of the classical goodness of fit test statistics X2, G2, GM2, and NM2 in testing quality of process represented as the trinomial distribution with dip null hypothesis and to devise a control chart for the trinomial distribution with...

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Main Author: Wichai Chattinnawat
Format: Journal
Published: 2018
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http://cmuir.cmu.ac.th/jspui/handle/6653943832/59422
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spelling th-cmuir.6653943832-594222018-09-10T03:15:00Z The demerit-based control chart for trinomial distribution Wichai Chattinnawat Business, Management and Accounting Purpose: The purpose of this paper is to investigate the properties of the classical goodness of fit test statistics X2, G2, GM2, and NM2 in testing quality of process represented as the trinomial distribution with dip null hypothesis and to devise a control chart for the trinomial distribution with dip null hypothesis based on demerit control chart. Design/methodology/approach: The research involves the linear form of the test statistics, the linear function of counts since the marginal distribution of the counts in any category is binomial or approximated Poisson, in which the uniformly minimum variance unbiased estimator is the linear function of counts. A control chart is used for monitoring student characteristics in Thailand. The control chart statistics based on an average of the demerit value computed for each student as a weighted average lead to a uniformly most powerful unbiased test marginally. The two-sided control limits were obtained using percentile estimates of the empirical distribution of the averages of the demerit. Findings: The demerit control chart of the weight set (1, 25, 50) shows a generally good performance, robust to direction of out-of-control, mostly outperforms the GM2 and is recommended. The X2,NM2 are not recommended in view of inconsistency and bias. The performance of the demerit control chart of the weight set (1, 25, 50) does not dramatically change between both directions. Practical implications: None of the multivariate control charts for counts presented in the literature deals with trinomial distribution representing the practical index of the quality of the production/process in which the classification of production outputs into three categories of good, defective, and reworked is common. The demerit-based control chart presented here can be applied directly to this situation. Originality/value: The research considers how to deal with the trinomial distribution with dip null hypothesis which no research study so far has presented. The study shows that the classical Pearson's X2, Loglikelihood, modified Loglikelihood, and Neyman modified X2 could fail to detect an "out-of-control". This research provides an alternative control chart methodology based on demerit value with recommended weight set (1, 25, 50) for use in general. © Emerald Group Publishing Limited. 2018-09-10T03:15:00Z 2018-09-10T03:15:00Z 2009-05-22 Journal 0265671X 2-s2.0-70349640381 10.1108/02656710910956175 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=70349640381&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/59422
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
topic Business, Management and Accounting
spellingShingle Business, Management and Accounting
Wichai Chattinnawat
The demerit-based control chart for trinomial distribution
description Purpose: The purpose of this paper is to investigate the properties of the classical goodness of fit test statistics X2, G2, GM2, and NM2 in testing quality of process represented as the trinomial distribution with dip null hypothesis and to devise a control chart for the trinomial distribution with dip null hypothesis based on demerit control chart. Design/methodology/approach: The research involves the linear form of the test statistics, the linear function of counts since the marginal distribution of the counts in any category is binomial or approximated Poisson, in which the uniformly minimum variance unbiased estimator is the linear function of counts. A control chart is used for monitoring student characteristics in Thailand. The control chart statistics based on an average of the demerit value computed for each student as a weighted average lead to a uniformly most powerful unbiased test marginally. The two-sided control limits were obtained using percentile estimates of the empirical distribution of the averages of the demerit. Findings: The demerit control chart of the weight set (1, 25, 50) shows a generally good performance, robust to direction of out-of-control, mostly outperforms the GM2 and is recommended. The X2,NM2 are not recommended in view of inconsistency and bias. The performance of the demerit control chart of the weight set (1, 25, 50) does not dramatically change between both directions. Practical implications: None of the multivariate control charts for counts presented in the literature deals with trinomial distribution representing the practical index of the quality of the production/process in which the classification of production outputs into three categories of good, defective, and reworked is common. The demerit-based control chart presented here can be applied directly to this situation. Originality/value: The research considers how to deal with the trinomial distribution with dip null hypothesis which no research study so far has presented. The study shows that the classical Pearson's X2, Loglikelihood, modified Loglikelihood, and Neyman modified X2 could fail to detect an "out-of-control". This research provides an alternative control chart methodology based on demerit value with recommended weight set (1, 25, 50) for use in general. © Emerald Group Publishing Limited.
format Journal
author Wichai Chattinnawat
author_facet Wichai Chattinnawat
author_sort Wichai Chattinnawat
title The demerit-based control chart for trinomial distribution
title_short The demerit-based control chart for trinomial distribution
title_full The demerit-based control chart for trinomial distribution
title_fullStr The demerit-based control chart for trinomial distribution
title_full_unstemmed The demerit-based control chart for trinomial distribution
title_sort demerit-based control chart for trinomial distribution
publishDate 2018
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=70349640381&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/59422
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