다중가설검정을 이용한 다변량 공정관리
- 다중가설검정을 이용한 다변량 공정관리
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- With the development of high-capacity computer storage and the rapidly growing ability to process large amounts of data, multivariate control charts have received increasing attention as a means for performing quality control analysis. Existing univariate and multivariate control charts are a sequential hypothesis testing approach to monitoring the process mean or variance using a single statistic plot. These charts can therefore be interpreted in terms of p-value. By adopting a p-value approach, a control chart can be used with a multiple comparison procedure.
This thesis proposes a multiple hypothesis approach to developing new multivariate control schemes based on a novel error rate, the False Discovery Rate which is defined as the expected portion of true null hypothesis among the total number of rejected hypotheses, is used as a controlled error rate. To control the False Discovery Rate, the Benjamini-Hochberg procedure is used. This thesis proposes two different approaches based on existence of the plotted statistics distribution because this procedure requires p-values.
For the multivariate Shewhart control chart, which is used for a known distribution, plotted Hotelling T^2 statistics are used to compute the corresponding p-values. The Benjamini-Hochberg procedure is then used to control the false discovery rate, which is applied to the proposed control scheme. Some numerical simulations are carried out to compare the performance of the proposed control scheme in terms of the average run length. The proposed method outperforms the ordinary multivariate Shewhart control chart in terms of average run length for all mean shifts.
For the multivariate exponentially weighted moving average control chart, which is used for an unknown distribution, the nonparametric density estimation is used to estimate an in-control state distribution before computing p-values. The Benjamini-Hochberg procedure is then applied to develop a new procedure for controlling the False Discovery Rate. Some numerical simulations are performed to determine the performance of the proposed method in terms of the average run length. The performance of proposed method is better than that of the ordinary multivariate exponentially weighted moving average control chart in terms of average run length for all shift sizes.
This thesis proposes new multivariate statistical process control schemes for controlling the False Discovery Rate. Both proposed methods are better than ordinary methods in terms of average run length for all shift sizes. Also, ordinary multivariate statistical process control methods assume the normality of the dataset. This assumption is not realistic. In other words, in most cases, the distribution of plotted statistics cannot be derived. Therefore, the proposed methods may be more powerful for practical use.
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