1、1This module was developed by Business Process Improvement.For more modules,please contact us at 281-304-9504 or visit our website 2概述Overvieww 假设你在监控一个变量(如：长度、纯度，宽度等）Suppose you are monitoring a variable（length,purity,width,etc).w 变量处于统计状态控制下。The variable is in statistical control.w 公司已发布了变量的规格及标准。
2、The company has place specifications or standards on this variable.w 问题是：程序能否符合规格或标准？程序能否符合规格或标准？Is the process capable of meeting the specification or standard?w 此单元解释并回答这个问题。This module introduces how to answer that question.3目标Objectivesw 此单元中你将学到以下内容：In this module you will learn:1.属性数据中工序能力的定义T
3、he definition of process capability for attributes data.2.可变数据中工序能力的定义The definition of process capability for variables data.3.如何计算工序能力How to calculate the process capability.w 程序的改进并不是说使程序变为统计状态控制之下。Process improvement is not bringing a process into statistical control.w 把程序变为统计状态控制的程序就是说把应当受控制的程序
4、进行改变。Bringing a process into statistical control is putting the process where it should be.w 一旦程序处于统计状态控制时，程序改进便开始了。Once the process is in statistical control,real efforts at process improvement can begin.w 工序能力是衡量程序符合标准或客户规格是否有效率的方法之一。它也可衡量程序改进成就的方法之一。4属性数据的工序能力Process Capability for Attributes Dat
5、aw 属性数据有两种类型：是/否及计算。我们已学过是/否数据的P图表和计算数据的C图表。w 若想决定工序能力，则必须用统计来控制程序。对于属性数据来说，工序能力可用控制图表的平均数来解释，P图表中的平均废品率就是工序能力（确保程序受控）。例如：如你在监测及时交货的百分比，并且及时的平均百分比为95%，那么你就有95%的及时交货能力。For the p chart,the average fraction defective is the process capability(assuming the process is in control).For example,if you are m
6、onitoring percentage of on-time deliveries and the average percentage on time is 95%,your process is capable of 95%on-time deliveries.w 如用C图表对客户每月投诉的数字进行监控，工序能力就可定义为每月客户投诉的平均数字。如平均数字是3，那么你的程序每月就会发生3宗投诉。If you are monitoring the number of customer complaints per month using a c chart,the process capa
7、bility is defined as the average number of complaints per month.If the average is 3,your process is capable of producing 3 customer complaints per month.5属性数据的工序能力Process Capability for Attributes Dataw 在处理属性数据时，肯定会有不合格品或废品。w 如从没有不合格品，那么以最近出货为例，属性控制图并不能帮你进行持续不断地改进。w 当程序质量改进，真正的问题是，如何使用可变数据，因为其使用频率比较
8、高。例如：你也许想把及时交货转变成实际交货时间。通过跟踪实际时间，变量会继续减少会，甚至不会出现拖时的交货。.w 其它单元讲述可变数据。6工序能力的定义Process Capability Explanationw 客户期望买到相同质量，符合他们规格的产品。产品是生产的，而不是通过分拣，或重新生产的。w 我们可看得出控制图表能够分辨产品的质量是否稳定，但它并不能告诉我们产品是否符合客户标准。要想解决这一问题，我们重新回到柱状图上。.w 柱状图显示的是程序中的变量。一旦我们的程序受控，我们便知道是否取样和建立昨天的、今天的、或明天的产品的柱状图，根据形状、平均水平、及标准偏差等柱状图看起来一样。
9、？w 对于受统计控制及普通式分布的程序，我们可作工序能力分析。工序能力指数Cp 和 Cpk是两个具有代表性的指数。本单元会介绍这方面的知识。.7工序能力的定义Process Capability Explanationw你的体重符合由保险公司公布的指导原则呢？Is your weight capable of meeting the guidelines set by insurance companies?w 例如：你的身高是5英尺9英寸，男，那根据大城市人寿保险公司规定，你的体重应在139至175磅之间。.w Joe，5英尺9英寸高，用他个人图表对他的体重进行追踪。Joe每周称一次体重。他
10、想知道时否他的体重符合保险公司的标准。w 控制图表显示Joe 的“体重”过程受控。图表的中心线是Joe 真正重量的假想值。假定平均值为155：155kXX8工序能力的定义Process Capability Explanationw 他个人体重（人口标准偏差）的偏差可以从图表的范围内偏离平均值。假若假想标准偏差为2：The variation in his individual weighings(population standard deviation)is estimated from the average range on the range chart.Suppose that t
11、he estimated standard deviation is 2:？w 下一步就Joe 在个人结果的基础上（体重）建立柱状图。比如Joe建立的柱状图就象下一图表。The next step is for Joe to construct a histogram based on the individual results(weighings).Suppose that the histogram Joe constructed looks like the following.2128.1R9工序能力的定义Process Capability Explanationw 柱状图显示正态
12、分布（钟的形状）。为了更能明白这一点，在 Joe的柱状图上添加了正态分布线。w 又因为柱状图与正态分布稳合，假设Joe的“体重”过程可以用正态分布表示。Since the histogram appears to be normally distributed,Joe makes the assumption that his weight process can be represented by a normal distribution.w 因此，Joe将使用正态分布图而不用实际的柱状图来确定是否他的体重符合保险的指导原则。Thus,instead of using the actual
13、 histogram,Joe will use the normal distribution to determine if his weight is capable of meeting the insurance guidelines.10工序能力的定义Process Capability Explanation-3-2-10123X123-1-2-3-3-2-10123X123-1-2-3X123-1-2-3w 因而，Joe 用下列正态分布取代他的柱状图。So Joe replaces his histogram with the normal distribution below.
