工程方法_6sigma_09工序能力分析ppt課件

1、Capability Analysis過程能力分析.測量階段流程圖流程圖(Process mapping)C&E矩陣初步分析可能因子FMEA進一步分析可能因子測量系統(tǒng)定義,MSAY 的穩(wěn)定性判定,過程能力分析二次FMEA可能因子總結分析階段定義階段魚骨圖(Fishbone).Learning Objectives學習目的Process Control vs Process Capability 過程控制和過程能力Process Capability過程能力:Specification, Process and Control Limits.規(guī)格,過程和控制界限Process Potential

2、 vs Process Performance過程潛在的和實際的表現(xiàn)Short-Term vs Long-Term Process Capability短期和長期過程能力“Six Sigma” Quality ; “ 6Sigma”水平; Introduction to Z-score Z-值介紹Process Capability for Non-Normal Data非正態(tài)分布的過程能力Cycle-Time (Exponential Distribution)循環(huán)時間(指數(shù)分布)Reject Rate (Binomial Distribution)不合格(剔除)率(二項式分布)Defect

3、 Rate (Poisson Distribution)缺陷率(泊松分布).Process Control vs Process Capability過程控制和過程能力1. Process Control過程控制Means the process is operating in statistical control, i.e. common causes are the only source of variation.意味是過程在穩(wěn)定狀態(tài)下生產(chǎn),也就是說, 一般原因(偶然原因)是變異的唯一原因Refers to “voice of the process”, i.e. one only n

4、eeds data from the process to determine if a process is in control.起源于”過程的聲音”,也就是說,唯一來源于過程的數(shù)據(jù)來判定過程是否受控.Track performance of the process to verify if it forms a stable distribution over time, typically with a control chart with control limits computed from the process data only.隨著時間過去,反饋過程的表現(xiàn)來驗證它是否來自

5、于一個穩(wěn)定的分布,一般地,利用從過程數(shù)據(jù)計算控制界限的控制圖來完成.Just because a process is in control does not necessarily mean it is a good process.僅僅因為過程受控并不一定說它是個好過程.2. Process Capability過程能力The “goodness” of a process is measured by process capability過程的 “好壞”是過程能力測量的Compares “voice of the process” with “voice of the customer”

6、, which is given in terms of specs. or requirements比較 “過程聲音”和 “客戶聲音”,哪一個是根據(jù)規(guī)格或需要給出的?Measures how well a stable distribution (process in control) matches up with customers specs.測量一個穩(wěn)定的分布(過程受控)符合客戶規(guī)格的程度.Process Control vs Process Capability過程控制和過程能力首先判定過程穩(wěn)定,確定數(shù)據(jù)分布是正態(tài)的,再計算過程能力和西格碼質量水平.What is Capabili

7、ty 過程能力是.When process is under control, capability is decided by customer demand and process performance(Product or service quality shifting degree). The more the process meets the customer need, the better the capability will be.過程在受控狀態(tài)下時,客戶要求與過程表現(xiàn)(產(chǎn)品品質或服務的品質變動程度)的比值, 如果過程表現(xiàn)越能滿足客戶要求,則過程能力越充分,反之則不足.

8、Process Capability過程能力Process Capability studies can過程能力研究可以: indicate the consistency of the process output顯示過程輸出的穩(wěn)定性indicate the degree to which the output meets specifications表明輸出滿足規(guī)格的程度be used for comparison with another process or competitor可以與另一過程或竟爭對手相比較.Process Variation過程變異Process Variation

9、 is the inevitable differences among individual measurements or units produced by a process.過程變異是不可避免的差別在單個測量或過程生產(chǎn)單位之間.Sources of Variation變異的來源: within unit 產(chǎn)品內 (positional variation) 位置的變異 between units 單位之間 (unit-unit variation) 產(chǎn)品-產(chǎn)品的變異 between lots 產(chǎn)品批之間 (lot-lot variation) 批批的變異 between lines

10、生產(chǎn)線之間(line-line variation) 線-線之間的變異 across time 不同時間 (time-time variation) 時間-時間的變異 measurement error 測量誤差(repeatability & reproducibility) 重復性和再現(xiàn)性.Types of Variation變異的類型1. Positional Variation位置變異Same process, variation at differing locations simultaneously: 相同的過程,隨不同位置而產(chǎn)生的變異Temperature variations

11、 inside a thermal chamber溫度變異在一個烘箱中Cavity-to-cavity variations in an injection mold洞坑差別在一個注塑模中2. Cyclical Variation重復誤差Sequential repetitions of a process over fairly short time, say, less than 15 mins: 在一定短的時間內某過程的連續(xù)重復,比方說, 少于15分鐘:Variations between consecutive batches of a process同一過程的連續(xù)批次之間的變異Dif

12、ferences from lot to lot of raw materials不同批次原材料之間的差別3. Temporal Variation時間的變異Variations over longer periods of time, such a several hours, days or weeks. 長期的變異, 例如幾個小時,幾天或幾個星期.Inherent or Natural Variation固有或自然的變異Due to the cumulative effect of many small unavoidable causes歸因于許多小的,不可避免的因素共同的結果A pr

