Measurement System Analysis Workshop
测量系统分析
I want to get better understanding of my processes, what should I do?
我希望能更了解我的制程，该怎么做呢？
To Measure and Analysis them! You have no other choice.
测量你的制程，分析得到的数据，没有别的选择。
是
否
正
常
独立
处理
过程
控制图
调整
测量 (过程的声音)
(量具/测量系统 )
交付
客户
Quality of Measurement Data 测量数据的质量
The Quality of Measurement Data测量数据的质量
Defined by the statistical properties of multiple measurements obtained from a measurement system operating under stable conditions.稳定条件下运行某一测量系统得到的多次测量结果的统计特性
The Statistical Properties统计特性
Bias & Variance偏倚和方差
Too much Variance or unacceptable bias on double cause Bad Quality of Measurement Data偏差太大或变差太大都将直接导致低质量的测量数据
Terminology 术语
Measurement测量
The assignment of numbers/values to material things to represent the relations among them with respect to particular properties 赋值给具体事物以表示他们之间关于特殊特性的关系
Gage量具
Device used to obtain measurements, includes go/no-go devices 任何用来获取测量结果的装置，经常用来特指用在车间的装置，包括用来测量合格/不合格装置
Summary of Terms术语
Basic equipment 基本的设备
Discrimination, readability, resolution分辨力、可读性、分辨率
Alias: smallest readable unit, measurement resolution, scale limit, or detection limit 别名: 最小的读数的单位、测量分辨率、刻度限度或探测限度
an inherent property fixed by design由设计决定的固有特性
smallest scale unit of measure or output for an instrument测量或仪器输出的最小刻度单位
always reported as a unit of measure总是以测量单位报告
10 to 1 rule of thumb 1:10经验法则
Summary of Terms术语
Basic equipment 基本的设备
Effective resolution有效分辨率
The sensitivity of a measurement system to process variation for a particular application对于一个特定的应用, 测量系统对过程变差的灵敏性
smallest input that results in a usable output signal of measurement产生有用的测量输出信号的最小输入值
always reported as a unit of measure总是以一个测量单位报告
Summary of Terms术语
Basic equipment 基本的设备
Reference value 基准值
accepted value of an artifact 人为规定的可接受值
requires an operational definition需要一个可操作的定义
used as the surrogate for the true value作为真值的替代
True value 真值
actual value of an artifact 物品的实际值
unknown and unknowable未知的和不可知的
Terminology 术语
Measurement System测量系统
The collection of instruments or gages, standards, operations, methods, fixtures, software, personnel, environment and assumptions used to quantify a unit of measure or fix assessment to the feature characteristic being measured; the complete process used to obtain measurements. 用来对被测特性赋值的操作、程序、量具、设备、软件以及操作人员的集合；用来获得测量结果的整个过程。
Summary of Terms 术语
Standard 标准
Accepted basis for comparison 用于比较的接受基准
Criteria for acceptance 用于判定接受与否的标准
Known value, within stated limits of uncertainty, accepted as a true value已知数值, 在表明的不确定度界限内, 作为真值被接受
Reference value 基准值
A standard should be an operational definition: a definition which will yield the same results when applied by the supplier or customer, with the same meaning yesterday, today, and tomorrow.一个标准应该是一个可操作的定义: 由供应商或顾客应用时, 在昨天、今天和明天都具有同样的含义, 产生同样的结果.
爺爺說 :
“眼看為真”
测量 (过程的声音)
(量具/测量系统 )
观测值变差
是
否
正
常
独立
处理
过程
控制图
调整
交付
客户
变异源
观测值变差
评价人变差(再现性)
产品/制程变差
线性
准确度（偏倚）
稳定性
重复性
测量系统变差
量具变差
观测值变差
评价人变差(再现性)
线性
准确度（偏倚）
稳定性
重复性
测量系统变差
量具变差
产品/制程变差
变异源
讨论:
仪器校正合格
等同
测量系统可接受?
Summary of Terms 术语
Location variation位置变差
Accuracy准确度
“closeness” to the true value, or to an accepted reference value
“接近”真值或可接受的基淮值
ASTM includes the effect of location and width errors
ASTM包括位置和寛度误差的影响
Measurement System’s Average
Bias
Reference Value
Summary of Terms 术语
Location variation 位置变差
Bias 偏倚
difference between the observed average of measurements and the reference value 测量结果的观测平均值与基准值的差异
a systematic error component of the measurement system
测量系统的系统误差分量
Summary of Terms术语
Location variation 位置变差
Stability 稳定性
the change in bias over time偏倚随时间的变化
a stable measurement process is in statistical control with respect to location一个穏定的测量
过程是关于位置的统计受控
alias: drift别名:漂移
Time
Reference Value
Summary of Terms 术语
Location variation位置变差
Linearity线性
the change in bias over the normal operating range整个正常操作范围的偏倚改变
the correlation of multiple and independent bias errors over the operating range整个操作范围的多个并且独立的偏倚误差的相互关系
a systematic error component of the measurement system测量系统的系统误差分量
Size N
Bias
Size 1
Bias
Summary of Terms 术语
Width variation 幅度变差
Repeatability重复性
variation in measurements obtained with one measuring instrument when used several times by an appraiser while measuring the identical characteristic on the same part同一评价人，采用同一种仪器，多次测量同一零件的同一特性时获得的测量值变差
the variation in successive(short term) trails under fixed and defined conditions of measurement
在固定和规定的测量条件下
连续（短期）试验变差
Repeatability
Summary of Terms 术语
Width variation 幅度变差
Repeatability重复性
commonly referred to as .-Equipment Variation通常指. - 设备变差
instrument(gage) capability or potential
仪器（量具）的能力或潜能
within-system variation系统内变差
Summary of Terms 术语
Width variation 幅度变差
Reproducibility再现性
Summary of Terms 术语
Width variation 幅度变差
Reproducibility再现性
variation in the average of the measurements made by different appraisers using the same gage when measuring a characteristic on one part 不同的评价人，采用相同的仪器，测量同一零件同一特性时测量平均值的变差
for product and process qualification, error may be appraiser, environment(time), or method 用以产品/制程资格认定，误差可能来自评价人、设备、时间或方法
commonly referred to as .-Appraiser Variation 通常指评价人变差 AV (Appraiser Variation)
Summary of Terms 术语
Width variation 幅度变差
Reproducibility再现性
between system(conditions) variation 系统间(条件)变差
ASTM E456-96 includes repeatability, laboratory, and environmental effects as well as appraiser effects
ASTM E456-96 包括重复性、实验室、环境及评价人影响
A
Reproducibility
再现性
Appraiser
C
B
Summary of Terms 术语
Width variation 幅度变差
GRR or Gage R&R (GRR或量具 R&R)
gage repeatability and reproducibility: the combined estimate of measurement system repeatability and reproducibility
量具重复性及再现性 : 测量系统重复性和再现性合成的评估
measurement system capability; depending on the method used, may or may not include the effects of time
测量系统能力; 取决于使用的方法，可能包括或不包括时间的影响
A
Reference value
C
B
GRR
Summary of Terms
System variation系统变差
Uncertainty 不确定度
an estimated range of values about the measured value in which the true value is believed to be contained
关于测量值的数值估计范围, 相信真值包括在此范围内
The Measurement Process 测量过程
Statistical Properties of Measurement System 测量系统统计特性
a measurement system that could produce measurements like that would be said to have the statistical properties of zero variance, zero bias, and zero probability of mis-classifying any product it measured.
