六西格玛管理的统计评价方法研究与应用
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摘要
六西格玛(6σ)管理是以顾客满意度为中心,以数据为驱动力,通过持续的质量改进项目实现企业竞争优势和效益最大化。它作为一种全新的量化科学管理模式,加速推动经济全球化发展,逐步形成并建立面向全球的质量平台,从它诞生至今的20余年里,世界六西格玛管理理念和方法由制造业向医疗、教育、金融等多领域迅速延伸。伴随着六西格玛管理在各行业逐步开展,原有六西格玛系统科学理论和相关统计技术也在不断深入和完善。
本文以六西格玛管理统计技术为切入点,将研究内容分为三个部分。
第一部分研究六西格玛管理过程能力评价。首先从理论上分别阐述各类过程能力评价内容和方法,在现有的过程能力估计基础上,重点分析几类过程能力的可靠性评估方法,通过质量特性过程能力估计的置信区间和临界值表,为供货方和购买方准确决策提供可靠依据；针对非正态质量特性的处理提出使用Rosenblatt变换方法,建立基于Burr-XII分布和Pearn过程能力指数的非正态过程能力计算方法；将原有反映质量与成本关系的“经济符合成本模型”扩展为以财务核算为依据的质量收入-成本模型,同时建立基于逆概率函数的额外成本计量模型。
第二部分研究过程控制图的理论方法。针对相关数据的特性,使用蒙特卡罗模拟比较残差控制图、指数加权移动平均控制图和模型控制图在过程稳定和过程失控两种状态下的控制能力,分析参数对各类控制图的影响,根据平均链长比较各类控制图的控制效果。建立基于非平稳数据ARIMA模型的相关控制图；针对异方差数据的特征,改变原有控制限恒定的方法,由方差波动性建立变控制限的异方差控制图,考虑多维异方差数据控制图建立的必要性和可行性,采用主成份降维方法建立多维异方差数据的联合控制图,并把控制图应用于金融等数据过程异常点监控。
第三部分是过程评价系统的研制。鉴于目前市场上过程评价专用软件缺乏,研究开发融合了传统计算方法和本文所提出的统计技术,编写形成R语言计算函数提供给使用者；整个系统具体包括数据处理、过程评价、过程控制和过程效益四大模块,针对中小企业在质量功能展开中实际问题,形成一套界面友好,操作简便的六西格玛质量管理系统,有效提高中小企业竞争力。
The aim of six sigma management is that improves and achieves the competitive advantage and the maximum profit through continuous quality improvement projects which is based on customer satisfaction and data-driven. It is a new model of quantitative scientific management when the resource allocation and circulation are accelerating the development of economic globalization, and establishes a global quality platform. It's been 20 years since the birth, six sigma had been applied to health care, education, finance and so on. Moreover, the scientific methods and statistical techniques of six sigma system are gradually developing.
In this paper, the studies of six sigma statistical techniques are divided into three parts.
The first part is the study of capability evaluation of six sigma management process, and evaluates the reliability of several types of process capability based on the existing estimates of process capability, then, suggests a reliable method to suppliers and buyers for decision-making. For non-normal quality characteristics of a process, propose rosenblatt a new method for transformation and calculating PCIs using Burr-Ⅻdistribution and pearn method is developed. Correcting the primary quality cost model, and presenting the quality profit model and extra cost model based on inverse probability function.
The second part studies the theoretical method of process control charts for autocorrelation and heteroscedasticity data. The simulations are carried out to investigate and compare the control ability when the process is out of control between several control charts, then, selects the optimal control chart for establishing a non-stationary series control charts-ARIMA model. By variance volatility, a changing control limits for heteroscedasticity control chart is proposed. For data of multi-dimensional heteroscedasticity, establishing a joint control charts using principal component method, control charts are applied to process monitoring of finance data.
The third part is the process control and evaluation system development, which based on R language, including process control, process evaluation and process effectiveness. For practical problems in the quality function deployment, the developed evaluation system of six sigma management has a friendly interface and the simplicity of operator, and will improve competitiveness of the Small and Medium Enterprise.
本文以六西格玛管理统计技术为切入点,将研究内容分为三个部分。
第一部分研究六西格玛管理过程能力评价。首先从理论上分别阐述各类过程能力评价内容和方法,在现有的过程能力估计基础上,重点分析几类过程能力的可靠性评估方法,通过质量特性过程能力估计的置信区间和临界值表,为供货方和购买方准确决策提供可靠依据；针对非正态质量特性的处理提出使用Rosenblatt变换方法,建立基于Burr-XII分布和Pearn过程能力指数的非正态过程能力计算方法；将原有反映质量与成本关系的“经济符合成本模型”扩展为以财务核算为依据的质量收入-成本模型,同时建立基于逆概率函数的额外成本计量模型。
第二部分研究过程控制图的理论方法。针对相关数据的特性,使用蒙特卡罗模拟比较残差控制图、指数加权移动平均控制图和模型控制图在过程稳定和过程失控两种状态下的控制能力,分析参数对各类控制图的影响,根据平均链长比较各类控制图的控制效果。建立基于非平稳数据ARIMA模型的相关控制图；针对异方差数据的特征,改变原有控制限恒定的方法,由方差波动性建立变控制限的异方差控制图,考虑多维异方差数据控制图建立的必要性和可行性,采用主成份降维方法建立多维异方差数据的联合控制图,并把控制图应用于金融等数据过程异常点监控。
第三部分是过程评价系统的研制。鉴于目前市场上过程评价专用软件缺乏,研究开发融合了传统计算方法和本文所提出的统计技术,编写形成R语言计算函数提供给使用者；整个系统具体包括数据处理、过程评价、过程控制和过程效益四大模块,针对中小企业在质量功能展开中实际问题,形成一套界面友好,操作简便的六西格玛质量管理系统,有效提高中小企业竞争力。
The aim of six sigma management is that improves and achieves the competitive advantage and the maximum profit through continuous quality improvement projects which is based on customer satisfaction and data-driven. It is a new model of quantitative scientific management when the resource allocation and circulation are accelerating the development of economic globalization, and establishes a global quality platform. It's been 20 years since the birth, six sigma had been applied to health care, education, finance and so on. Moreover, the scientific methods and statistical techniques of six sigma system are gradually developing.
In this paper, the studies of six sigma statistical techniques are divided into three parts.
The first part is the study of capability evaluation of six sigma management process, and evaluates the reliability of several types of process capability based on the existing estimates of process capability, then, suggests a reliable method to suppliers and buyers for decision-making. For non-normal quality characteristics of a process, propose rosenblatt a new method for transformation and calculating PCIs using Burr-Ⅻdistribution and pearn method is developed. Correcting the primary quality cost model, and presenting the quality profit model and extra cost model based on inverse probability function.
The second part studies the theoretical method of process control charts for autocorrelation and heteroscedasticity data. The simulations are carried out to investigate and compare the control ability when the process is out of control between several control charts, then, selects the optimal control chart for establishing a non-stationary series control charts-ARIMA model. By variance volatility, a changing control limits for heteroscedasticity control chart is proposed. For data of multi-dimensional heteroscedasticity, establishing a joint control charts using principal component method, control charts are applied to process monitoring of finance data.
The third part is the process control and evaluation system development, which based on R language, including process control, process evaluation and process effectiveness. For practical problems in the quality function deployment, the developed evaluation system of six sigma management has a friendly interface and the simplicity of operator, and will improve competitiveness of the Small and Medium Enterprise.
引文
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