綠帶培訓(xùn)之控制圖

1、Timken Lean6Sigma Training 鐵姆肯L6S培訓(xùn)Introduction to Control Charts控制圖簡(jiǎn)介Control Chart Basics控制圖基礎(chǔ)X-Bar and S Control Charts均值和標(biāo)準(zhǔn)差控制圖Individuals Control Charts單值控制圖Other Common Control Charts其他常見(jiàn)控制圖Final Thoughts結(jié)束語(yǔ)Understanding Variation Revisited理解波動(dòng)-回顧Recall that we defined three categories of proce

2、ss variation:回憶一下，我們把過(guò)程波動(dòng)定義為三種類(lèi)型：Common Cause Variation: Natural background variation or process noise that is always present and is inherent to the system. This is small scale variation. 偶因波動(dòng)：自然本底波動(dòng)或過(guò)程噪音，它是一直出現(xiàn)的，并且是系統(tǒng)固有的。Special Cause Variation: Large scale variation that may permanently change the

3、 process due to some assignable or special sources of variation. The causes are external. 異因波動(dòng)：大幅度的波動(dòng)，也許會(huì)由于一些可歸因的或特殊的波動(dòng)源，而永久性地改變過(guò)程。原因是外部的。Systematic Variation: Large scale variation that systematically changes the process mean and is inherent to the process.系統(tǒng)波動(dòng)：大幅度的波動(dòng)，有規(guī)律地改變了過(guò)程的均值，是過(guò)程固有的。A stable o

4、r in control process is subject to only common cause variation. An unstable or out of control process is subject to common cause, special cause and/or systematic variation. 一個(gè)穩(wěn)定的過(guò)程是指只存在偶因的波動(dòng)。 不穩(wěn)定的過(guò)程是指存在偶因，異因和/或系統(tǒng)波動(dòng)的過(guò)程。Understanding Variation Revisited理解波動(dòng)-回顧A control chart is basically a signal dete

5、ction device, which attempts to distinguish special and systematic causes of variation from common cause variation. 控制圖基本上是一個(gè)信號(hào)檢測(cè)手段，目的是把異波和系統(tǒng)波動(dòng)從偶波中區(qū)別開(kāi)來(lái)。If a process is performing acceptably, one wants to maintain that process so that it continues to perform at that level free of special causes. 如果一個(gè)

6、過(guò)程的表現(xiàn)是可以接受的話，有人想維護(hù)那個(gè)過(guò)程，以便過(guò)程能夠持續(xù)地保持沒(méi)有異因波動(dòng)的狀態(tài)。In the case of our KPIs, we would like to shift process performance from an undesirable state to a desired state. 就我們的KPI而言，我們希望過(guò)程績(jī)效能從我們不想要的狀態(tài)轉(zhuǎn)到想要的狀態(tài)。We are purposely trying to introduce a special cause in our process that will move it from the undesirable

7、 level to the desired level. 我們有意地在我們的過(guò)程中引進(jìn)了異因的概念，這一概念實(shí)施將有助于從不想要的狀態(tài)轉(zhuǎn)變成想要的狀態(tài)。Introduction to Control Charts控制圖簡(jiǎn)介Detecting and maintaining improvement require that we monitor our processes over time. 探測(cè)和維護(hù)改進(jìn)要求我們隨時(shí)監(jiān)控過(guò)程。We have already discussed how project KPIs need to be plotted over time in order to

8、provide baseline information about changes in process level. 關(guān)于過(guò)程水平改變，為了提供基線信息，我們已經(jīng)討論了如何圖示KPI。This section focuses on how time series data can be monitored using control charts. 本節(jié)課程將重點(diǎn)討論，如何使用控制圖來(lái)控制時(shí)序數(shù)據(jù)。 There are various types of control charts. 有多種類(lèi)型的控制圖。Which chart is used depends on the type of