一个能产生理想测量结果的测量系统，应具零方差、零偏倚、和对所测的任何产品错误分类为零概率的统计特性。
The Measurement Process 测量过程
Fundamental properties of a “Good” Measurement System 优良测量系统的基本特性
Adequate discrimination and sensitivity: 10 to 1 Rule;足够的分辨率（10：1原则）
In statistical control, only common causes, no special causes;具统计稳定性，亦即测量系统的变差只能是由于普通原因而非特殊原因造成的
For Product control: variability of the measurement system must be small compared to specification limits; 对于产品控制, 测量系统的变异性与公差相比必须小
For Process control: the variability of the measurement system ought to demonstrate effective resolution and be small compared to manufacturing process variation.对于过程控制: 测量系统的变异性应该显示有效的分辨率并且与制造过桯变差相比要小
The Measurement Process 测量过程
Sources of variation (变异源 )
Measurement System Variability
测量系统变差
人Person
标准Standard
工件Work piece
环境Environment
仪器Instrument
The Effects of Measurement System Variability
测量系统变差的影响
The cumulative effect of all the sources of variation is often called Measurement System Error
所有变异源的总影响通常称为 测量系统变差
Product control:产品控制
Is the part in a specific category?
零件在某一类别?
Process control:制程控制
Is the process variation stable and acceptable?
制程变差稳定、可接受?
The Effects of Measurement System Variability
测量系统变差的影响
Effect on Product decisions对产品决策的影响
Type I error(producer’s risk or false alarm): a good part will sometimes be called “bad”第一类错误(生产者风险/假警报): 一个好的零件有时被误判为“不合格”
The Effects of Measurement System Variability
测量系统变差的影响
Type II error(consumer’s risk or miss rate): a bad part will sometimes be called “good”第二类错误(消费者风险/漏判率): 一个不合格的零件有时被误判为“合格”
The Effects of Measurement System Variability
测量系统变差的影响
Effect on Product decisions
I: bad parts will always be called bad
II: potential wrong decision can be made
III: good parts will always be called good
II
II
I
I
III
LSL
USL
Target
Improve process: parts produced in III
Improve measurement system: reduce II areas
The Effects of Measurement System Variability
测量系统变差的影响
对产品决策的影响
I: 不合格零件总是判断为不合格
II: 可能做出错误的判断
III: 合格零件总是判断为合格
II
II
I
I
III
LSL
USL
Target
改进制程：生产的产品集中在区域 III
改进测量系统：减少区域 II面积
The Effects of Measurement System Variability
Effect on Process decisions
calling a common cause a special cause
calling a special cause a common cause
For example, if Cpmsa =2, the Cpactual should >= in order that Cpobs >=
obs2 = actual2 + msa2
Cp = Tolerance Range / 6
Cpobs-2 = Cpactua-2 + Cpmsa-2
测量系统变差的影响
对制程决策的影响
将普通原因判断为特殊原因
将特殊原因判断为普通原因
例如, 若Cp(测量系统) =2, the Cp(实际) should >= in order that Cp(观察) >=
观察2 = 实际2 + 测量系统2
Cp(Capability Index) = 公差范围 / 6
Cp观察-2 = Cp实际-2 + Cp测量系统-2
Evaluating a Measurement System
评估测量系统
Three fundamental issues must be addressed 三个基本要素
adequate sensitivity: adequate discrimination and effective resolution足够的灵敏度：足够的分辨率
be stable 稳定
the statistical properties(errors) are consistent over the expected range and adequate for the purpose of measurement (product or process control) 统计特性（误差）在预期量程是一致的，且足够用以测量用途
Evaluating a Measurement System
评估测量系统
Discrimination 分辨率
the amount of change from a reference value that an instrument can detect and faithfully indicate, also referred to as readability or resolution测量系统检出并如实指示被测特性中极小变化的能力
unacceptable for analysis if it cannot detect the variation of the process若不能测定出过程的变差，这种分辨率用于分析是不可接受的
Evaluating a Measurement System
评估测量系统
Discrimination 分辨率
unacceptable for control if it cannot detect the special cause variation若不能测定出特殊原因的变差，这种分辨率用于控制是不可接受的
The best indication of inadequate discrimination can be seen on the SPC range chart for process variation不可接受的分辨率可通过极差图最好的显示出来
Impact of Number of Distinct Categories
数据分级的影响
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Bias:偏倚
a) Instrument needs calibration仪器需要校准
b) worn instrument, equipment or fixture
仪器、设备或夹紧装置的磨损
c) worn or damaged master, error in master
磨损或损坏的基准, 基准出现误差
d) improper calibration or use of the setting master
校准不当或调整基准的使用不当
e) poor quality instrument - design or conformance
仪器质量差－设计或一致性不好
f) linearity error线性误差
g) wrong gage for the application应用错误的量具
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Bias:偏倚
h) different measurement method - setup, loading, clamping, technique
不同的测量方法－设置、安装、夹紧、技术
