單邊規格CNPU信賴下界複式抽樣計算法

Abstract

製程能力指標被廣泛地應用在製造業，作為衡量產品製程的表現。在現實上，許多製程並不服從常態分配，因此，有學者提出一系列衡量非常態製程的指標稱為CNp(u,v)。在本篇研究中，我們考慮非常態分配且單邊規格的製程能力指標CNPU。首先，我們以模擬的方式產生四個不同參數的韋伯分配，透過複式抽樣法建構出指標CNPU的四種信賴下界，此外，根據抽樣樣本和真實母體的尾點比值關係，我們提出了一個校正項D(α,n)來修正指標C^NPU，再根據這些信賴下界的涵蓋率來比較四個複式抽樣法的績效。實驗的結果顯示校正項D(α,n)確實能使涵蓋率提升且bootstrap-t (BT) 方法較其他方法具有較佳的表現。

Process capability indices have been proposed in the manufacturing industry to provide numerical measures on process potential and performance for normal processes. In earlier studies, a class of flexible capability indices, called CNp(u,v), is considered for processes with non-normal distributions. In this thesis, we considered lower confidence bound for non-normal process with one-sided specification limits based on CNPU. Firstly, we simulate four Weibull distributions with different shape parameters α and use bootstrap method to obtain a lower confidence bound on CNPU. According to the ration R of bootstrap samples to population distribution, we propose a correction factor D(α,n) to modify the index C^NPU. In addition, a performance comparison among four kinds of bootstrap approach for 95% lower confidence bounds is conducted based on coverage rate. The computational results indicate that the correction factor D(α,n) indeed improves the coverage rates and the bootstrap-t (BT) method has the best performance of the coverage rate.