标题: | 应用Tukey’s 管制图监控韦伯 新制程之百分位数 Developing the Tukey’s Control Chart for Monitoring the Percentile of a Start-up Weibull Process |
作者: | 苏致萱 唐丽英 李荣贵 Su, Chih-Hsuan Tong, Lee-Ing Li, Rong-Kwei 工业工程与管理系所 |
关键字: | 新制程;Weibull分布;百分位数;Tukey’s管制图;Start-up Process;Weibull distribution;percentiles;Tukey’s control chart |
公开日期: | 2017 |
摘要: | 建构传统的Shewhart管制图时,制程资料须服从常态分布且有足够的历史资料来估计制程参数。然而现今产业竞争越来越激烈,许多新开发制程不易搜集到足够的观测值来检查资料是否符合常态分布或准确的估计制程参数,因此无法有效应用Shewhart管制图来监控新制程。针对此类新制程监控问题,Quesenberry(1991)提出Q管制图。然而Q管制图须假设制程分布服从某些特定的机率分布(如:常态、二项分布等),因此当新制程呈非常态分布时,Q管制图即不适用,有些产品之可靠性数据(如:材料失效时间、材料所能承受之应力的极值(extreme value)或百分位数(percentile)等)常呈现韦伯(Weibull)分布,如何有效侦测出此类可靠性数据发生偏移对于维持产品的品质是非常重要的。Padgett et al. (1990)针对Weibull百分位数提出Shewhart-type管制图,但此管制图需收集足够的样本资料才能准确地估计制程参数,并不适用于监控Weibull新制程之百分位数。由于Tukey’s 管制图可适用于少量资料且不需假设制程为何种统计分布,本研究乃针对仅有少量资料之Weibull分布的新制程资料,提出一套监控Weibull 百分位数 之Tukey’s管制图,以有效监控Weibull新制程之低百分位数。本研究藉由模拟方法,在Weibull分布之不同的参数组合、样本组数与百分位数下,找出合适的Tukey’s管制图之管制界限系数值(k值),并比较本研究所提出之新制程Weibull percentile Tukey’s管制图、Q管制图与Shewhart-type管制图的侦测制程变异之能力。经由敏感度分析显示,当样本组数增加时,Weibull percentile Tukey’s 管制图与Padgett et al. (1990)Shewhart-type管制图在大多数的情况下侦测能力皆会上升。当制程稳定或发生正向偏移时,本研究所提出之Weibull percentile Tukey’s 管制图的侦测能力皆表现较佳;当制程平均数发生负向偏移时,Shewhart-type管制图的侦测能力则表现较佳;本研究所提出之Weibull percentile Tukey’s 管制图的侦测能力在大多数的情况下皆较Q管制图的侦测能力佳。 The conventional Shewhart’s control charts require that the process data follow a normal distribution and a large data set is needed for setting up the control limits. However, constructing the Shewhart’s control charts for a start-up process is difficult because not enough data can be collected to estimate the process parameters accurately. To solve this problem, Quesenberry(1991) proposed the Q chart for the start-up process. Q chart also assumes that the process distribution follows some specific distributions such as Normal or Binomial distributions. That is, the Q chart is not appropriate if the data of a start-up process follow a non-normal distribution. The Weibull distribution is widely used to describe the reliability data. Padgett et al. (1990)’s developed a Shewhart-type control chart for the Weibull process. However, no control charts has been developed for a start-up Weibull process. Turkey’s control chart can be applied to any distribution with small data set. Therefore, the main objective of this study is to utilize Turkey’s control chart to monitor the percentile of a start-up Weibull process. The sensitivity analysis is conducted to verify the effectiveness of the proposed percentile Tukey’s control chart for a start-up Weibull process. Through simulations, we found out the suitable control limit coefficient k of Turkey’s control chart under parameters, sample sizes for monitoring the percentile of Weibull distribution. We also compared our works with Q charts and Padgett et al. (1990)’s Shewhart-type control chart. The results of the sensitivity analysis indicated that when the process is stable or has a positive shift, the Weibull percentile Turkey’s control chart outperforms the Shewhart-type control chart and the Q chart. When the process mean has a negative shift, Shewhart-type control chart performs better than Weibull percentile Turkey’s control chart and Q charts. Moreover, the detective ability of the Weibull percentile Turkey’s control chart and Shewhart-type control chart increase when the sample sizes increase. |
URI: | http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070353305 http://hdl.handle.net/11536/141121 |
显示于类别: | Thesis |