i) measuring the wrong characteristic测量错误的特性
j) distortion (gage or part) (量具或零件)变形
k) environment - temperature, humidity, vibration, cleanliness
环境－温度、湿度、振动、清洁的影响
l) violation of an assumption, error in an applied constant
违背假定, 在应用常量上出错
m) application - part size, position, operator skill, fatigue, observation error
(readability, parallax)
应用－零件尺寸、位置、操作者技能、疲劳, 观察错误(易读性、 视差)
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Stability稳定性
a) Instrument needs calibration, reduce the calibration interval
仪器需要校准, 需要减少校准时间间隔
b) Worn instrument, equipment or fixture 仪器、设备或夹紧装置的磨损
c) Normal aging or obsolescence正常老化或退化
d) Poor maintenance – air, power, hydraulic, filters, corrosion, rust, cleanliness
缺乏维护 – 通风、动力、液压、过滤器、腐蚀、锈蚀、清洁
e) Worn or damaged master, error in master
磨损或损坏的基准, 基准出现误差
f) Improper calibration or use of the setting master
校准不当或调整基准的使用不当
g) Poor quality instrument – design or conformance
仪器质量差－设计或一致性不好
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Stability稳定性
h) Instrument design or method lacks robustness
仪器设计或方法缺乏稳健性
i) Different measurement method – setup, loading, clamping, technique
不同的测量方法－设置、安装、夹紧、技术
j) Distortion (gage or part) (量具或零件)变形
k) Environmental drift – temperature, humidity, vibration, cleanliness
环境变化－温度、湿度、振动、清洁度
l) Violation of an assumption, error in an applied constant
违背假定, 在应用常量上出错
m) Application – part size, position, operator skill, fatigue, observation
error (readability, parallax)
应用－零件尺寸、位置、操作者技能、疲劳,
观察错误(易读性、视差)
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Linearity线性
a) Instrument needs calibration, reduce the calibration interval
仪器需要校准, 需要减少校准时间间隔
b) Worn instrument, equipment or fixture仪器、设备或夹紧装置的磨损
c) Poor maintenance – air, power, hydraulic, filters, corrosion, rust,
cleanliness
缺乏维护 – 通风、动力、液压、过滤器、腐蚀、锈蚀、清洁
d) Worn or damaged master(s), error in master(s) - minimum/ maximum
磨损或损坏的基准, 基准出现误差 – 最小/最大
e) improper calibration(not covering the operating range) or use of the
setting master(s)
校准(不包括工作范围)不当或调整基准的使用不当
f) Poor quality instrument – design or conformance
仪器质量差－设计或一致性不好
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Linearity线性
g) Instrument design or method lacks robustness
仪器设计或方法缺乏稳健性
h) Wrong gage for the application应用错误的量具
i) Different measurement method – setup, loading, clamping, technique 不同的测量方法－设置、安装、夹紧、技术
j) Distortion (gage or part) changes with part size
(量具或零件)随零件尺寸变化的变形
k) Environment – temperature, humidity, vibration, cleanliness
环境－温度、湿度、振动、清洁度
l) violation of an assumption, error in an applied constant
违背假定, 在应用常量上出错
m) Application – part size, position, operator skill, fatigue, observation
error (readability, parallax) 应用－零件尺寸、位置、操作者技能、
疲劳, 观察错误(易读性、视差)
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Repeatability重复性
within part (sample): form, position, surface finish, taper, sample consistency零件(样品)内部: 形状、位置、表面加工、锥度、样品一致性
within instrument: repair, wear, equipment or fixture failure, poor quality or maintenance
仪器内部: 修理、磨损、设备或夹紧装置故障, 质量差或维护不当
within standard: quality, class, wear
基准内部: 质量、级别、磨损
within method: variation in setup, technique, zeroing, holding, clamping, point density
方法内部: 在设罝、技术、零位调整、夹持、夹紧、点密度的变差
within appraiser: technique, position, lack of experience, manipulation skill or training, feel, fatigue
评价人内部: 技术、职位、缺乏经验、操作技能或培训、感觉、疲劳
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Repeatability重复性
within environment: short-cycle fluctuations in temperature, humidity, vibration, lighting, cleanliness
环境内部: 温度、湿度、振动、亮度、清洁度的短期起伏变化
violation of an assumption - stable, proper operation
违背假定－穏定、正确操作
instrument design or method lacks robustness, poor uniformity
仪器设计或方法缺乏稳健性, 一致性不好
wrong gage for the application 应用错误的量具
Distortion (gage or part), lack of rigidity (量具或零件)变形, 硬度不足
application - part size, position, operator skill, fatigue, observation error (readability, parallax)
应用－零件尺寸、位置、操作者技能、疲劳, 观察误差(易读性、视差)
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Reproducibility再现性
Between-parts (samples) : average difference when measuring types of parts A, B, C, etc, using the same instrument, operators, and method.