14、11工序能力的定义Process Capability Explanationw 在正态分布图中，曲线的高点便是它的平均值。因此，Joe的平均值=155。过程输出大约68%位于平均值的1 内。约95%位于平均值的2内。约99.7%位于平均值的3范围内。如想算出这些不同距离的值，在平均值上加或减正确的标准偏差数字。+1 from the average:155+2=157-1 from the average:155-2=153+2 from the average:155+2(2)=159-2 from the average:155-2(2)=151+3 from the average:1
15、55+3(2)=161-3 from the average:155-3(2)=149 12工序能力的定义Process Capability Explanationw 现在Joe便可把这此值加在正态分布上了。Joe can now add these values to the normal distribution.-3-2-10123X123-1-2-3-3-2-10123X123-1-2-3X123-1-2-314915115315515715916113工序能力的定义Process Capability Explanationw 根据这一分析，Joe 的重量就应在153与157磅之间
16、68%？151与159磅之间95%，149与161磅之间为99.7%Based on this analysis,Joes weight is between 153 and 157 pounds 68%of the time;between 151 and 159 pounds 95%of the time;and between 149 and 161 pounds 99.7%of the time.w 因而Joe的“重量”程序受统计的控制，而且可以表现一种正态分布。现在Joe就可对比上面由保险公司公布的指导原则了。Since Joes weight process is in stati
17、stical control and can be represented by a normal distribution,Joe can now compare the above distribution to the guidelines set by the insurance company.w 上限为175磅；下限为139磅。The upper limit is 175 pounds;the lower limit is 139 pounds.139 149 151 153 155 157 159 161 Upper GuidelineLower Guideline17514工序
18、能力的定义Process Capability Explanationw 因为分布完全符合指导原则Joe的“体重”过程能够符合保险公司的指导原则。另外，又因Joe的体重过程受控，过程输出（Joe的体重）将继续符合那些原则的。w 客户想知道他们买的产品是否符合他们规格，如：程序是否受控（一致和可预测的）？程序输出（分布）完全符合规格？w 有两个数学指数可帮助客户来确定，这两个指数会在下一步进行介绍。139 149 151 153 155 157 159 161 Upper GuidelineLower Guideline17515工序能力-Cp 的测量方法Measure of Process C
19、apability-Cpw 假定质量参数-机器的设置时间，受统计控制，其的分布正常（钟的形状）并非每一次便可得到设置时间。像所有质量特征，设置时间有内在的，正常的偏差值。（共同的原因偏差）w 我们称这个偏差为自然公差（NT）用6来解释。自然公差有时可以称之为工序能力。它描述的是当程序受统计控制时，什么样的程序能生产。-3-2-10123X123-1-2-3-3-2-10123X123-1-2-3X123-1-2-3616Cpw 自然公差就是-3s to+3s 如果规格或标准位于公布之外，程序符合规格。规格上限减去规格下限就是工程公差。-3-2-10123X123-1-2-3NT=6ET=USL
20、-LSLUSLLSL-3-2-10123X123-1-2-3-3-2-10123X123-1-2-3X123-1-2-3NT=6ET=USL-LSLUSLLSL17Cp 计算Calculation-3-2-10123X123-1-2-3NT=6ET=USL-LSLUSLLSL-3-2-10123X123-1-2-3-3-2-10123X123-1-2-3X123-1-2-3NT=6ET=USL-LSLUSLLSL 6LSLUSLNTETCp18Cpw 如果工程公差小于自然公差(i.e.,Cp 1.0),程序便不能符合规格。.w 如果工程公差等于或大于自然公差(i.e.,Cp 1.0）能实施并不
21、能保证所有的产品或服务符合规格的从而被接受。w 程序有一个Cp 1.0，没有生产规格范围内的产品或没有提供服务。另外，就无法计算出的 Cp 值。A process can have a Cp 1.0 and produce no product or service within specifications.In addition,Cp values cant be calculated for one-sided specifications.w 工序能力更好的测量方法就是Cpk。A better measure of process capability is Cpk.22Cpkw Cp
22、k 重视的是程序所注重的。takes into account where the process is centered.w Cpk.的值是两个工序能力指数的最小值。The value of Cpk is the minimum of two process capability indices.w 工序能力为Cpu,，即工序能力以规格上限基础。One process capability is Cpu,which is the process capability based on the upper specification limit.w 另一个是Cpl，即工序能力以规格下限为基础。