9、data (and the statistic of interest) and ones ability to form subgroups. 使用何種控制圖，取決于數(shù)據(jù)的類(lèi)型和個(gè)人構(gòu)成子組的能力。Introduction to Control Charts控制圖簡(jiǎn)介In the following plot, the control limits are calculated from the data that was obtained prior to implementing the solution. 在下面的圖中，控制限是根據(jù)實(shí)施解決方案之前收集到的數(shù)據(jù)進(jìn)行繪制的。When ne

10、w process data is plotted against these control limits, there is clear evidence that a special cause has occurred. 當(dāng)新的過(guò)程數(shù)據(jù)加入到這些控制限中時(shí)，就會(huì)出現(xiàn)異因的明顯證據(jù)。In this case, that special cause was desirable! 在這種情況下，異因是需要的。SolutionSummary of Basic Control Charts基本控制圖總結(jié)連續(xù)型數(shù)據(jù)離散型數(shù)據(jù)計(jì)數(shù)比例可以分組不可分組Control Chart Basics控制圖基礎(chǔ)

11、A control chart consists of four basic elements:一個(gè)控制圖包括四項(xiàng)基本要素：A statistic that is plotted at regular time periods. 等時(shí)間段繪制的統(tǒng)計(jì)量。A time axis to show the time ordering of the plotted statistic. 顯示時(shí)間順序的時(shí)間軸。A center line representing the overall process average. 代表總過(guò)程平均數(shù)的中線Upper and lower control limits t

12、hat show the limits of variability, assuming only common causes of variation are present.顯示波動(dòng)界限的上下控制限，假設(shè)只出現(xiàn)偶因波動(dòng)。For a normal distribution, 99.73% of all values fall within 3 standard deviations of the mean.對(duì)于一個(gè)正態(tài)分布，所有值的99.73%落在均值的正負(fù)三個(gè)標(biāo)準(zhǔn)差以?xún)?nèi)。The idea is that it is unlikely that points will fall outsid

13、e the control limits unless some special cause has occurred. 觀點(diǎn)是，點(diǎn)落在控制限外面的可能性很小，除非出現(xiàn)異因的情況。Control Chart Basics控制圖基礎(chǔ)Control limits can be used for process diagnosis or for ongoing process maintenance. 控制限可以用作過(guò)程診斷，或正在進(jìn)行的過(guò)程維護(hù)。When used for process diagnosis-control limits are calculated from the given

14、data, and the plot is studied for evidence of special or systematic variation. 當(dāng)用于過(guò)程診斷時(shí)， 控制限可根據(jù)給定的數(shù)據(jù)進(jìn)行計(jì)算，然后研究圖形，以分析出異波或系統(tǒng)波動(dòng)。When used for process maintenance, control limits are computed from data taken when the process is likely to be stable.當(dāng)用于過(guò)程維護(hù)時(shí)，控制限是根據(jù)穩(wěn)定過(guò)程中收集來(lái)的數(shù)據(jù)進(jìn)行計(jì)算的。During the Improve Phase,

15、 control charts for project KPIs have an emphasis of process diagnosis (have we improved?). 在改進(jìn)階段，用于項(xiàng)目KPI的控制圖著重強(qiáng)調(diào)過(guò)程診斷（過(guò)程是否改進(jìn)？）During the Control Phase, the KPI for the improved process is plotted on a control chart with an emphasis of maintenance. 在控制階段，在控制圖上繪制用于改進(jìn)過(guò)程的KPI，重點(diǎn)強(qiáng)調(diào)過(guò)程維護(hù)。Control Chart Basic

16、s控制圖基礎(chǔ)We will first discuss control charts used when process data is continuous.我們將先討論連續(xù)型數(shù)據(jù)的控制圖。In deriving control chart limits, it is desirable to estimate variation using samples gathered over a period where it is unlikely that any special cause has intervened. 在推導(dǎo)控制限時(shí)，需要收集沒(méi)有異因干擾的一段時(shí)間的過(guò)程波動(dòng)樣本數(shù)據(jù)，然后

17、再根據(jù)這些數(shù)據(jù)估計(jì)波動(dòng)標(biāo)準(zhǔn)差。In a manufacturing situation, this is often accomplished by selecting samples of parts that are produced at almost the same time since they are not likely to have been affected by special cause variation. 在制造業(yè)環(huán)境中，通常選取同一時(shí)間段生產(chǎn)的零件作為樣本，這樣過(guò)程受異因波動(dòng)影響的可能性不大。Variation is estimated within each