零件(样品)之间 : 使用同样的仪器、同样的操作者和方法时, 当测量零件的类型为A、B、C时的均值差。
Between-instruments : average difference using instruments A, B, C, etc., for the same parts, operators and environment. Note : in this study reproducibility error is often confounded with the method and/or operator.
仪器之间 : 同样的零件、操作者、和环境, 使用仪器A、B、C等的均值差。注意: 在这种研究情况下, 再现性错误常与方法和/或操作者混淆。
Between-standards : average influence of different setting standar5ds in the measurement process.
标准之间 : 测量过程中不同的设定标准的平均影响
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Reproducibility再现性
Between-methods : average difference caused by changing point densities, manual versus automated systems, zeroing, holding or clamping methods, etc.方法之间 : 改变点密度, 手动与自动系统相比, 零点调整, 夹持或夹紧方法等导致的均值差。
Between-appraisers (operators) : average difference when appraisers A, B, C, etc, caused by training, technique, skill and experience. This is the recommended study for product and process qualification and a manual measuring instrument.
评价人(操作者)之间 : 评价人A、B、C等的训练、技术、技能和经验不同导致的均值差。对于产品及过程资格以及一台手动测量仪器, 推荐进行此研究。
Possible Causes of Variation of Measurement System测量系统变差的可能原因
Reproducibility再现性
Between-environment : average difference in measurements over time 1, 2, 3, etc. caused by environmental cycles; this is the most common study for highly automated systems in product and process qualifications.
环境之间 : 在第1、2、3等时间段内测量, 由环境循环引起的均值差。这是对较高自动化系统在产品和过程资格中最常见的研究。
Violation of an assumption in the study
违背研究中的假定
Instrument design or method lacks robustness
仪器设计或方法缺乏稳健性
Operator training effectiveness操作者训练效果
Application – part size, position, observation error
应用－零件尺寸、位置、观察误差(易读性、视差)
Preparation for a Measurement System Study
测量系统研究准备
Two important areas need to be assessed:两个重要的研究项目：
verify the correct variable is being measured at the proper characteristic location
系统在测量正确的变量
determine what statistical properties the measurement system needs to have in order to be acceptable
确定该测量系统需要怎样的可接受统计特性
Preparation for a Measurement System Study
测量系统研究准备
Phase 1第一阶段
to verify the correct variable is being measured at the proper characteristic location per measurement system design specification 用以验证是否按照测量系统的设计规范, 在适当的特性位置正在测量正确的变量
to evaluate the effect of the operating environment on the measurement system 评估环境对测量系统的影响
Phase 2第二阶段
to provide ongoing monitoring of the key sources of variation for continued confidence in the measurement system(such as gage RR test)
持续监视主要变差源, 提供测量系统的置信(如GRR)
Preparation for a Measurement System Study
测量系统研究准备
The approach to be used should be planned.计划将要使用的方法
For instance, determine by using engineering judgement, visual observations, or a gage study, if there is an appraiser influence in calibrating or using the instrument.例如通过工程决策，直接观察或量具研究决定，是否评价人在校准或使用仪器时产生影响；有些测量系统的再现性可以忽略，例如按键
The number of appraisers, sample parts, and repeat readings should be determined in advance:评价人数量、样品数量、及重复读数次数应预先确定：
Criticality of dimension - critical dimensions require more parts / trails;
尺寸的关键性 - 关键尺寸需要更多的样品和/或试验
Part configuration - bulky or heavy parts may dictate fewer parts and more trails 零件规格 - 大而重的零件可规定较少样品及较多试验
The appraisers chosen should be selected from those who normally operate the instrument.评价人的选择应从日常操作该仪器的人中选出。
Preparation for a Measurement System Study
测量系统研究准备
Selection of the sample parts is critical for proper analysis and depends entirely on the design of MSA study, purpose of the measurement system, and availability of part samples that represent the production process.样品选择对于适当的研究非常重要，且取决于测量系统研究的设计
For product control, “conformance or non-conformance to the feature specification(100% or sampling)”, samples need not cover the entire process range; Assessment of the measuring system→ %GRR to Tolerance对于产品控制 - “符合/不符合产品特定规格”, 样品的选择无需覆盖整个规格范围
For process control, “process stability, direction and compliance with the natural variation”, the sample parts must be selected from the process and represent the entire production operating range. → %GRR to process variation or TV 对于制程控制 - “过程稳定性，方向及自然变差的符合情况”, 样品必须从过程中选取并代表整个工作范围
Preparation for a Measurement System Study 测量系统研究准备
The instrument should have a discrimination that allows at least one-tenth of the expected process variation of the characteristic to be read directly.
仪器分辨率应允许至少直接读取特性的预期过程变差的十分之一
Assure that the measuring method is measuring the dimension of the characteristic and is following the defined measurement procedure.
确保测量方法在按规定的测量步骤测量特征尺寸
Preparation for a Measurement System Study
测量系统研究准备
The study manner is very important:进行研究的方式非常重要：
The random order to avoid any possible knowledge bias;
测量应按随机顺序，以确保研究过程中产生的任何漂移或变化将随机分布。使用盲测方式。
the readings should be recorded to the practical limit of the instrument discrimination. Analog devices should be recorded to one-half the smallest graduation or limit of sensitivity and resolution.设备读数应估计到可得到的最接近的数字，模拟(Analog)设备应读取最小刻度的一半
The study should be managed and observed by a person who understands the importance of conducting a reliable study.
研究工作应由知其重要性且仔细认真的人进行
Each appraiser should use the same procedure/step to obtain the measurements每一位评价人应采取相同的方法/步骤来获取数据
Analysis of the results
结果分析
Acceptability criteria - Location error
允收标准 - 位置误差
bias and linearity
偏倚和线性
re-calibration or an offset correction to minimize the error
从新校正或偏移修正以最小化误差
Analysis of the results
结果分析
Acceptability criteria - Width error
允收标准 - 幅度误差
under 10% error – acceptable 低于10% - 接受
10% to 30% error - may be acceptable based on importance of application, cost of measurement device, cost of repair, etc.