23、The other is Cpl,which is the process capability based on the lower specification limit.w 在代数学上，Cpk可解释为：Algebraically,Cpk is defined as:Cpk=最小值Minimum(Cpu,Cpl)3XUSLCpu 3LSLXCpl23CpkX=+3X=+2X=+1X=X=-1X=-2X=-3LSLUSLX=-LSLUSL-X=33X=+3X=+2X=+2X=+1X=+1X=X=X=-1X=-1X=-2X=-2X=-3X=-3LSLUSLX=-LSLX=-LSLUSL-X=U
24、SL-X=3333Cpl 1.0 means nothing below LSLCpu 1.0 means nothing above the USL 3XUSLCpu 3LSLXCpl24Cpkw Cpk 大于1.0意味着无规格原料。？A Cpk greater than 1.0 means essentially there is no out of spec material.w 如果仅有一个规格，Cpk 等于 Cpu 或 Cpl，？If there is only one specification,Cpk equal Cpu or Cpl,the specification that
25、 is present.X=+3X=+2X=+1X=X=-1X=-2X=-3LSLUSLX=-LSLUSL-X=33X=+3X=+2X=+2X=+1X=+1X=X=X=-1X=-1X=-2X=-2X=-3X=-3LSLUSLX=-LSLX=-LSLUSL-X=USL-X=333325Cpk 实例Examplew 银行作出承诺：不得让等候的客户超出5分钟的排队时间，在收集了50个人的调查数据。记录的时间为0.1分。平均是4.1分标准偏差为0.4。程序符合标准吗?A bank has made a commitment that no person will have to wait longer
26、 than 5 minutes in line to be served.Data has been collected for fifty people.The time to the nearest 0.1 minutes was recorded.The average was 4.1 minutes with a standard deviation of 0.4.Is the process capable of meeting the standard?w 因而只有1个标准（规格上限=5分钟），Cpk 完全等于Cpu。Since there is only one standard
27、(USL=5 minutes),Cpk is simply equal to Cpu.w 因而 Cpu=Cpk=0.75。Cpk小于1，有人会等侍超出5分多。75.2.19.0)4.0(31.40.53XUSLCpu26%Out of Specifications不符合规格w 一旦算出了工序能力，便可确定标准或规格的时间的%。如Cpk 小于1，就不符合。下一页表格就可说明这一点。w 用这一表格，查询一下Cpu 或 Cpl的计算值。表格会给出不合规格的时间的%。如 Cpu 与 Cpl小于1，查找二者的值，结果可得出不合规格总的百分比。拿排队等候作为实例，Cpu=0.75。从表格中可得知有1.22
28、%的人将会等候5分钟。？如Cpk 的值小于0（规格上限低于平均值或平均值大于规格下限），这个表格并不能用来确定不合规格的%。If the Cpk is less than zero(means the USL is lower than the average or the average is greater than the LSL),this table cannot be used to determine the%of out of spec.27 Cpu or Cpl%Not Meeting Standard Cpu or Cpl%Not Meeting Standard Cpu
29、or Cpl%Not Meeting Standard 1.00 0.13 0.66 2.39 0.32 16.85 0.99 0.15 0.65 2.56 0.31 17.62 0.98 0.16 0.64 2.74 0.30 18.41 0.97 0.18 0.63 2.94 0.29 19.22 0.96 0.20 0.62 3.14 0.28 20.05 0.95 0.22 0.61 3.36 0.27 20.90 0.94 0.24 0.60 3.59 0.26 21.77 0.93 0.26 0.59 3.84 0.25 22.66 0.92 0.29 0.58 4.09 0.24
30、 23.58 0.91 0.32 0.57 4.36 0.23 24.51 0.90 0.35 0.56 4.65 0.22 25.46 0.89 0.38 0.55 4.95 0.21 26.43 0.88 0.41 0.54 5.26 0.20 27.43 0.87 0.45 0.53 5.59 0.19 28.43 0.86 0.49 0.52 5.94 0.18 29.46 0.85 0.54 0.51 6.30 0.17 30.50 0.84 0.59 0.50 6.68 0.16 31.56 0.83 0.64 0.49 7.08 0.15 32.64 0.82 0.69 0.48
31、 7.49 0.14 33.72 0.81 0.75 0.47 7.93 0.13 34.83 0.80 0.82 0.46 8.38 0.12 35.94 0.79 0.89 0.45 8.85 0.11 37.07 0.78 0.96 0.44 9.34 0.10 38.21 0.77 1.04 0.43 9.85 0.09 39.36 0.76 1.13 0.42 10.38 0.08 40.52 0.75 1.22 0.41 10.93 0.07 41.68 0.74 1.32 0.40 11.51 0.06 42.86 0.73 1.43 0.39 12.10 0.05 44.04
