Monitoring Schemes for Two-dimensional Profiles with Random Effects
博士 === 國立交通大學 === 統計學研究所 === 106 === As high-tech advances rapidly, industrial production lines are getting more and more complicated. Developing suitable monitoring schemes for complicated processes as such has drawn much attention in the area of quality control. Among them, profile monitoring has...
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ndltd-TW-106NCTU53370032019-05-16T00:08:11Z http://ndltd.ncl.edu.tw/handle/97fgjg Monitoring Schemes for Two-dimensional Profiles with Random Effects 二維隨機效應剖面資料之監控方法 Lin, Szu-Han 林思涵 博士 國立交通大學 統計學研究所 106 As high-tech advances rapidly, industrial production lines are getting more and more complicated. Developing suitable monitoring schemes for complicated processes as such has drawn much attention in the area of quality control. Among them, profile monitoring has been a growing and promising area of research in statistical process control (SPC) in recent years. Most research work in the literature focused on one-dimensional profiles. As technologies are advancing, two-dimensional profiles have become key quality characteristics for more and more processes; however, no monitoring schemes have been developed in the literature at the present time. Consider nonlinear two-dimensional profiles with random effects. Under a random-effect model and adopting the nonparametric regression approach, we propose using second-order multilinear principal component analysis (MPCA) to develop profile monitoring schemes. The multilinear principal component scores of two-dimensional profiles obtained from the multilinear principal component analysis are utilized to construct control charts. In Phase II, the average run length (ARL) performance of a control chart varies as the process parameter estimates from the Phase I analysis vary in each application. Consequently, the ARL becomes a random variable due to the so-called “practitioner-to-practitioner” variation. We develop an algorithm to construct a control limit with which practitioners would have a high “confidence” that the actual in-control ARL will exceed the nominal in-control ARL level. In Phase I, if two-dimensional profiles come from a normal distribution, we develop a control chart based on the distribution of the in-control ARL. If two-dimensional profiles violate the normal assumption, we develop a distribution-free control chart. The false-positive rate and false-negative rate are considered as the performance measures for Phase I analysis. Some real data analyses are provided to demonstrate the applicability of the proposed control charts. Horng Shiau Jyh-Jen 洪志真 2017 學位論文 ; thesis 86 zh-TW |
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博士 === 國立交通大學 === 統計學研究所 === 106 === As high-tech advances rapidly, industrial production lines are getting more and more complicated. Developing suitable monitoring schemes for complicated processes as such has drawn much attention in the area of quality control. Among them, profile monitoring has been a growing and promising area of research in statistical process control (SPC) in recent years. Most research work in the literature focused on one-dimensional profiles. As technologies are advancing, two-dimensional profiles have become key quality characteristics for more and more processes; however, no monitoring schemes have been developed in the literature at the present time. Consider nonlinear two-dimensional profiles with random effects. Under a random-effect model and adopting the nonparametric regression approach, we propose using second-order multilinear principal component analysis (MPCA) to develop profile monitoring schemes. The multilinear principal component scores of two-dimensional profiles obtained from the multilinear principal component analysis are utilized to construct control charts. In Phase II, the average run length (ARL) performance of a control chart varies as the process parameter estimates from the Phase I analysis vary in each application. Consequently, the ARL becomes a random variable due to the so-called “practitioner-to-practitioner” variation. We develop an algorithm to construct a control limit with which practitioners would have a high “confidence” that the actual in-control ARL will exceed the nominal in-control ARL level. In Phase I, if two-dimensional profiles come from a normal distribution, we develop a control chart based on the distribution of the in-control ARL. If two-dimensional profiles violate the normal assumption, we develop a distribution-free control chart. The false-positive rate and false-negative rate are considered as the performance measures for Phase I analysis. Some real data analyses are provided to demonstrate the applicability of the proposed control charts.
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author2 |
Horng Shiau Jyh-Jen |
author_facet |
Horng Shiau Jyh-Jen Lin, Szu-Han 林思涵 |
author |
Lin, Szu-Han 林思涵 |
spellingShingle |
Lin, Szu-Han 林思涵 Monitoring Schemes for Two-dimensional Profiles with Random Effects |
author_sort |
Lin, Szu-Han |
title |
Monitoring Schemes for Two-dimensional Profiles with Random Effects |
title_short |
Monitoring Schemes for Two-dimensional Profiles with Random Effects |
title_full |
Monitoring Schemes for Two-dimensional Profiles with Random Effects |
title_fullStr |
Monitoring Schemes for Two-dimensional Profiles with Random Effects |
title_full_unstemmed |
Monitoring Schemes for Two-dimensional Profiles with Random Effects |
title_sort |
monitoring schemes for two-dimensional profiles with random effects |
publishDate |
2017 |
url |
http://ndltd.ncl.edu.tw/handle/97fgjg |
work_keys_str_mv |
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