在10% 与30%之间 - 根据应用的重要性、量具成本、维修的费用等，可能是接受的
Over 30% error - not acceptable, improvement of the measurement system is necessary.
高于30% - 不接受，测量系统必须改善
The number of the distinct categories should be greater than or equal to 5明显的分类数量应大于或等于5
Variable Gage Study 計量型測量系統研究
Bias Study偏倚指南
参考值 偏倚
重複性
d2於附錄C
确定稳定性指南
Guidelines For Determining Stability
进行研究 Conducting the Study
取一个样本并建立相对于可溯源标准的基准值。 如果该样品不可获得， 选择一个落在产品测量中程数的生产零件， 指定其为稳定性分析的标准样本。 对于追踪测量系统稳定性， 不需要一个已知基准值。 Obtain a sample and establish its reference value. If one is not available, select a production part that falls in the mid-range of the production measurements as the master sample.
Known reference value is not required.
2. 定期(天，周)测量标准样本3~5次， 样本容量和频率应该基于对测量系统的了解。 On a periodic basis (daily/weekly), measure the master sample three to five times. The sample size and frequency should be based on knowledge of the measurement system.
将数据按时间顺序划在 X & R 或 X & S 控制图上状态。Plot the data on an bar X & R or bar X & S control chart in time order.
结果分析-作图法 Analysis of Results-Graphical
4. 建立控制限并用标准控制图分析评价失控或不穏定状态。 Establish control limits and evaluate for out of control or unstable conditions.
确定线性的指南
Guidelines For Determining Linearity
进行研究 Conducting the study
线性按以下指南评价：
Linearity can be evaluated using the following guidelines:
选择 g5 个零件， 由于过程变差， 这些零件测量值覆盖量具的操作范围。Select g5 parts whose measurements, due to process variation, cover the operating range of the gage.
用全尺寸检验测量每个零件以确定其基准值并确认了包括量具的操作范围。Have each part measured by layout inspection to determine its reference value and to confirm that the operating range of the subject gage is encompassed.
进行研究 Conducting the study
通常用这个仪器的操作者中的一个测量每个零件 m 10次。 Have each part measured m 10 times on the subject gage by one of the operators who normally use the gage.
注 ： 随机地选择零件以使评价人对测量偏倚的〝记忆〞最小化。Note : Select the parts at random to minimize appraiser “recall” bias in the measurement.
结果分析-作图法 Analysis of Results-Graphical
计算每次测量的零件偏倚及零件偏倚均值。Calculate the part bias Bias Reference value
在线性图上划出单值偏倚和相基准值的偏倚均值。Plot the individual biases and the bias averages with respect to the reference values on a linear graph.
结果分析-作图法 Analysis of Results-Graphical
用下面等式计算和划出最佳拟合线和置信带。Calculate and plot the best fit line and confidence band. 对于最佳拟合直线， 用公式 :
= 基准值 reference value
= 偏倚平均值 bias average
拟合优度 Goodness of fit (R2) =
7. Linearity(线性) = Slope (斜率) x Process Variation(過程變差)
% Linearity(线性) =
100[Linearity(线性) / Process Variation(過程變差)]
划出〝偏倚=0〞线， 评审该图指出特殊原因和线性的可接受性。Plot the “bias=0” line and review the graph for indications of special causes and acceptability of the linearity.
Analysis of results – Numerical 结果分析-数据
If the graphical analysis indicates that the measurement system linearity is acceptable then the following hypothesis should be true. 如果作图分析显示测量系统线性可性受， 则下面的假设就成立：
H0: a=0 斜率(slope) =0
不推翻原假设， 如果 ( do not reject if)
If the above hypothesis is true, then the measurement system has the same bias for all reference value. For the linearity to be acceptable this bias must be zero. 如果以上的假设是成立的， 则测量系统对所有的基准值有相同的偏倚 。对于可接受的线性，偏倚必须为 0。
H0: a=0 截距intercept(偏倚bias) =0
不推翻原假设， 如果 ( do not reject if)
Variable Gage R&R
计量型Gage R&R
Three acceptable methods for this study:三种研究方法
Range method极差法
Average and Range method平均值极差法
ANOVA method方差分析法
with some in-process measurement systems there are no human appraisers, if all the parts are handled, fixtured and measured by the same equipment, then reproducibility is zero; .,only a repeatability study is needed, however, multiple fixtures are used, then the reproducibility is the between-fixture variation.某些测量系统没有评价人，若所有的部件均由同一设备处理、固定及测量，那么再现性就为零；当使用了不同的工装，那么再现性就表现为工装间变差
Guidelines For GR&R-Range Method 极差法指南
五个零件 (5 parts), 二个评价人 (2 appraisals)
平均极差(R) Average ®=
- ∑R/5 = =
- GR&R = (R)/d2*(m2,g5)
= ()/
- 过程变差 Process var.=
- %GR&R = 100(GR&R/过程变差 (process var.)) = %
5
4
3
2
1
極差
Range
評價人B
Appraisal B
評價人A
Appraisal A
零件Part
樣本數是 5, (10)，80 (90)%的機會可檢測到不可接受的測量系統
Sample # 5,(10), 80 (90)% chance that a non-acceptable measurement system can be identified.
重複性 Repeatability (EV) MSA
重复性变差(EV) 的估算, EV estimation
d*2 ( m= 3, g = 5*2)
App
App
Part
Test
Ave.
