过程能力分析研究及其在电子和冷轧辊产品生产中的应用
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摘要
过程能力分析作为统计过程控制(Statistical Process Control,SPC)的核心内容,是保证产品质量的重要工具和手段,正日益受到人们的关注和重视,尤其在六西格玛质量管理方法蔚然成风,“大质量”概念普遍兴起韵大环境下,如何对产品生产流程的能力进行分析,特别是针对生产环境中的不同情况和特征,如非正态过程、小样本条件、多工序及多特性等,提出相应的过程能力分析方法,对于有效地指导企业及其质量工作者进行质量改善,明确造成质量缺陷的原因、工序、特性等方面均具有重要的理论意义和实际价值。
传统上进行过程能力分析要基于三个基本假设:过程处于统计控制状态;特性数据服从正态分布;观测数据样本充足且相互独立。然而,在现实中,这三个条件并不都能得到满足,如数据服从非正态分布、小批量生产条件或采样样本量较小、乃至于多工序、多特性情况的出现,均会给企业和生产者进行过程能力分析造成不便,甚至出现误解、错用的情况。为了解决这一问题,本文总结与分析了统计过程控制及其过程能力分析研究近年来的发展现状,结合企业的生产实际情况,在对山西某机械制造有限公司及浙江某电子有限公司的实地调研与案例实施的基础上,开展了过程能力分析及其指数计算的若干热点问题的研究和应用工作。该研究是985工程流程工业综合自动化科技创新平台研究项目、辽宁省科技厅计划项目和国家杰出青年科学基金项目的重要组成部分,同时也是企业技术攻关项目“冷轧辊过程数据管理系统”、“冷轧辊质量评价与改善系统”和企业管理咨询项目“达峰电子质量管理与改善顾问服务项目”中的核心内容。
本文首先概述了统计过程控制的基础理论,包括统计过程控制的概念、控制图的分类介绍、过程能力分析的意义及其指数计算的概念与研究综述;然后,进一步分别考虑生产中会出现的实际情况,包括传统情况、非正态数据、小样本条件、多工序及多特性情况提出相应的过程能力分析与指数计算方法,结合企业实际案例应用,提供相应的解决方法和合理建议;最后另辟蹊径,指出传统的单纯依靠过程能力指数值(ProcessCapability Index,PCI)进行过程能力分析及决策的不足之处,结合实际应用,建立了基于过程能力图进行过程能力分析的改善流程图。本文的研究工作主要围绕以下五个关键问题展开。
第三章作为关键问题1,是基于DMAIC(Define-Measure-Analysis-Improve-Control)质量改善模型的过程能力分析的相关研究和应用,也是传统的过程能力分析的流程展示。本章以某电子产品的实际生产为例,按照DMAIC流程,在综合分析和定位质量缺陷原因的基础上,对其测量系统进行评价,并在其稳定可靠的情况下,通过试验设计选择、确定、优化关键因子及其水平设置,运用SPC技术对波峰焊工序进行控制图监控,待其稳定后进行过程能力分析及其指数计算。
此后的章节均是针对过程能力分析的特殊情况展开的相关研究和应用。
第四章作为关键问题2,旨在进行非正态数据情况下过程能力分析的研究和应用。针对实际生产中数据不服从正态分布的情况,分析了造成数据非正态的原因及数据的非正态性对过程能力分析的影响,并对过程能力分析中多种处理非正态数据的方法进行了相关的劣势分析和简单比较,首次采用Root Transformation法将非正态的数据转换为正态数据,并将之运用于某电子产品的实际生产中,在实例中通过与Box-Cox转换法的比较,验证了该方法的合理性和有效性。
第五章作为关键问题3,旨在进行小样本条件下过程能力分析的研究和应用。在分析样本量对指数C_p、C_(pk)点估计值及其置信区间的影响后,随机模拟产生了不同小样本容量的正态分布、t分布、卡方分布、对数正态分布数据,分别利用标准Bootstrap法、百分位数Bootstrap法、修正偏差后的百分位数Bootstrap法、t分位数Bootstrap法仿真产生这几种不同分布的四种置信区间,并通过双因子方差分析法比较了样本容量及不同方法对C_p、C_(pk)点估计值及其置信区间的影响,得到了一些有价值的结论。同时结合某电子产品的实际生产流程,以其点红胶工序中破坏性采样的红胶推力特性为研究对象,采用Bootstrap法中的PTB法进行过程能力分析,分析结果为企业提供合理的建议。
第六章作为关键问题4,主要围绕多工序及多特性的多元过程能力分析展开。结合企业的生产实际,在考虑工序和特性的多元性的基础上,建立了多元质量控制与改进模型;针对工序的多元性,以某钢铁公司某种轧辊产品为例,利用改进的田口质量损失函来确定关键工序并进行多工序过程能力分析及其指数计算,通过案例验证了此方法的合理性和有效性;针对特性的多元性,建立了基于Luce(?)o指数进行多元特性过程能力分析的流程图,结合某电子产品的生产实际,用于计算波峰焊工序中5个过程特性的多元过程能力指数,基于计算结果为企业提供了合理的建议。
第七章作为关键问题5,是基于过程能力图的过程能力分析的研究和应用。在明确单纯依靠指数的计算与估计进行过程能力分析的缺陷后,基于过程能力指数的临界值,使用假设检验方法来进行过程能力的分析和判断;分析了样本规格对于指数的临界值的影响,为企业进行合理采样提供依据;并对基于PCI假设检验的过程能力图的图形形式进行了推导证明,建立了基于过程能力图进行过程能力分析的改善流程图。结合某电子产品的实际生产,开展了基于多特性过程能力分析-MCPCA图的过程能力分析,通过实例验证了过程能力图像的优势。
As a core content of statistical process control (SPC), process capability analysis is an important tool and method to gurantee quality of products, and process capability analysis is raising more and more attention now, especially under the environment that "Six Sigma" and "Total Quality Management" are popularly used and become common practice. This thesis analyzes the capability of products in different situations, such as the data is non-normal distributed, the sampling size is small, even the stages and characteristics are mutiple, and it also proposes the corresponding methods of process capability analysis for above cases. The methods are helpful to enterprises for quality improving, and they are profound of theoretical and practical significance.
Traditionally, there are three basic hypotheses in process capability analysing: the process is in control, the data is normal distributed, the data is independent and with large samples. However, they are not all satisfied in reality, such as the data is non-normal distributed, the samplings are in small sizes or the production is in small batch, even the stages and characteristics are multiple. All these situations bring inconvenience to enterprises and their operators, even cause misunderstanding and misapplication. To solve these problems, this