常態混合分佈良率之區間估計

Abstract

良率為評估製程能力與品質的重要指標，目前被廣泛地應用於品質管制、環境監控與其他研究領域。假設目標族群服從常態混合分佈時，如何有系統地建構良率的信賴區間是目前尚未解決的問題。本研究提出一個針對常態混合分佈良率的區間估計方法，利用馬可夫鍊蒙地卡羅法自參數的廣義置信分佈抽樣並計算信賴區間。透過分析一筆實際環境監控的資料說明新方法的可行性，並藉由模擬評估新方法的表現。根據模擬結果，新方法所建構的信賴區間能提供足夠的覆蓋率。

Conformance proportions, which are often employed in quality control, environmental monitoring, and many other areas, are important indices for evaluating product quality and process capability. When the population of interest is assumed to have a normal mixture distribution and specification limits are set by a quality engineer, estimating conformance proportions can be a practical issue. Under the framework of normal mixture distributions, a new method is proposed in this study to obtain confidence intervals for conformance proportions. More specifically, a Markov chain Monte Carlo sampler is developed to generate realizations from the generalized fiducial distributions. The required interval estimates can then be calculated by using the obtained realizations. A real-world environmental monitoring example is used to demonstrate that the proposed method is feasible in practice. Based on simulation results, it is shown that the proposed method can maintain the empirical coverage rate sufficiently close to the nominal level.