13、ocess operating with only chance causes of variation present is said to be “in statistical control” 如果一個過程運行時只存在固有原因變異的作用,就說它處在“統(tǒng)計控制狀態(tài)”.Types of Variation變異的類型一般原因.Special or Assignable Variation特殊的可查明的變異May be due to可能歸因與 : a) improperly adjusted machine 不正確的調機 b) operator error 員工錯誤 c) defective r

14、aw material 有缺陷的原材料A process operating in the presence of assignable causes of variation is said to be “out-of-control”.如果一個過程運行時存在可指出原因變異,則稱該過程“失控Types of Variation變異的類型異常原因.Process Capability vs Specification Limits過程能力和規(guī)格界限a)b)c)a) Process is highly capableb) Process is marginally capablec) Proce

15、ss is not capablea)過程能力高b)過程能力一般c)過程能力差.Three Types of Limits三種類型的界限Specification Limits (LSL and USL) created by design engineering in response to customer requirements to specify the tolerance for a products characteristicProcess Limits (LPL and UPL)measures the variation of a processthe natural 6

16、 limits of the measured characteristicControl Limits (LCL and UCL)measures the variation of a sample statistic (mean, variance, proportion, etc)規(guī)格界限 (LSL and USL)由設計工程部門根據(jù)客戶要求確定的產(chǎn)品性能公差。過程界限(LPL and UPL) 用來測量過程的變異為所測量特性的自然公差(六倍標準差(6)界限控制界限(LCL and UCL)用來測量樣本統(tǒng)計量的變異(均值，方差比例等).Distribution ofIndividual

17、Values (x)Distribution ofSample Averages (x) Three Types of Limits三種類型的界限單值分布樣本均值分布.Process Capability Indices過程能力指數(shù)Two measures of process capability:過程能力的兩種測量Process Potential過程潛力CpProcess Performance過程表現(xiàn)CpuCplCpk.Process Potential過程潛力The Cp index assesses whether the natural tolerance (6) of a pr

18、ocess is within the specification limits. 工序能力指數(shù)Cp用以評價是否一個過程的自然公差(6)處于規(guī)格界限以內.Traditionally, a Cp of 1.0 indicates that a process is judged to be “capable”.if the process is centered within its engineering tolerance, 0.27% of parts produced will be beyond specification limits. Cp Reject Rate1.000.270

19、 %1.330.007 %1.506.8 ppm2.002.0 ppbProcess Potential過程潛力一般地: Cp等于1.0代表該過程被判斷為有能力的.-比如,如果過程中心與規(guī)格中心重合,此時該過程有0.27%的產(chǎn)品出現(xiàn)在規(guī)格以外.供參考.a)b)c)a) Process is highly capable (Cp2)b) Process is capable (Cp=1 to 2)c) Process is not capable (Cp2)b)過程能力尚可(Cp=1 to 2)c)過程能力差(Cp1.5)b) Process is capable (Cpk=1 to 1.5)c

20、) Process is not capable (Cpk1)a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk 1.5)b)過程績效 一般(Cpk=1 to 1.5)c)過程績效差(Cpk1).Example 1例1Specification Limits規(guī)格界限:4 to 16 gMachine機器Mean平均值Std Dev標準偏差(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the corresponding Cp and Cpk for each machine.計算每一臺機器相應的Cp and Cpk .Examp

21、le 1A.Example 1B.Example 1C.Example 1D.Process Capability過程能力For a normally distributed characteristic, the defective rate F(x) may be estimated via the following:對于服從正態(tài)分布的特性,缺陷率F(x)可以通過下式求得For characteristics with only one specification limit:對于只存在單邊規(guī)格的特性,缺陷率計算如下:a)LSL onlyb)USL onlyLSLUSL.Example

22、2例2Specification Limits規(guī)格界限:4 to 16 gMachine機器Mean平均值Std Dev標準偏差(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the defective rate for each machine.試計算每一機器的不合格品率.Example 2Mean Std Dev ZLSL ZUSL F(xUSL) F(x) 10 4 -1.51.5 66,807 66,807133,614 10 2 -3.03.0 1,350 1,350 2,700 7 2 -1.54.5 66,807 3 66,811 13 1 -9

23、.03.0 0 1,350 1,350Lower Spec Limit= 4 gUpper Spec Limit= 16 g.Example 3Of 1000 components produced by a machine, 248 pieces are greater than 10.27 cm in length (customers specification). If the lengths of the components are normally distributed with a mean of 10.10 cm, what is the standard deviatio

24、n?在1000個同一機器生產(chǎn)的產(chǎn)品中,248個長度大于10.27cm(客戶規(guī)格), 如產(chǎn)品的長度是平均值為10.10cm,問其標準偏差是多少?.Process Potential vs Process Performance過程潛力和過程能力(a) Poor Process Potential (b) Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to center mean to reduce variation(a) 差的過程潛力( b) 差的過程

