标题: | 应用无母数Bootstrap法建构新制程之Q管制图 Applying Nonparametric Bootstrap Method to Construct Q Control Chart for Start-up process |
作者: | 刘昱承 唐丽英 洪瑞云 Liu, Yu-Cheng Tong, Lee-Ing Horng, Ruey-Yun 工业工程与管理系所 |
关键字: | Bootstrap方法;Q管制图;Weibull制程分布;新制程;Bootstrap method;Q control chart;Weibull distribution;start-up process |
公开日期: | 2017 |
摘要: | 传统Shewhart管制图建构时制程资料须服从常态分配并且需要有足够的历史资料才能有效建构管制图之管制界线。然而为因应厂商、顾客日新月异之要求,不断推出新的产品,使的生产周期缩短,导致一些产品缺少足够历史资料来建构传统Shewhart管制图。针对此问题,Quesenberry (1991) 提出Q管制图,以在仅有少量资料的情况下有效建构管制图。在利用Q管制图管制新制程资料,需假设制程资料彼此独立且呈常态分布;若制程资料分布呈现非常态分布时,使用Q管制图可能会增加型一误差(Type I error)和型二误差(Type II error)发生的机率,而无法准确地侦测出变异。因此,本研究利用无母数复式模拟法(Bootstrap methods)增生资料,并利用两种复式信赖区间(Percentile Bootstrap,PB; Bias-corrected and accelerated bootstrap,BCa)来建构Q管制图之管制界线。最后本研究模拟制程资料呈Weibull分布的各种参数情况下,进行敏感度分析以验证本研究提出之无母数复式Q管制图在不同样本组数以及不同偏态下之有效性。本研究结果显示,在多数情况下以PB信赖区间所建构之Q管制图之管制界线在制程稳定的状态下,平均连串长度(〖ARL〗_0)最佳,BCa和传统Q管制图较差;当制程平均数产生偏移时,在大多数情况下利用PB信赖区间所建立之Q管制图其管制效果皆能优于传统Q管制图,因此,整体而言,当新制程资料呈非常态分布(如:Weibull分布)时,在Weibull分布不同的参数组合下,和传统Q管制图相比,本研究提出之无母数复式Q管制图有较佳的监控能力。 Traditional Shewhart control chart reguires that the process data follow a normal distribution and also need sufficiently large data to accurately construct the control chart. However, in response to the ever-changing requirements from customers, the design of new products, the shortening of the production cycle, resulting in lack of sufficient historical data to build the traditional Shewhart control chart. Previous study has proposed a Q chart to effectively construct a control chart with only a small amount of data. In applying the Q control chart to control the new process data, it is still necessary to require that the process data are independent of each other and are normally distributed. If the distribution of the process data is non-normal, utilizing the Q chart may increase the probability of a type 1 error and type 2 error. Conseguently the Q chart can not accurately detect the process variation. Therefore, this study utilizes the Bootstrap Methods to generate data and that constructs the Q-chart using two types of Boostrap confidence intervals (Percentile Bootstrap (PB) and Bias-corrected and accelerated bootstrap (BCa)). The sensitivity analysis was carried out to verify the effectiveness of the proposed method of Boostrap Q-chart under various sample sizes and various values of parameter combinations of a Weibull distribution. The results of this study show that, in most cases, the average run length 〖ARL〗_(0 )of PB method has the largest values. When the process averages are shifted, in most cases the Q-control chart established using the PB confidence interval is superior to the traditional Q-control chart. Therefore, in general, when the new process data is presented in non-normal process (such as: Weibull distribution), the proposed non-parametric PB method is recommended to construct the Q-control chart. |
URI: | http://etd.lib.nctu.edu.tw/cdrfb3/record/nctu/#GT070453336 http://hdl.handle.net/11536/141076 |
显示于类别: | Thesis |