18、of these samples, and then these estimates are combined. 波動(dòng)是根據(jù)每個(gè)樣本估計(jì)的，然后再將這些估計(jì)合并起來(lái)。Control Chart Basics控制圖基礎(chǔ)Consider, for example, a production situation where piston rings are being produced, and where the outside diameter (OD) is of interest (Pistons.jmp). 比如，生產(chǎn)活塞時(shí)，活塞環(huán)的外徑是重要因素。At the beginning of

19、each hour, five consecutively produced piston rings are taken from production, and their OD is measured. 在每個(gè)小時(shí)開(kāi)始時(shí)，連續(xù)測(cè)量五個(gè)活塞環(huán)的外徑，并記錄數(shù)據(jù)。The samples of size five are called subgroups. 這里的五個(gè)樣品稱(chēng)為子組。Control Chart Basics控制圖基礎(chǔ)Each subgroup is fairly likely to be affected only by common cause variation. 每個(gè)子組可

20、以認(rèn)為只受偶因波動(dòng)的影響。注：用于控制限的西格瑪是基于標(biāo)準(zhǔn)差的Control Chart Basics控制圖基礎(chǔ)It is generally a good idea to plot averages rather than individual measurements:一般說(shuō)來(lái)，圖示均值要比圖示單個(gè)值要好。Plotting subgroup averages on control charts helps ensure that the underlying normality assumption applies. 用子組均值繪制控制圖，幫助保證應(yīng)用下面的常態(tài)假設(shè)。Subgroups a

21、llow the construction of control limits where the variability estimate is likely to be free of special causes. 子組可以繪制沒(méi)有異因的控制圖。These limits make the chart more capable of detecting process changes. 這些界限使得控制圖更有能力識(shí)別過(guò)程改變。Note: The subgroups must be logical to the process under review, not just random gr

22、oupings of data.注：子組要有邏輯性，不能把數(shù)據(jù)隨便分組。Rational Subgrouping合理分組The most sensitive kinds of control charts, called Shewhart charts, are based on the idea of rational subgrouping. 最敏感的控制圖，叫作休哈特圖，是基于合理分組的觀點(diǎn)。Instead of plotting individual values on a control chart, we plot the mean and standard deviation (

23、or range) of a subgroup of parts sampled from the process at some regular time interval. 在某一相同的時(shí)間間隔，我們把樣本的均值，標(biāo)準(zhǔn)差（或極差）標(biāo)在控制圖上，而不是把樣本的單值標(biāo)在控制圖上面。By doing so, we minimize the possibility that the subgroup contains the effects of a special cause of variation. Rational subgroups are considered to exhibit o

24、nly common cause variation. 通過(guò)這樣做，我們使得子組中異波的影響最小化了。合理分組被當(dāng)作只存在偶因波動(dòng)。A typical approach to rational subgrouping is to form subgroups from consecutive parts taken from the production line. 合理分組的通常方法是：從生產(chǎn)線中取得連續(xù)的加工零件，組成子組。When data on all parts is recorded, one often constructs rational subgroups based on

25、 criteria such as Shift, Day, or Week. 當(dāng)所有零件的數(shù)據(jù)記錄好了以后，通常按照標(biāo)準(zhǔn)進(jìn)行分組，比如：班次，天或周。X-Bar and S Control Charts均值和標(biāo)準(zhǔn)差控制圖Case Study: Elapsed Time Data ()案例分析：共用時(shí)間分析The data in this the number of days between the initiation of an action and its completion, recorded on the completion date. 該文件中的數(shù)據(jù)是活動(dòng)開(kāi)始日期與完成日期之間相

26、隔的天數(shù)，是在完成日期進(jìn)行記錄的。This data was collected for actions terminated in April and May of 2002. 這些數(shù)據(jù)是為2002年4-5月份結(jié)束的活動(dòng)而記錄的。We will construct a control chart subgrouped by day. 我們將按照天來(lái)繪制控制圖。X-Bar and S Control Charts均值和標(biāo)準(zhǔn)差控制圖An X-bar and S chart actually consists of two charts: one is a plot of subgroup mea