thesis firstly analyses and summarises the recent years development of SPC and process capability analysis, then combined with the actual production situations of enterprises, some researches and application are developed which based on investigations to a mechnical company in Sanxi and an electronic company in Zhejiang. This thesis is a constituent part of "985 project scientific and technological innovation of Integrated Automation of Process Industry platform research project", "Liaoning provincial division of sicence and technology planning project" and "National Natural Science Funds for Distinguished Young Scholar project". It is also a core content of enterprises' technical studing project-"Process data management system of cold roller" and "Quality appriasing and improvming system of cold roller" in Sanxi, and enterprises' consultant and management project-"Quality management and improving consultant project of electronic company of Dafeng".
In Chapter 2, basic theories about SPC are firstly introduced, including the concepts of SPC, the classifications of control charts, the meanings of process capability analysis and different definitions of their indices calculating, the literatures of their theroies are also overviewed in detail; and then combined with the real cases of producing, the thesis proposes methods of process capability analysis corresponding to traditional cases, non-normal data cases, small sampling size cases, and the cases of multi-stages and multi-characteristics, it also provides reasonable suggestions and solutions to enterprises based on the practical application; finally, the thesis points out the deficiency of process capability analyzing and decision making, which only based on process capability indices calculating in traditional way. Combined with the practical application, a quality improving flowchart based on process capability plots is constructed. As a whole, this thesis focuses on the following five key problems.
As the key problem 1, chapter 3 is an application of process capbility analysis whose model is DMAIC (Define-Measure-Analysis-Improve-Control), and it is a revelation of traditional flow of process capability analysis. Taking the production of some electronic products as an example, and following the flow of DMAIC, this chapter firstlly analyzes the causes and locates the stages of quality defects, and then an analysis of measurement system is developed. Based on reliable and stable measurement system, design of experiment (DOE) is developed for choosing, determining and optimizing the critical factors and their relative settings. This chapter employs SPC to wave solering, and the control chart is used for controlling and diagnosing the stage of wave solering, the further calculation and analysis of process capability are developed after the process is in control.
The later chapters are research and application of different and special cases of process capability analysis.
As the key problem 2, chapter 4 focuses on the solution of non-normal data in real production. Considering the data is non-normal distributed in some actual production, this chapter firstly analyzes the causes and influences of nonnormality to process capability analysis, and then some simple comparisons and limitation analysis are made according to different methods, which are used for dealing with non-normal data. This thesis firstly adopts Root Transformation method to translate non-normal data into normal, and then makes an application of it to some electronic products. The rationality and validity of this method are vertified after comparing with Box-Cox transformation method.