Range
Average and Range Method平均值极差法
Decompose into R&R, but not their interaction
分解成重复性及再现性，但是无两者交互作用
Commend procedure is as follows:推荐的方法如下：
obtain a sample of n>5 (., n=10) parts that represent the actual or expected range of process variation取多于5个样品 (例如, n=10)代表了实际或预期的过程变差范围
select 3 appraisers, and number the sample parts that are not visible to the appraisers选取3个评价人，给样品编号，该编号评价人并不知道
Calibrate the gage before conducting the study进行试验前校准量具
Let appraiser A measure n parts in a random order and keep record让评价人A随机测量每一个样品并做好记录
Let B and C measure the same n parts without seeing each other’s readings让B和C测量每一个样品并做好记录，彼此之间不知另一个人的测量结果
repeat the cycle two times more using a different random order of measurement打乱样品的顺序，再次分别由三位评价人测量并记录
GRR data collection sheet
(平均值极差法)测量数据收集表
Analysis of results – Graphical 结果分析 - 图形
Analysis of results – Graphical 结果分析 - 图形
Average Chart:平均值图
one half or more of the averages fall outside of the control limit, can detect part to part variation
控制限内的面积代表测量误差，若一半或以上的平均值落在控制限以外，表明测量系统足以检查出试件间变差
Range Chart:极差图all range in control - all appraisers are doing the same job
若所有极差受控，所有评价人在采用同一种方法测量
some appraisers have some out of control ranges - the measurement system is sensitive to appraiser technique and needs improvement
极差图有超出控制线–测量系统是对评价人技术敏感, 则系统须改善
Run Chart:趋势图
no any outlier
没有outlier
Numerical calculation 数字计算
Analysis of GRR studies GRR 研究结果分析
If Repeatability > Reproducibility若重复性 > 再现性
the instrument needs maintenance仪器需要维护
the gage may need to be redesigned to be more rigid量具应重新设计来提高刚度
the clamping or location for gaging needs to be improved夹紧及检验点需要改进
there is excessive within-part varition存在过大的零件内变差
if Reproducibility > Repeatability若再现性 > 重复性
the appraiser needs to be better trained in how to use and read the gage instrument评价人需要更好的培训如何使用量具仪器及读数
calibrations on the gage dial are not clear量具刻度盘上的读数不清楚
a fixture of some sort may be needed to help the appraiser use the gage more consistently需要某种夹具帮助评价人提高使用量具的一致性
Attribute Gage Study – Short Method
计数型测量系统-小样法
Short Method 小样法
Short method conducted by selecting 20 parts. Two appraisers measure all parts twice in a manner that will prevent appraiser bias. In selecting 20 parts, some of the parts are slightly below and above both specification limits. 小样法通过选取20个零件来进行，然后两位评价人以一种能防止评价人偏倚的方式两次测量所有零件，选取的20个零件中，一些零件会少许低于或高于规范限值
Gage is acceptable if all measurement decisions (four per part) agree, if not, gage must be improved and re-evaluated if the gage cannot been improved, it is unacceptable. 若所有测量结果（每个零件4次）一致则接受该量具，否则须改进量具或重新评价，若量具不能改进，该测量系统不被接受
Short Method (Sample)小样法(示例)
G
G
G
NG
G
G
NG
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
NG
G
G
NG
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
G
NG
G
G
NG
NG
G
G
G
G
NG
G
G
G
G
G
G
G
G
G
NG
NG
G
G
NG
NG
G
G
G
G
G
G
G
G
G
G
G
G
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2
1
2
1
Appraiser 評價人B
Appraiser 評價人 A
RUBBER HOUSE . (GO/NO-GO PLUG GAGE) 橡胶软管内径(通过/不通过塞规)
There are 34 times where A-1 = 1 and B-1 = 1 ( that is of the 50 parts checked there were 34 matches by A and B on their FIRST check)
总共有34次A-1 = 1及 B-1 = 1 (于第一次试验中, 于50个零件中共34个检查结果为A与B相同)
Table 12: Attribute Study Data Set
pg 127
Attribute Measurement Systems – Risk Analysis Methods( Hypothesis Test Analysis)
计数型测量系统– 风险分析法 (假設檢驗分析法 )
There are 32 times where A-2 = 1 and B-2 = 1 ( that is of the 50 parts checked there were 32 matches by A and B on their SECOND check)
总共有32次A-2 = 1及 B-2 = 1 (于第二次试验中, 于50个零件中共32个检查结果为A与B相同)
There are 31 times where A-3 = 1 and B-3 = 1 ( that is of the 50 parts checked there were 31 matches by A and B on their THIRD check)
总共有31次A-3 = 1及 B-3 = 1 (于第三次试验中, 于50个零件中共31个检查结果为A与B相同)
Total : where A=1 and B=1 = 34+32+31= 97
Count & Expected Count Calculations
计算与期望的计算
A * B Crosstabulation (A * B交叉表)
44
6
50
3
97
100
47
103
150
Count 计算
Expected Count
Count
Expected Count
Count
Expected Count
.00
A
Total
.00
B
Total
期望的计算
總計
A * B Crosstabulation
44
6
50
3
97
100
47
103
150
Count
Expected Count
Count
Expected Count
Count
Expected Count
.00
A
Total
.00
B
Total
The expected counts is calculated using the the following formula (based on Chi-Square)
期望的计算按下公式 (基于Chi-Square)
Expected Count = Column Total x [Row Total/Grand Total]
期望的计算 = 列总数 x [行总数/总数]
F按rom the A*B Crosstabulation Table, A * B交叉表
Column Total列总数 = 103
Row Total行总数= 100
The Grand Total总数= 150
For A=1 and B=1
Expected Count期望的计算
= 103 x [100/150] =
97
po=對角線單元中觀測值的總和(左至右) pe=對角線單元中期望值的總和(左至右)
Kappa > (max: 1) “ good to excellent agreement 表示好的一致性”
Kappa < “ poor agreement 表示差的一致性”
A * REF Crosstabulation (A * 基準交叉表)
45
5
50
3
97
100
48
102
150
Count 計算
Expected Count
Count
Expected Count
Count
Expected Count
.00
A
Total
.00
基準
Total
期望的計算
總計
REF
C
B
A
C
B
A
koppa
Effectiveness 有效分
No. of match 三次相同
Total Inspected總檢查數
80
90
84
40
45
42
50
50
50
Appraiser C
評價人
Appraiser B
評價人
Appraiser A
評價人
Effectiveness = number of correct decisions / total opportunities for a decision
有效分 = 正確判斷的數量 /判斷的機會總數
Miss Rate1: Calling a “BAD” part GOOD.漏发警报的比例=“坏的判为好”
= 3/48 = %
1 Type II error, Consumer’s risk (II型错误 : 消费者风险)
2 Type I error, Producer’s risk (I型错误 : 生产者风险)
False Alarm Rate2: Calling a “GOOD” part BAD.误发警报的比例=“好的判为坏”
= 5/102 =%
交叉表结果的意义通常有一个误解
Misconception of cross-tabulation results
评价人B*基准的结果是 B*REF Crosstabulation：
%
%
%
在基准值内 % within REF
Total
150
102
48
计算(count)
总计
%
%
%
在基准值内 % within REF
103
100
3
计算(count)
%
%
%
在基准值内 % within REF
47
2
45
计算(count)
.00
B
.00
总计(total)
基准 (REF)
The purpose of the inspection is to find all the nonconforming parts, most people look at the upper left corner as a measure if the effectiveness of finding bad parts. This percent is the probability of saying a part given that it is bad.