27、ns (the X-bar chart) and the other is a plot of subgroups standard deviations (the S chart).均值和標(biāo)準(zhǔn)差控制圖實(shí)際上包含兩張圖，一個(gè)是子組均值圖，另一個(gè)是子組標(biāo)準(zhǔn)差圖。Note that the control limits vary in size as a result of the fact that the subgroup sizes are not constant. 由于子組大小不一致，控制限也根著變化。X-Bar and S Control Charts均值和標(biāo)準(zhǔn)差控制圖The X-ba

28、r chart shows all points within the control limits. 均值圖顯示了所有在控制圖限里面的點(diǎn)。There is no evidence of unusual patterns. The process averages approximately 21 days. 沒(méi)有產(chǎn)生不正常振紋的證據(jù)。過(guò)程的平均天數(shù)大約為21天。We conclude that there is no evidence of special or systematic causes. 我們得出的結(jié)論是沒(méi)有異因或系統(tǒng)因素。X-Bar and S Control Charts均值

29、和標(biāo)準(zhǔn)差控制圖The S chart, on the other hand, shows several points falling outside the control limits. 另一方面，標(biāo)準(zhǔn)差圖顯示了一些點(diǎn)落在了控制限的外面。The S chart is very sensitive to non-normality, and elapsed time data tends to be fairly skewed. 標(biāo)準(zhǔn)差圖對(duì)不正?，F(xiàn)象是很敏感的，共用的時(shí)間數(shù)據(jù)趨勢(shì)有明顯偏斜。On this chart we are observing evidence of skewness

30、. 在這張圖上，我們看到了偏斜的現(xiàn)象。 Individuals Control Charts單值控制圖Continuous data that cannot be subgrouped can be monitored by an Individuals and Moving Range chart . 連續(xù)數(shù)據(jù)不能分成子組，可以由單值和移動(dòng)極差圖來(lái)監(jiān)控。The centerline for the Individual Measurement chart is the average of the data collected. 單值測(cè)量圖的中線是收集到數(shù)據(jù)的均值。Since individ

31、ual measurements are plotted on the individuals chart, and control limits based on a normal distribution, the individuals chart will not work well if the data is not normally distributed. 既然單值測(cè)量值是繪制在單值圖上的，控制限是基于正態(tài)分布的，單值控制圖的效果會(huì)不理想。The normality of the data should always be tested before using an indi

32、viduals control chart. 在使用單值控制圖之前，應(yīng)該先檢查一下，數(shù)據(jù)的正態(tài)性。Individuals Control Charts單值控制圖Other Key Points:其他關(guān)鍵點(diǎn)：To use an individuals chart, individual observations must be independent. 為了使用單值控制圖，必須獨(dú)立地對(duì)單值進(jìn)行觀測(cè)。Individual charts are not very sensitive, and so the control limits are often tightened. Unfortunate

33、ly, this will result in more false signals. 單值控制圖很敏感，因此，控制限通常很?chē)?yán)格，但不幸的是，這將導(dǎo)致較多的錯(cuò)誤信號(hào)。Why? With 3 limits, 0.27% of observations will fall outside the control limits by chance alone. In contrast, approximately 5% of observations will fall outside 2 limits by chance alone. 為什么？在三西格瑪控制限內(nèi)，只有0.27%的觀測(cè)值落在控制限外

34、面。相反，大約有5%的觀測(cè)值將落在二西格瑪控制限內(nèi)。Individuals Control Charts單值控制圖Consider the production costs in ProductionCosts2.jmp. 考慮生產(chǎn)成本These are weekly production costs for a manufacturing operation. 對(duì)于制造工廠，有一個(gè)周生產(chǎn)成本的統(tǒng)計(jì)。This data cannot be subgrouped in any reasonable way. 這些數(shù)據(jù)不能以任何合理的方法進(jìn)行分組。An individuals control ch