32、0.72 1.54 0.38 12.71 0.04 45.22 0.71 1.66 0.37 13.35 0.03 46.41 0.70 1.79 0.36 14.01 0.02 47.61 0.69 1.92 0.35 14.69 0.01 48.80 0.68 2.07 0.34 15.39 0.00 50.00 0.67 2.22 0.33 16.11 Calculate Cpu and Cpl.If either are less than zero,use this table to determine the%out of spec.If both are less than ze
33、ro,add the results together to determine the total%out of spec.28Cpk 练习题Exercisew A manufactured part has the following length specs:USL=1.005 inches,LSL=0.995 inches.w The process is in control with an average of 1.001 inches and a standard deviation of.0015 inches.w What is the value of Cpk的值等于多少呢
34、?Is any material being produced out of specifications?如果是的话，值为多少呢If so,how much?3XUSLCpu3LSLXCpl%of parts not meeting the standard=Cpk=Minimum(Cpu,Cpl)=29Cpk 练习题Exercise厂商定于回复客户投诉最多需要10天。而客户投诉的数据表明仅需要6.5天,平均起来,用6.5天回复客户的投诉是1.4的标准偏差。程序能符合标准的天数吗？如果不是的话，客户投诉的多少%不符合标准？A manufacturer has set a maximum of
35、 ten days to respond to a customer complaint and fix the process that generated the complaint.Data on customer complaints indicate that it takes,on average,6.5 days to respond to the complaint with a standard deviation of 1.4.Is the process capable of meeting the standard of 10 days?If not,what perc
36、ent of the customer complaints are not meeting the standard?3XUSLCpu3LSLXCpl%of customer complaints not meeting the standard=Cpk=Minimum(Cpu,Cpl)=30Cpk 练习题Exercisew 机械工厂正用个体图表监控每周%的生产率。个体图表是受控的。平均数是72.76%,标准偏差为8.36。最小规格是85%。机械工厂能否符合规格？多少百分比的周不符合规格？A machine shop is monitoring%productivity on a weekl
37、y basis using an individuals chart.The individuals chart is in control.The average is 72.76%with a standard deviation of 8.36.The minimum specification is 85%.Is the machine shop capable of meeting this specification?What%of the weeks does not meet the specification?3XUSLCpu3LSLXCpl%of weeks not mee
38、ting the standard=Cpk=Minimum(Cpu,Cpl)=31Cpk 练习答案Exercise Answers3XUSLCpu3LSLXCpl%not meeting the standardCpk.89.83.481.33NoneNone.89.83.480.380.647.49 Part ComplaintsMachine Shop32概要Summaryw 本单元主要介绍工序能力This module has introduced process capability.w 对于属性数据来讲，受控的平均值为工序能力。程序必须受统计控制。For attributes dat
39、a,the average on the control chart is the process capability.The process must be in statistical control.w 对于可变数据来说，工序能力并不能被确定，除非程序受统计控制和个别测量法处于正态分布。For variables data,process capability cannot be determined unless the process is in statistical control and the individual measurements are normally dis
40、tributed.w Cpk 值近似于可变数据工序能力的测量方法。Cpk values are the appropriate measure of process capability for variables data.33应用Applicationsw 想一想我们在工作中的程序。什么样的程序的Cpk 值可被确定和监控。在下面记录你的答案。Think about your processes at work.For what processes should Cpk values be determined and monitored?Record your responses below.