As the key problem 3, chapter 5 focuses on process capability analysis with small samples. After analyzing the influences of sampling size to the point estimations and confidence intervals of C_p and C_(pk), a serious of random data that is namely normal distributed, student t distributed, chi-square distributed and lognormal distributed are simulated with different sample sizes. Based on these simulated data and four Bootstrap methods, i.e. Standard Bootstrap (SB), Percentile Bootstrap (PB), Biased-corrected Percentile Bootstrap (BCPB), Percentile-t Bootstrap (PTB), the confidence intervals of C_p and C_(pk) are simulated and computed, and then some comparisons and analysis of different Bootstrap methods and sample sizes are made through two factors analysis of variance (ANOVA) method. Some valuable conclusions are made at last. Combined with the production of some electronic products, the thrust power of red agglutinant with devastatingly sampling and small samples is taken as the characteristic to be studied, and the PTB method is used for process capability analysis. Analyzing the results, some valuable suggestions are provided to enterprises.
As the key problem 4, chapter 6 focuses on the analysis of mutivariable process capability, including the analysis of multi-stages and multi-characteristics. Combined with the actual production of enterprises, and considering the plurality of stages and characteristics, this chapter constructs a model of multivariable quality controlling and improving. In view of the plurality of stages, this chapter takes the production of cold roller as an example, and a simple improvement in Taguchi quality loss function is made to locate the key stages and analyze the process capability of multi-stages. The rationality and validity of this method are vertified through an application in cold roller production. In view of the plurality of characteristic, a flowchart of multi-characteristics process capability analysis is constructed, it is based on the Luceno index. Combined with the actual production of some electronic products, the method and the idea of the model is used for calculating the process capability indices (PCIs) of 5 process characteristics in wave soldering stage. Some suggestions and advicies are provided to enterprise according to the results.
As the key problem 5, chapter 7 focuses on the process capability plots and their application. Considering the defects of process capability analyzing only with process capability indices, the hypothesis testing is used for process capability analyzing and decision making based on the critical values of PCIs. An analysis of the influence of sample scale to crtical values of PCIs is made, it is helpful to enterprises for reasonal sampling. The graph forms of process capability plots are proved, and the quality improving flowchart based on process capability plots is constructed. Combined with the actual production of some electronic products, the analysis of process capability based on multi-characteristics process capability analysis (MCPCA) chart is developed. The superiority of process capability plots is finally proved by a practical application.
传统上进行过程能力分析要基于三个基本假设:过程处于统计控制状态;特性数据服从正态分布;观测数据样本充足且相互独立。然而,在现实中,这三个条件并不都能得到满足,如数据服从非正态分布、小批量生产条件或采样样本量较小、乃至于多工序、多特性情况的出现,均会给企业和生产者进行过程能力分析造成不便,甚至出现误解、错用的情况。为了解决这一问题,本文总结与分析了统计过程控制及其过程能力分析研究近年来的发展现状,结合企业的生产实际情况,在对山西某机械制造有限公司及浙江某电子有限公司的实地调研与案例实施的基础上,开展了过程能力分析及其指数计算的若干热点问题的研究和应用工作。该研究是985工程流程工业综合自动化科技创新平台研究项目、辽宁省科技厅计划项目和国家杰出青年科学基金项目的重要组成部分,同时也是企业技术攻关项目“冷轧辊过程数据管理系统”、“冷轧辊质量评价与改善系统”和企业管理咨询项目“达峰电子质量管理与改善顾问服务项目”中的核心内容。
