标题: 产品品质良率与制程损失指标
Production Quality Yield and Process Loss Indices
作者: 张英仲
Y. C. Chang
彭文理
W. L. Pearn
工业工程与管理学系
关键字: 非对称规格;偏误;复式抽样方法;信赖下界;最大概似估计量;最小平方估量;制程损失指标;品质良率;均匀最小变异不偏估计量;信赖上界;Asymmetric tolerances;Bias;Bootstrap methods;Lower confidence bound;MLE;MSE;Process loss indices;Quality yield;UMVUE;Upper confidence limit
公开日期: 2003
摘要: 在制造工业对于量测制程绩效好坏,制程良率是最为常见的判断标准。而一个更为先进的测量公式,称为品质良率指标 Yq,把顾客损失考虑进来。针对任意分配的制程,品质良率指标可以计算制程的品质良率。品质良率的作法是,针对产品品质特性偏离目标值之变异程度,对于良率作一个处罚的动作,也就是把平均的产品损失考虑进来。换句话说,制程良率减掉在规格内的产品损失就是品质良率。制程损失指标 Le 的定义为二次期望损失除以制程规格长度一半的平方。在文献上,在 Yq 指标的研究局限于样本的点估计。决策者可能会对 Yq 的信赖下界有兴趣,而不是纯粹只有点估计量。另一方面,文献上大部份在品质保证领域的研究都专注于探讨制程规格是对称的情况。然而,非对称规格很可能产生于开始时规格是对称的,但是制程的分配是偏态或是服从非常态分配的情况。在非对称规格的情况之下,使用传统的 Yq 和 Le 来衡量制程绩效是有风险的,很可能所获得的结果会使人误解实际的状况。本文针对 Yq 指标求取其信赖下界,并且推广 Yq 和 Le 指标来处理非对称规格的制程。本文的具体贡献主要有三方面。第一方面是提出两个可靠的方法来把 Yq 的点估计值变换成信赖下界,来衡量制程的品质良率。其中一个方法是在常态分配的假设下,针对超低不良率的生产制程品质良率的测量。另一个方法则是针对任意的制程分配,我们提出复式抽样方法来获得品质良率的信赖区间下界。第二方面是把传统的 Yq 和 Le 指标推广成可以处理非对称规格的制程。我们在文中证实了此推广的优点,并且研究非对称规格的 Yq 和 Le 指标估计量的一些统计性质。第三方面,我们研究了传统 Yq 和 Le 指标自然估计量的一些统计性质。本文所获得的研究成果,有助于从事品管工作者对于好的 Yq 和 Le 指标估计量的选择,并且在评估制程能力提供更有效的决策方式。
Process yield is the most common criterion used in the manufacturing industry for measuring process performance. A more advanced measurement formula, called the quality yield index (Yq), has been proposed to calculate the quality yield for arbitrary processes by taking customer loss into consideration. Quality yield penalizes yield for the variation of the product characteristics from its target, which presents a measure of the average product loss. In other words, quality yield is calculated as process yield minus process loss within the specifications. Process loss index Le is defined as the ratio of the expected quadratic loss to the square of half specification width. In the literature, only sample point estimate for Yq is investigated. The decision maker would be interested in a lower bound on Yq rather than just the sample point estimate. Most research in quality assurance literature has focus on cases in which the manufacturing tolerance is symmetric. However, asymmetric tolerances can also arise in situations where the tolerances are symmetric to begin with, but the process distribution is skewed or follows a non-normal distribution. Under asymmetric tolerances situation, using Yq and Le would be risky and probably the results obtained are misleading. This dissertation focus on obtaining lower bounds on Yq and extending Yq and Le to handle processes with asymmetric tolerances. The concrete contributions of this dissertation are threefold. The first is to propose two reliable approaches for measuring Yq by converting the estimated value into a lower confidence bound. One approach is for production processes with very low fraction of defectives under normality assumption. For arbitrary underlying distributions, we propose a bootstrap approach to obtain lower confidence bound on quality yield. The second is to generalize Yq and Le for asymmetric tolerances. The merit of the generalization is justified, and some statistical properties of the estimated generalization are investigated. The third is to investigate the statistical properties of these natural estimators for Yq and Le. The results obtained in this dissertation are useful to the practitioners in choosing good estimators and making reliable decisions on judging process capability.
URI: http://140.113.39.130/cdrfb3/record/nctu/#GT009033816
http://hdl.handle.net/11536/38879
显示于类别:Thesis


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