Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables

This research provides a derivation of the analytical formulae to compute the average time to signal (ATS) value of the exponentially weighted moving average (EWMA) cumulative count of conforming (CCC) chart using the Markov chain technique. In the current literature, this chart is evaluated using s...

Full description

Saved in:

Bibliographic Details
Main Author:	Salihu, Abubakar Sani
Format:	Thesis
Language:	English
Published:	2021
Subjects:	QA1 Mathematics (General) QA1-939 Mathematics
Online Access:	http://eprints.usm.my/52451/1/ABUBAKAR%20SANI%20SALIHU%20-%20TESIS24.pdf
Tags:	Add Tag No Tags, Be the first to tag this record!

id	my-usm-ep.52451
record_format	uketd_dc
spelling	my-usm-ep.524512022-04-29T22:54:14Z Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables 2021-09 Salihu, Abubakar Sani QA1 Mathematics (General) QA1-939 Mathematics This research provides a derivation of the analytical formulae to compute the average time to signal (ATS) value of the exponentially weighted moving average (EWMA) cumulative count of conforming (CCC) chart using the Markov chain technique. In the current literature, this chart is evaluated using simulation. Additionally, the variable sampling interval (VSI) EWMA CCC chart is also proposed to increase the sensitivity of the basic EWMA CCC chart in detecting process shifts. The optimal designs of the VSI EWMA CCC chart are obtained based on the Markov chain procedure by minimizing the expected delay time in detecting a process shift. The optimal parameters that minimize the average time to signal (ATS) criterion are provided and can be directly used in practice. Four charts, i.e. the basic CCC, VSI CCC, EWMA CCC and VSI EWMA CCC charts are considered in the numerical comparison using the ATS criterion. The VSI EWMA CCC chart has an impressive performance in comparison to the basic CCC, VSI CCC and EWMA CCC charts. An illustrative example via real data from an injection moulding process producing an array of micro-prism of an optical element is given to demonstrate the implementation of the VSI EWMA CCC chart in practice. In addition, this research proposes a two-sided run sum ratio chart to monitor the ratio of two normal variables. A Markov chain procedure is applied to evaluate the statistical performance of the chart based on the average run length (ARL) and expected average run length (EARL) criteria. Numerical comparisons with the Shewhart ratio and synthetic ratio charts based on the zero state analysis reveal that the run sum ratio chart has a better sensitivity in most cases. 2021-09 Thesis http://eprints.usm.my/52451/ http://eprints.usm.my/52451/1/ABUBAKAR%20SANI%20SALIHU%20-%20TESIS24.pdf application/pdf en public phd doctoral Universiti Sains Malaysia Pusat Pengajian Sains Matematik
institution	Universiti Sains Malaysia
collection	USM Institutional Repository
language	English
topic	QA1 Mathematics (General) QA1-939 Mathematics
spellingShingle	QA1 Mathematics (General) QA1-939 Mathematics Salihu, Abubakar Sani Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables
description	This research provides a derivation of the analytical formulae to compute the average time to signal (ATS) value of the exponentially weighted moving average (EWMA) cumulative count of conforming (CCC) chart using the Markov chain technique. In the current literature, this chart is evaluated using simulation. Additionally, the variable sampling interval (VSI) EWMA CCC chart is also proposed to increase the sensitivity of the basic EWMA CCC chart in detecting process shifts. The optimal designs of the VSI EWMA CCC chart are obtained based on the Markov chain procedure by minimizing the expected delay time in detecting a process shift. The optimal parameters that minimize the average time to signal (ATS) criterion are provided and can be directly used in practice. Four charts, i.e. the basic CCC, VSI CCC, EWMA CCC and VSI EWMA CCC charts are considered in the numerical comparison using the ATS criterion. The VSI EWMA CCC chart has an impressive performance in comparison to the basic CCC, VSI CCC and EWMA CCC charts. An illustrative example via real data from an injection moulding process producing an array of micro-prism of an optical element is given to demonstrate the implementation of the VSI EWMA CCC chart in practice. In addition, this research proposes a two-sided run sum ratio chart to monitor the ratio of two normal variables. A Markov chain procedure is applied to evaluate the statistical performance of the chart based on the average run length (ARL) and expected average run length (EARL) criteria. Numerical comparisons with the Shewhart ratio and synthetic ratio charts based on the zero state analysis reveal that the run sum ratio chart has a better sensitivity in most cases.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Salihu, Abubakar Sani
author_facet	Salihu, Abubakar Sani
author_sort	Salihu, Abubakar Sani
title	Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables
title_short	Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables
title_full	Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables
title_fullStr	Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables
title_full_unstemmed	Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables
title_sort	proposed control charts for monitoring cumulative counts of conforming items and ratio of two variables
granting_institution	Universiti Sains Malaysia
granting_department	Pusat Pengajian Sains Matematik
publishDate	2021
url	http://eprints.usm.my/52451/1/ABUBAKAR%20SANI%20SALIHU%20-%20TESIS24.pdf
_version_	1747822182448234496

Proposed Control Charts For Monitoring Cumulative Counts Of Conforming Items And Ratio Of Two Variables

Similar Items