本文首先概述了统计过程控制的基础理论,包括统计过程控制的概念、控制图的分类介绍、过程能力分析的意义及其指数计算的概念与研究综述;然后,进一步分别考虑生产中会出现的实际情况,包括传统情况、非正态数据、小样本条件、多工序及多特性情况提出相应的过程能力分析与指数计算方法,结合企业实际案例应用,提供相应的解决方法和合理建议;最后另辟蹊径,指出传统的单纯依靠过程能力指数值(ProcessCapability Index,PCI)进行过程能力分析及决策的不足之处,结合实际应用,建立了基于过程能力图进行过程能力分析的改善流程图。本文的研究工作主要围绕以下五个关键问题展开。
第三章作为关键问题1,是基于DMAIC(Define-Measure-Analysis-Improve-Control)质量改善模型的过程能力分析的相关研究和应用,也是传统的过程能力分析的流程展示。本章以某电子产品的实际生产为例,按照DMAIC流程,在综合分析和定位质量缺陷原因的基础上,对其测量系统进行评价,并在其稳定可靠的情况下,通过试验设计选择、确定、优化关键因子及其水平设置,运用SPC技术对波峰焊工序进行控制图监控,待其稳定后进行过程能力分析及其指数计算。
此后的章节均是针对过程能力分析的特殊情况展开的相关研究和应用。
第四章作为关键问题2,旨在进行非正态数据情况下过程能力分析的研究和应用。针对实际生产中数据不服从正态分布的情况,分析了造成数据非正态的原因及数据的非正态性对过程能力分析的影响,并对过程能力分析中多种处理非正态数据的方法进行了相关的劣势分析和简单比较,首次采用Root Transformation法将非正态的数据转换为正态数据,并将之运用于某电子产品的实际生产中,在实例中通过与Box-Cox转换法的比较,验证了该方法的合理性和有效性。
第五章作为关键问题3,旨在进行小样本条件下过程能力分析的研究和应用。在分析样本量对指数C_p、C_(pk)点估计值及其置信区间的影响后,随机模拟产生了不同小样本容量的正态分布、t分布、卡方分布、对数正态分布数据,分别利用标准Bootstrap法、百分位数Bootstrap法、修正偏差后的百分位数Bootstrap法、t分位数Bootstrap法仿真产生这几种不同分布的四种置信区间,并通过双因子方差分析法比较了样本容量及不同方法对C_p、C_(pk)点估计值及其置信区间的影响,得到了一些有价值的结论。同时结合某电子产品的实际生产流程,以其点红胶工序中破坏性采样的红胶推力特性为研究对象,采用Bootstrap法中的PTB法进行过程能力分析,分析结果为企业提供合理的建议。
第六章作为关键问题4,主要围绕多工序及多特性的多元过程能力分析展开。结合企业的生产实际,在考虑工序和特性的多元性的基础上,建立了多元质量控制与改进模型;针对工序的多元性,以某钢铁公司某种轧辊产品为例,利用改进的田口质量损失函来确定关键工序并进行多工序过程能力分析及其指数计算,通过案例验证了此方法的合理性和有效性;针对特性的多元性,建立了基于Luce(?)o指数进行多元特性过程能力分析的流程图,结合某电子产品的生产实际,用于计算波峰焊工序中5个过程特性的多元过程能力指数,基于计算结果为企业提供了合理的建议。
第七章作为关键问题5,是基于过程能力图的过程能力分析的研究和应用。在明确单纯依靠指数的计算与估计进行过程能力分析的缺陷后,基于过程能力指数的临界值,使用假设检验方法来进行过程能力的分析和判断;分析了样本规格对于指数的临界值的影响,为企业进行合理采样提供依据;并对基于PCI假设检验的过程能力图的图形形式进行了推导证明,建立了基于过程能力图进行过程能力分析的改善流程图。结合某电子产品的实际生产,开展了基于多特性过程能力分析-MCPCA图的过程能力分析,通过实例验证了过程能力图像的优势。
As a core content of statistical process control (SPC), process capability analysis is an important tool and method to gurantee quality of products, and process capability analysis is raising more and more attention now, especially under the environment that "Six Sigma" and "Total Quality Management" are popularly used and become common practice. This thesis analyzes the capability of products in different situations, such as the data is non-normal distributed, the sampling size is small, even the stages and characteristics are mutiple, and it also proposes the corresponding methods of process capability analysis for above cases. The methods are helpful to enterprises for quality improving, and they are profound of theoretical and practical significance.
Traditionally, there are three basic hypotheses in process capability analysing: the process is in control, the data is normal distributed, the data is independent and with large samples. However, they are not all satisfied in reality, such as the data is non-normal distributed, the samplings are in small sizes or the production is in small batch, even the stages and characteristics are multiple. All these situations bring inconvenience to enterprises and their operators, even cause misunderstanding and misapplication. To solve these problems, this thesis firstly analyses and summarises the recent years development of SPC and process capability analysis, then combined with the actual production situations of enterprises, some researches and application are developed which based on investigations to a mechnical company in Sanxi and an electronic company in Zhejiang. This thesis is a constituent part of "985 project scientific and technological innovation of Integrated Automation of Process Industry platform research project", "Liaoning provincial division of sicence and technology planning project" and "National Natural Science Funds for Distinguished Young Scholar project". It is also a core content of enterprises' technical studing project-"Process data management system of cold roller" and "Quality appriasing and improvming system of cold roller" in Sanxi, and enterprises' consultant and management project-"Quality management and improving consultant project of electronic company of Dafeng".
