| Summary: | 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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