Adaptive multivariate double sampling and variable sampling interval Hotelling's T2 charts |
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| Authors: | Mahfuza Khatun Michael BC Khoo WC Yeong WL Teoh ZL Chong |
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| Affiliation: | 1. School of Mathematical Sciences, Universiti Sains Malaysia, Penang, Malaysia;2. Department of Operations and Management Information Systems, Faculty of Business and Accountancy, Universiti Malaya, Kuala Lumpur, Malaysia;3. School of Mathematical and Computer Sciences, Heriot‐Watt University Malaysia, Putrajaya, Malaysia;4. Department of Physical and Mathematical Science, Faculty of Science, Universiti Tunku Abdul Rahman, Jalan Universiti, Kampar, Perak, Malaysia |
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| Abstract: | In this article, two adaptive multivariate charts, which combine the double sampling (DS) and variable sampling interval (VSI) features, called the adaptive multivariate double sampling variable sampling interval T2 (AMDSVSI T2) and the adaptive multivariate double sampling variable sampling interval combined T2 (AMDSVSIC T2) charts, are proposed. The real purpose of using the proposed charts is to provide flexibility by enabling the sampling interval length of the DS T2 chart to be varied so that the chart's sensitivity can be enhanced. The fundamental difference between the two proposed charts is that when a second sample is taken, the AMDSVSI T2 chart uses the information of the combined sample mean vectors while the AMDSVSIC T2 chart uses the information of the combined T2 statistics, in deciding about the process status. This research is motivated by existing combined DS  and VSI  charts in the literature, which show convincing performance improvement over the standard DS  chart. Consequently, it is believed that adopting this existing approach in the multivariate case will enable superior multivariate DS charts to be proposed. Numerical results show that the proposed charts outperform the existing standard T2 and other adaptive multivariate charts, in detecting shifts in the mean vector, for the zero‐state and steady‐state cases. The performances of both charts when the shift sizes in the mean vector are unknown are also measured. The application of the AMDSVSI T2 chart is illustrated with an example. |
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| Keywords: | average time to signal double sampling expected average time to signal variable sampling interval |
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and VSI 
charts in the literature, which show convincing performance improvement over the standard DS 
chart. Consequently, it is believed that adopting this existing approach in the multivariate case will enable superior multivariate DS charts to be proposed. Numerical results show that the proposed charts outperform the existing standard T2 and other adaptive multivariate charts, in detecting shifts in the mean vector, for the zero‐state and steady‐state cases. The performances of both charts when the shift sizes in the mean vector are unknown are also measured. The application of the AMDSVSI T2 chart is illustrated with an example.