由于检验的目的是找出所有的不合格品，许多人将左上角当作对发现不合格品有效性的测量。这个百分比是将不合格零件确认为不合格的概率：
Pr (认为零件不合格 calling the part bad \ 零件不合格a bad part)
假设过程改善到 Pp/Ppk = ，制造者感兴趣的概率是 ：
Assuming that the process is improved to Pp/Ppk = , probability of interest to the producer is.
Pr (不合格零件 the part is bad\ 零件被判断为不合格 it is called bad)
必须应用贝叶理论 per Bayes’ theorem。
Pr (不合格 bad\判不合格 called bad) =
Pr(判不合格called bad\不合格bad)*Pr(不合格bad)
Pr(判不合格called bad\不合格 bad)+Pr(判不合格called bad\合格bad)*Pr(合格good)
Pr(不合格bad\判不合格called bad)= .938*(.0027)
.938*(.0027)+.020*(.9973)
Pr(不合格bad\判不合格called bad)= .11
零件被认为不合格，这个零件真的不合格的可能性只有十分之一。
if the part called bad there is only a 1 out of 10 chance that it is true bad 。
Effectiveness(accuracy on detection of good and bad parts)
有效性(正确探测好与坏的零件)
number of correct decisions/total opportunities for a decision
正确判定的数量/判断的机会总数
False Alarm Rate(the chance of rejecting good parts)
误发警报比例(拒收好的零件的机会)
FA/(total good correctly identified + FA)
误发警报量(FA)/(判定“好”的准确量+ FA)
Miss Rate(the chance of not rejecting bad parts)
漏发警报比例(接受坏的零件的机会)
Miss/(total bad correctly identified + Miss)
漏发警报量/(判定“坏”的准确量+ 漏报)
A subject matter decision criteria as follow判定准则:
Result 结果
Signal Detection theory信號探測法
Determine an approximation of the width of the region II area and from this, the measurement system GRR. 确定区域II的寛度的近似值, 并因此确定测定测量系统GRR.
+ = accepted with total agreement in Table 12 (一致接受表12)
- = rejected with total agreement in Table 12(一致拒绝表12)
x = disagreement in Table 12
(结果不一致表12)
Ref Value Code Ref Value Code
- +
- +
- +
- +
- +
- +
x +
x +
x +
x +
x +
x +
+ +
+ +
+ +
+ x
+ x
+ x
+ x
+ x
+ -
+ -
+ -
+ -
+ -
dUSL
dLSL
Let di = distance between the last part accepted by all appraisers to the first part rejected by all (for each specification).
di = 从被所有人接受的最后一个零件到被所有评价人拒绝的第一个零件(对于每个规范)之间的距离.
Then, 则
d = average (di)
d = 平均值(di)
is an estimate1 of the width of region II areas and, thus, an estimate of the
是区域II寛度的估计值, 而估计的
In this example, 此例:
dLSL=– =
dUSL=– =
d =
or the estimated %GRR is, %GRR = 29%,
或%GRR的估值为%GRR = 29%
([d average/]/[Tol/6]) ([d 平均/]/[容差/6])
The actual %GRR = 25%, so this estimate will lead to the same evaluation of the measurement system.
真实的%GRR = 25%, 因此估计值有相同的结果.
USL = .545
LSL = .450
容差Tolerance = USL – LSL =
If Ppk>1, compare measurement system to process.
如Ppk>1, 测量系统与过程变差比较.
If Ppk<1, compare measurement system to tolerance.
如 Ppk<1, 测量系统与产品公差比较.
In this example, the Ppk = (see p. 125, “Scenario”), so the process is greater than the tolerance and this measurement system should therefore be compared to tolerance.
比例中 : Ppk =, 过程变差比公差大, 测量纟统与公差进行比较.
目标
Zone I = parts agreed by all appraisers to be rejected.
区域 I = 该零件所有评价人同意拒絶.
Zone II = questionable parts without 100% agreement,
surrounding each specification limit.
区域 II = 未有100% 同意的问题零件, 这些零件围绕于规格边缘.
Zone III = parts agreed by all appraisers to be accepted.
区域 III = 零件被所有评价人接受.
