非正态过程能力分析与控制方法研究
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摘要
统计过程控制理论已成为推动质量管理发展的一种有效的质量应用基本理论,为持续质量改进发展做出了重大贡献。但是传统的统计过程控制理论基于质量特性值服从正态分布的假设,而在某些实际生产过程中,质量特性值往往服从非正态分布。针对非正态过程,传统的统计过程控制理论将失效。因此,非正态过程能力分析与控制问题已成为目前迫切需要研究的一个课题。
本文首先介绍了非正态过程的特点和检验、统计过程控制中的过程能力分析和控制图方法的基础理论和知识。从更为具有实际应用价值的角度,结合曼-惠特尼U(Mann-Whitney U)检验的原理,对生产中非正态过程的稳定性进行研究。对偏度校正(SC)控制图和比例加权方差(SWV)控制图的进行应用研究。并对SC控制图、SWV控制图、WV控制图以及休哈特控制图进行比较研究,得出结论:SC控制图和SWV控制图能够对非正态过程进行很好地监控。提出了一种修正的加权方差过程能力指数,相对于BAI & CHOI提出的加权方差过程能力指数和WU提出的加权方差过程能力指数更具稳健性。另外,本文将生产过程中以及供应商管理中的删减问题进行还原,也就是将截尾处理的问题引入过程能力评价。通过对截尾样本的统计学原理的研究,能够科学地还原原始未截尾处理的样本的统计特性。
本文以非正态质量特性值的本质属性为切入点,以非正态过程能力分析与控制的理论为主线,运用统计学原理、数学推导、实证研究、比较分析法对非正态过程能力分析与控制的理论进行深入探讨,对非正态过程稳定性问题、对不同非正态过程控制方法、不同非正态过程能力评价方法、以及正态截尾处理的过程能力评价问题进行理论研究和实证分析,构建非正态过程能力分析与控制方法的理论基础和应用框架,完善统计过程控制体系。
Statistical process control (SPC) has been become an effective form of quality application to promote quality management development and made a significant contribution to continuous quality improvement. Traditional SPC theory is based on a fundamental assumption that the process data are normal. However, in many conditions the process data are non-normal. Under the circumstances, the traditional SPC theory becomes invalid. Therefore, the problem of process capability analysis and control methods in non-normal processes has become an urgent issue to be solved.
The basic theory and knowledge of the characteristics and test methods for non-normal process, process capability analysis and control charts are first introduced in this paper. For practical points of view, non-normal data stability in manufacturing processes is studied with the principle of Mann-Whitney U test. Skewness Correction (SC) control chart and Scaled Weighted Variance (SWV) control chart application are studied to apply, separately. An analysis is made to compare SC control chart, SWVcontrol chart, Shewhart control chart, WV control chart. The comparative study shows that SC control chart as well as SWVcontrol chart can control non-normal processes well than other control methods. The paper presents a Modified Weighted Variance process capability index which is more robust than process capability indices proposed by BAI & CHOI and process capability indices proposed by WU. In addition, the practical application of estimators of truncated samples from the normal distribution is derived and illustrated, and the paper imports the truncated samples which are easy to appear in manufacturing processes or supplier management into process capability evaluation for the first time. It is scientific to fund the estimators of untruncated samples by the study of paper.
The paper is commenced by the nature of non-normal data and based on the main line of process capability analysis and control methods for non-normal processes. Statistics principle, mathematics derivation, comparative analysis and case study are employed to carry out the thorough examination to the theory of process capability analysis and control methods for non-normal processes. The theory base and application framework of process capability analysis and control methods in non-normal processes were found from several sets including non-normal process stability, non-normal process control methods, non-normal process capability evaluation as well as process capability evaluation of truncated samples from the normal distribution in order to perfect statistical process control system.
本文首先介绍了非正态过程的特点和检验、统计过程控制中的过程能力分析和控制图方法的基础理论和知识。从更为具有实际应用价值的角度,结合曼-惠特尼U(Mann-Whitney U)检验的原理,对生产中非正态过程的稳定性进行研究。对偏度校正(SC)控制图和比例加权方差(SWV)控制图的进行应用研究。并对SC控制图、SWV控制图、WV控制图以及休哈特控制图进行比较研究,得出结论:SC控制图和SWV控制图能够对非正态过程进行很好地监控。提出了一种修正的加权方差过程能力指数,相对于BAI & CHOI提出的加权方差过程能力指数和WU提出的加权方差过程能力指数更具稳健性。另外,本文将生产过程中以及供应商管理中的删减问题进行还原,也就是将截尾处理的问题引入过程能力评价。通过对截尾样本的统计学原理的研究,能够科学地还原原始未截尾处理的样本的统计特性。
本文以非正态质量特性值的本质属性为切入点,以非正态过程能力分析与控制的理论为主线,运用统计学原理、数学推导、实证研究、比较分析法对非正态过程能力分析与控制的理论进行深入探讨,对非正态过程稳定性问题、对不同非正态过程控制方法、不同非正态过程能力评价方法、以及正态截尾处理的过程能力评价问题进行理论研究和实证分析,构建非正态过程能力分析与控制方法的理论基础和应用框架,完善统计过程控制体系。
Statistical process control (SPC) has been become an effective form of quality application to promote quality management development and made a significant contribution to continuous quality improvement. Traditional SPC theory is based on a fundamental assumption that the process data are normal. However, in many conditions the process data are non-normal. Under the circumstances, the traditional SPC theory becomes invalid. Therefore, the problem of process capability analysis and control methods in non-normal processes has become an urgent issue to be solved.
The basic theory and knowledge of the characteristics and test methods for non-normal process, process capability analysis and control charts are first introduced in this paper. For practical points of view, non-normal data stability in manufacturing processes is studied with the principle of Mann-Whitney U test. Skewness Correction (SC) control chart and Scaled Weighted Variance (SWV) control chart application are studied to apply, separately. An analysis is made to compare SC control chart, SWVcontrol chart, Shewhart control chart, WV control chart. The comparative study shows that SC control chart as well as SWVcontrol chart can control non-normal processes well than other control methods. The paper presents a Modified Weighted Variance process capability index which is more robust than process capability indices proposed by BAI & CHOI and process capability indices proposed by WU. In addition, the practical application of estimators of truncated samples from the normal distribution is derived and illustrated, and the paper imports the truncated samples which are easy to appear in manufacturing processes or supplier management into process capability evaluation for the first time. It is scientific to fund the estimators of untruncated samples by the study of paper.
The paper is commenced by the nature of non-normal data and based on the main line of process capability analysis and control methods for non-normal processes. Statistics principle, mathematics derivation, comparative analysis and case study are employed to carry out the thorough examination to the theory of process capability analysis and control methods for non-normal processes. The theory base and application framework of process capability analysis and control methods in non-normal processes were found from several sets including non-normal process stability, non-normal process control methods, non-normal process capability evaluation as well as process capability evaluation of truncated samples from the normal distribution in order to perfect statistical process control system.
引文
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