| Summary: | 碩士 === 長庚大學 === 工商管理學系 === 101 === The quality characteristic of the product or process can be defined by a functional relationship between the response variable and one or more explanatory variables. This functional relationship is called a profile function. To monitor this profile, we collect a sample of data. However, when the cost is high, we might just collect one sample. This paper studies how to find the optimal method to monitor profile in this situation.
This paper uses the logistic regression model to describe the profile function, and uses iterative weighted least square estimation to estimate the maximum likelihood estimator of the parameter β in order to build the Shewhart control chart and EWMA control chart. Besides, we set three types of shifts, and five kinds of sample sizes. We find the average run length in different shifts and different sample sizes by simulation. Our results show that the EWMA control chart is better than Shewhart control chart in small shifts, and the Shewhart control chart is better than the EWMA control chart in large shifts. In addition, the more sample which are used to estimate the parameter β, the better performance in detecting shifts by control chart, but the differences are not significant.
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