2012-08-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/711047摘要：理想中對於品質(quality)的要求是希望所有的產品都能控制在固定的目標值(target value)，且不存在任何變異(variation)。但事實上，變異在製造或是量測過程中是無法避免的。因此，在實際應用上，一般調整為要求產品品質是落在以一個可接受或容許的範圍(acceptable or tolerance region)內，其動機在於檢查落於此範圍內的產品的比例，也就是良率(conformance proportion)。許多工業上的應用上，希望去估計一個隨機變數(random variable)超過某個給定界限(specification limit)或是落於某個給定範圍(specification interval)的比例，本質上即是在估計良率。 在良率的區間估計相關文獻中，Wang and Lam (1996)以及Perakis and Xekalaki (2002)皆提出於單變量常態分佈(simple univariate normal distribution)假設下的估計方法。Iyer and Patterson (2002)指出，利用Weerahandi (1993)提出的廣義樞紐量(generalized pivotal quantity, GPQ)概念，或許是估計良率區間的可行辦法。由於實際應用過程中，變異的來源通常不只一種，單變量常態分佈的假設前提不足以滿足大部份的應用需求，所以我們將提出能擴充至常態線型模式(normal linear model)假設下的良率區間估計方法。 於計畫的第一年，我們首先將討論容許區間(statistical tolerance intervals)及良率區間估計的關係及異同。同時我們將於均衡(balanced)常態線型模式假設下，分別利用廣義樞紐量及修正大樣本法(modified large sample, MLS)估計變異數成分(variance components)的概念，提出良率區間估計方法，並透過統計模擬(simulation)討論兩種估計方法的表現。計畫的第二年，我們將以非加權均方(unweighted mean squares)取代原來MLS方法中的均方，討論在非均衡(unbalanced)常態線型模式假設下良率的區間估計方法，也將執行統計模擬來討論估計方法的表現。 <br> Abstract: Ideally, the quality characteristic value should be controlled at the target value with no variation. However, in reality, variation in a manufacturing process is inevitable. Hence, the performance requirement is usually adjusted to be a specified acceptable (or tolerance) region. The underlying motive of using the acceptable region is to inspect the proportion of conforming products falling within it. In many industrial applications, it is desired to estimate the probability that a random variable exceeds a specification limit or falls between a specification interval, which is essentially the conformance proportion. The problem of computing confidence limits for conformance proportion of a simple univariate normal distribution has been studied by Wang and Lam (1996), and Perakis and Xekalaki (2002). Also, Iyer and Patterson (2002) indicated that the concepts of a generalized pivotal quantity (GPQ), presented by Weerahandi (1993), may be useful in tackling this problem. Since a practical process usually involves multiple sources of variation, the univariate normal distribution cannot adequately fit most situations. Thus, we consider a more general setting that can be applicable to a large class of normal linear models. In the first year, we will review statistical tolerance intervals for a random variable, and discuss their relationships to the interval estimation for conformance proportions. And, we will develop two methods, one is according to the concepts of a GPQ and the other is based on the modified large sample (MLS) method, for the balanced normal linear model scenarios. In the second year, we will discuss the unbalanced data scenarios by replacing original mean squares with appropriate unweighted mean squares. The performances of the proposed methods will be evaluated through simulation studies.容許區間廣義樞紐量修正大樣本法變異數成分generalized pivotal quantitymodified large sampletolerance intervalvariance component