35、art is appropriate, so long as the data has an approximately normal distribution. 只要數(shù)據(jù)有一個(gè)大約的正態(tài)分布， 單值控制圖是適當(dāng)?shù)?。Individuals Control Charts單值控制圖Detecting Process Shifts or Changes探測(cè)過(guò)程漂移或更改It is important to realize that control charts can result in two types of errors: 認(rèn)識(shí)到控制圖可能導(dǎo)致產(chǎn)生兩種類(lèi)型的錯(cuò)誤是很重要的。They can s

36、ignal a special cause when they should not. This is called a false positive. 沒(méi)有異因時(shí)，出現(xiàn)異因信號(hào)。這稱(chēng)為正錯(cuò)誤。They can fail to signal a special cause when they should. This is called a false negative. 有異因時(shí)，沒(méi)有出現(xiàn)異因信號(hào)。這稱(chēng)為負(fù)錯(cuò)誤。To date, we have only discussed a single test for special causes, namely a point falls beyo

37、nd the control limits. 到目前為止，我們只討論了異因的單點(diǎn)測(cè)試，即某一點(diǎn)落在控制限以外。If the statistic that is plotted has approximately a normal distribution, when the process is stable, points will exceed the control limits only about 0.27% of the time. 如果繪制的統(tǒng)計(jì)量大體上是一個(gè)正態(tài)分布，當(dāng)過(guò)程是穩(wěn)定時(shí)，點(diǎn)落在控制限外面的機(jī)會(huì)大約0.27%.Other Common Control Charts其他

38、常用控制圖Exponentially weighted moving average chart (EWMA): This control chart can be used with individuals as well as subgrouped data. Each point is a weighted average of current and past measurements at each time period. It can be useful in identifying trends since it typical signals them earlier tha

39、n an X-bar or IR chart. 指數(shù)加權(quán)移動(dòng)平均控制圖（EWMA）：這類(lèi)控制圖可以用于單值，也可以用于子組數(shù)據(jù)。每一點(diǎn)是在每一時(shí)間段上，當(dāng)前和過(guò)去測(cè)量值的加權(quán)平均。既然該圖會(huì)比均值或IR圖，通常能較早發(fā)出異因信號(hào)，則對(duì)識(shí)別趨勢(shì)很有幫助。P chart or chart for proportions: This control chart can be used with proportions data, defined when an entire item is considered to be either a success or a failure (good or

40、 bad). Examples include the proportion of input errors, proportion of expedited deliveries, or the proportion of “l(fā)ost” sales opportunities. P圖或比例圖：該控制圖可用于比例數(shù)據(jù)，當(dāng)整個(gè)事件被認(rèn)為成功或失?。ê没驂模r(shí)。樣本包括輸入錯(cuò)誤的比例，加快交貨期的比例，或損失銷(xiāo)售機(jī)會(huì)的比例。Final Thoughts結(jié)束語(yǔ)A stable process is not necessarily a capable process - the natural com

41、mon cause variation may be too large compared to the customer requirements. 穩(wěn)定的過(guò)程不一定是有能力的過(guò)程-自然偶因波動(dòng)與顧客的要求相比，也許太大了。Control limits are based on natural variation that is inherent to a process, while specification limits are imposed externally upon a process. 控制限是基于自然波動(dòng)之上的，它是過(guò)程的固有波動(dòng)。而規(guī)格限是強(qiáng)加在過(guò)程外部的。Also,

42、control limits on X-bar charts refer to averages, not individual parts. Specification limits apply to measures of individual parts. 另外，均值控制圖的控制限是有關(guān)均值的，不是單個(gè)零件的。而規(guī)格限是對(duì)單個(gè)零件的測(cè)量值。Do not judge process capability with respect to specification limits using control limits. You will seriously over rate your capability. 不要從規(guī)格限的方面來(lái)評(píng)價(jià)過(guò)程能力，要使用控制限。你將過(guò)高評(píng)估你的過(guò)程能力。Skills Practice技能練習(xí)A team was studying how long it takes to recruit an external person to fill an open position within