Analytic Method解釋法
Step:步驟:
1. Obtaining the reference values for several parts
獲得選擇零件的基準值
2. Evaluate a number of times (m), with
評價多次(m)
3. Total number of accepts (a)
接受的總數(a)
4. Determine the repeatability and bias
評價重復性和偏倚
PART SELECTION CRITERIA零件選擇條件
Smaller part must have a = 0
最小的零件必須a = 0
Largest part must have a = 20
最大的零件必須a = 20
And six other parts, 1≤ a ≤ 19
另外6 件, 1≤ a ≤ 19
If this criteria are not satisfied, more parts with known reference values ( X ) must be run through the gage until the above conditions are met.
如這標準不能滿足, 需要選擇更多的已知基準值(X )的零件, 用量具測量, 直到條件滿足為止.
Calculate 計算the P’a
If 如 a/m <, a≠0, P’a = ( a+)/m
If 如 a/m > , a≠20, P’a = ( a - )/m
If 如 a/m = , P’a =
Adjustment 調整:
Where a = 0, set P’a = 0 except large reference value with a = 0, in which P’a = 0 .025
a = 0 時, 設 P’a = 0 除去 a = 0的最大基準值, 此時其P’a = 0 .025
Where a = 20 then P’a = 1 except for the smallest reference value with a = 20 in which P’a =
a = 20 時, P’a = 1 , 除去 a = 20 最小基準值, 此時 P’a =
Bias偏倚 = Lower Specification Limit 下公差限 – XT (at P’a = )
Repeatability 重復性 = XT (at P’a = ) - XT (at P’a = )
t calculated 計算 = [ x Bias偏倚] / Repeatability重復性
If t calculated計算 is greater than 大於 ( ,19)
The Bias is significantly different from Zero.
則偏倚明顯偏離零.
Attribute Measurement Systems 计数型测量系统 Guidelines For Analytic Method解釋法指南
重复性
无调整
图31 : 絵制在正态概率纸上的计数型量具性能曲线
偏倚
NON-REPLICABLE GRR CASE STUDY
不可重复性GRR案例
David Benham, DaimlerChrysler Corporation
Study Approach 研究方向
appraisers should be similarly qualified and trained评价人须有相近能力
work instructions should be detailed etc.
工作指引须详细
The production process must be stable and the nature of its variation understood
生产过程须穏定及变差源已清楚
where is the process homogeneous and where is it heterogeneous? 过程中哪里出现相同及不同?
If the overall process appears to be stable AND CAPABLE, it may not make sense to do a non-replicable study 如过程为穏定及俱备能力, 还作不可重复性的GRR研究似乎是多余的
the overall capability includes measurement error
if the total product variation and location is OK, the measurement system may be considered acceptable.因总的能力已包括测量系统的误差, 若产品的变差及位置是可接受的, 则测量系统亦应可接受.
Sampling approach 零件的選擇
Since the original part cannot be re-measured due to its destruction 因零件會被破壞, 不能重覆測試
other similar (homogeneous) parts must be chosen for the study (for the other trials and other appraisers) 須選擇近似的其它零件進行測試
Assumption: that they are “duplicate” or identical parts. “假設” : 這樣的零件是“重覆”的或“完全相同”的
“duplicate” parts are re-measured across other trials and by other appraisers “重覆”指零件可作多次測試及多評價人測試
assumed to be identical, parts are used to represent Part 1, and so on for all 10 parts. 假設零件是相同的, 多個零件作為“零件一”, 全數“十”個零件處理相同.
“Part 1” is now Part 1-1, 1-2, 1-3, 1-4, 1-5, 1-6
“零件一”表達為零件1-1, 1-2, 1-3, 1-4, 1-5, 1-6
Sampling approach零件的選擇
The assumption must be made that all the parts sampled consecutively (within one batch) are identical enough that they can be treated as if they are the same. 為满足“假設”的要求, 零件須連續取樣.
If the particular process of interest does not satisfy this assumption, this method will not work.若須研究的過程不能滿足這“假設”, 此方法不能執行 .
These parts should be produced under production conditions as similar as possible. 零件須於極相近的生產條件下生產.
However, the parts chosen to represent part number 2, for example, must be chosen to be unlike part number 1, part number 3, 4, 5, etc. 對於作為“零件二 ”的零件, 須於“零件一”、 “零件二 ”及 “零件三 ”等不同.
groups of parts within each row are assumed to be identical, but groups of parts between, rows are assumed to be different. 同一行中零件須相同, 不同行的零件須不同.
within a row it is desirable to minimize variation by taking parts consecutively, thus representing part-to-part variation. 同一行中的零件須減少之間的變差, 此代表“零件間”變差.
Between rows it is desirable to maximize variation by taking parts from different lots, batches 不同行中須最大化其中的變差, 零件從不同批次、批號作抽取可達致此要求.
Part variation零件變差
part-to-part, shift-to-shift, day-to-day, lot-to-lot, batch-to-batch, week-to-week, etc.零件間, 班與班, 日與日, 批次間, 批號間, 星期與星期等等.
With parts the minimum variation would be part-to-part –When parts are not sampled consecutively (., part-to-part) 零件間的變差最少化可通過連續取樣達成.
More opportunity for variation to occur – different production operators, different raw material, different components, changes in environment, etc.最大化零件變差可通過 – 不同生產操作員, 不同原材料, 不同配件, 璄改變達成.
CASE STUDY
Refer to pdf file (參照pdf檔案)
CONCLUSIONS 總結
1. Only 10 of the 24 weld fixtures were included in this study. If the process variation due to all the fixtures is much larger than that of the 10 selected for this study, then the measurement system may be acceptable based on MSA guidelines.因只用24焊接機架中的10個作為研究, 若總體焊接機架的變差遠大於10個焊接機架造成的變差, 則MSA結果是可接受的.
2. It is impossible to separate all process variation from measurement system variation with this scheme.此項研究不可完全分開產品及MSA的變差.
The End
Thank you! 多謝!