In Chapter 2, basic theories about SPC are firstly introduced, including the concepts of SPC, the classifications of control charts, the meanings of process capability analysis and different definitions of their indices calculating, the literatures of their theroies are also overviewed in detail; and then combined with the real cases of producing, the thesis proposes methods of process capability analysis corresponding to traditional cases, non-normal data cases, small sampling size cases, and the cases of multi-stages and multi-characteristics, it also provides reasonable suggestions and solutions to enterprises based on the practical application; finally, the thesis points out the deficiency of process capability analyzing and decision making, which only based on process capability indices calculating in traditional way. Combined with the practical application, a quality improving flowchart based on process capability plots is constructed. As a whole, this thesis focuses on the following five key problems.
As the key problem 1, chapter 3 is an application of process capbility analysis whose model is DMAIC (Define-Measure-Analysis-Improve-Control), and it is a revelation of traditional flow of process capability analysis. Taking the production of some electronic products as an example, and following the flow of DMAIC, this chapter firstlly analyzes the causes and locates the stages of quality defects, and then an analysis of measurement system is developed. Based on reliable and stable measurement system, design of experiment (DOE) is developed for choosing, determining and optimizing the critical factors and their relative settings. This chapter employs SPC to wave solering, and the control chart is used for controlling and diagnosing the stage of wave solering, the further calculation and analysis of process capability are developed after the process is in control.
The later chapters are research and application of different and special cases of process capability analysis.
As the key problem 2, chapter 4 focuses on the solution of non-normal data in real production. Considering the data is non-normal distributed in some actual production, this chapter firstly analyzes the causes and influences of nonnormality to process capability analysis, and then some simple comparisons and limitation analysis are made according to different methods, which are used for dealing with non-normal data. This thesis firstly adopts Root Transformation method to translate non-normal data into normal, and then makes an application of it to some electronic products. The rationality and validity of this method are vertified after comparing with Box-Cox transformation method.
As the key problem 3, chapter 5 focuses on process capability analysis with small samples. After analyzing the influences of sampling size to the point estimations and confidence intervals of C_p and C_(pk), a serious of random data that is namely normal distributed, student t distributed, chi-square distributed and lognormal distributed are simulated with different sample sizes. Based on these simulated data and four Bootstrap methods, i.e. Standard Bootstrap (SB), Percentile Bootstrap (PB), Biased-corrected Percentile Bootstrap (BCPB), Percentile-t Bootstrap (PTB), the confidence intervals of C_p and C_(pk) are simulated and computed, and then some comparisons and analysis of different Bootstrap methods and sample sizes are made through two factors analysis of variance (ANOVA) method. Some valuable conclusions are made at last. Combined with the production of some electronic products, the thrust power of red agglutinant with devastatingly sampling and small samples is taken as the characteristic to be studied, and the PTB method is used for process capability analysis. Analyzing the results, some valuable suggestions are provided to enterprises.
As the key problem 4, chapter 6 focuses on the analysis of mutivariable process capability, including the analysis of multi-stages and multi-characteristics. Combined with the actual production of enterprises, and considering the plurality of stages and characteristics, this chapter constructs a model of multivariable quality controlling and improving. In view of the plurality of stages, this chapter takes the production of cold roller as an example, and a simple improvement in Taguchi quality loss function is made to locate the key stages and analyze the process capability of multi-stages. The rationality and validity of this method are vertified through an application in cold roller production. In view of the plurality of characteristic, a flowchart of multi-characteristics process capability analysis is constructed, it is based on the Luceno index. Combined with the actual production of some electronic products, the method and the idea of the model is used for calculating the process capability indices (PCIs) of 5 process characteristics in wave soldering stage. Some suggestions and advicies are provided to enterprise according to the results.
As the key problem 5, chapter 7 focuses on the process capability plots and their application. Considering the defects of process capability analyzing only with process capability indices, the hypothesis testing is used for process capability analyzing and decision making based on the critical values of PCIs. An analysis of the influence of sample scale to crtical values of PCIs is made, it is helpful to enterprises for reasonal sampling. The graph forms of process capability plots are proved, and the quality improving flowchart based on process capability plots is constructed. Combined with the actual production of some electronic products, the analysis of process capability based on multi-characteristics process capability analysis (MCPCA) chart is developed. The superiority of process capability plots is finally proved by a practical application.
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