| Summary: | 碩士 === 國立交通大學 === 統計學研究所 === 95 === The tolerance interval has long been a technique for manufacturer to verify if there is a reasonably large value confidence that ensures a proportion of production lot conforming to specification limits. This paper formally formulate this interest of “confidence” in terms of lot size and parameters involved in the underlying distribution of a product’s characteristic. With this formulation, any technique for prediction of manufacturer’s confidence may be evaluated for its efficiency and it also provides a wide room for this prediction through statistical inferences for the unknown confidence. We then study the power of the tolerance interval in detecting if there is a reasonably large manufacturer’s confidence for the production. We found that when the parameters involved in the distribution are known, the predicted manufacturer’s confidence is too optimistic in a value much more higher than the true confidence and when the parameters involved in the distribution are unknown, the predicted manufacturer’s confidence is too conservative in a value much lower than the true one. The inefficiency partly comes from the fact that tolerance interval does not use the information of lot size which is an ancillary statistic in the considered statistical model. For statistical inference of this unknown confidence, we introduce a point estimation technique that its results including a power comparison seems to be very promising for the manufacturer.
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