| Summary: | 博士 === 國立交通大學 === 統計學研究所 === 96 === The contents of this dissertation are divided into three main subjects.
In the first subject, a multivariate control chart for detecting decreases in process dispersion is proposed. The proposed chart is constructed based on the one-sided likelihood ratio test (LRT) for testing , where and are respectively the current and the in-control process covariance matrix of the distribution of the quality characteristic vector of interest. Both cases of known and unknown are considered. For each case, the LRT statistic is derived and then used to construct the control chart. A comparative simulation study is conducted and shows that the proposed control chart outperforms the existing two-sided-test-based control charts in terms of the average run length. The applicability and effectiveness of the proposed control chart are demonstrated through two real examples and two simulated examples.
By combining the above mentioned one-sided LRT-based control chart and the one-sided LRT-based control chart for detecting dispersion increases proposed by Yen and Shiau (2008), we propose a combined chart scheme for detecting both cases of dispersion increases and decreases. Both cases of known and unknown are considered. It is found that a combined chart using an equal tail probability to construct a control limit is biased. By simulation studies, the proposed combined chart scheme when using a set of unequal tail probabilities for the two charts outperforms the existing two-sided-test-based control charts in terms of the average run length, when the process dispersion increases or decreases. Two real examples and two simulated examples are used to illustrate the applicability and effectiveness of our proposed combined chart.
About the third subject, Hotelling's chart is a well-known statistical process control tool for simultaneously monitoring elements of the mean vector of a multivariate normal pro¬cess. But it has a drawback that an out-of-control (or a significant) value does not gives us direct information as to which variables in are likely to have caused the out-of-control condition. We propose a method, based on likelihood principle, for identifying a variable or a group of variables in a multivariate normal process with an unknown covariance matrix �n�nthat is likely to be responsible for the out-of-control condition signaled by a significant value. Unlike certain existing methods, our method is not a control/monitoring but a diagnostic tool. Two examples from earlier literatures and one based on simulation are used to illustrate the proposed method. Finally, we compare our results with that of other existing methods for these three examples.
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