25、能力試驗設計降低變異試驗設計均值對中降低變異.Alternative Process Performance Index選擇性的工序表現(xiàn)指數(shù)Process capability statistics measure process variation relative to specification limits. 過程能力統(tǒng)計量用以測量過程輸出相對于規(guī)格界限的變異The Cp statistic compares the engineering tolerance against the processs natural variation.Cp統(tǒng)計量比較設計公差和過程自然變異.The C

26、pk statistic takes into account the location of the process relative to the midpoint between specifications. If the process target is not centered between specifications, the Cpm statistic is preferred.Cpk統(tǒng)計量考慮了過程位置相對于規(guī)格中心的變化.如果過程目標不是規(guī)格中心,選用Cpm統(tǒng)計量更適用.Process Stability過程穩(wěn)定性A process is stable if the

27、distribution of measurements made on the given feature is consistent over time.當一個過程的某個給定的特性在一段時間內測量結果的分布呈現(xiàn)一致的特性,則說該過程是穩(wěn)定的.TimeStable Process穩(wěn)定過程TimeUnstable Process不穩(wěn)定過程ucllclucllcl.Within vs Overall Capability短期和長期過程能力Within Capability (previously called short-term capability) shows the inherent v

28、ariability of a machine/process operating within a brief period of time.內部能力(又叫短期能力)代表了一個過程或設備在短期內的固有變異.Overall Capability (previously called long-term capability) shows the variability of a machine/process operating over a period of time. It includes sources of variation in addition to the short-te

29、rm variability.總體能力(又叫長期能力)代表了一個過程或設備在經(jīng)過長時間運行后的變異.它包含了除短期變異之外的變異來源.Within vs Overall Capability短期和長期過程能力WithinOverallSample Size 30 50 units 100 unitsNumber of Lots single lot several lotsPeriod of Time hours or daysweeks or monthsNumber of Operators single operatordifferent operatorsProcess Potenti

30、al Cp PpProcess Performance Cpk Ppk供參考.Within CapabilityOverall CapabilityThe key difference between the two sets of indices lies in the estimates for Within and Overall .評估內部能力和總體能力的主要區(qū)別在于評估所用的標準差有區(qū)別 within and overallWithin vs Overall Capability短期和長期過程能力.Estimating計算 Within and OverallConsider the

31、 following observations from a control chart:從一個控制圖中考慮以下觀測值: S/NX1X2 XkMeanRangeStd Dev1x1,1x2,1 xk,1 X1 R1 S12x1,2x2,2 xk,2 X2 R2 S2: : : : : : :mx1,mx2,m xk,m Xm Rm SmThe overall variation Overall is estimated by:總體標準差Overall 的估計可用以下公式.Estimating計算 Within and OverallThe within variation Within may

32、 be estimated by one ofthe following methods:內部標準差Overall 可按下列方法中的一種進行評價(a) R-bar Method R-bar 方法方法whered2 is a Shewhart constant = (k) 其中 d2 為常數(shù)(b) S-bar Method S-bar 方法wherec4 is a Shewhart constant = (k) 其中 c4 為常數(shù)(c) Pooled Standard Deviation Method普爾標準偏差方法In MiniTab, the Pooled Standard Deviatio

33、n is the default method.在MiniTab 中,pooled Standard Deviation 方法為默認方法.Estimating計算 Within and OverallIn cases where there is only 1 observation per sub-group(i.e. k=1), the Moving Range Method is used, where在子組容量為1時,使用移動極差方法(Moving Range Method), The within variation Within is then estimated using ei

34、ther短期標準差Within 可用下式中的一個計算the Average Moving Range :方法移動極差平均值the Median Moving Range : 移動極差中位數(shù):.Example 4例4The length of a camshaft for an automobile engine is specified at 600 2 mm. Control of the length of the camshaft is critical to avoid scrap/rework.The camshaft is provided by external supplier

35、s. Assess the process capability for this supplier.“The data is available in “01-03”. Data are collected in subgroups of 5 each.某汽車發(fā)動機的凸輪軸長度規(guī)格為6002mm.控制該長度可以避免報廢和返工,每個子組收集5個長度數(shù)據(jù),該軸由外部供應商供應,請評估該供應商的過程能力.數(shù)據(jù)存儲在“01-03”中.實際操作MiniTab.Example 例5Histogram of the camshaft length suggests mixed populations. F

36、urther investigation revealed that there are two suppliers for the camshaft. Data were now collected on camshafts from each source without combining both. Subgroup size is 5 for each supplier.Are the two suppliers similar in performance?If not, what are your recommendations?從直方圖上可看出軸的長度為幾個總體的混合數(shù)據(jù).進一

37、步調查顯示有兩個供應商向公司供應該凸輪軸.數(shù)據(jù)來源于兩家供應商的產(chǎn)品.該兩家供應商的過程能力相同嗎?如果不同,你推薦使用哪一家的產(chǎn)品?實際操作MiniTab.Example 5MiniTab:Stat Quality Tools Capability Sixpack(Normal).Example 5.Example 5.Motorola 的原始定義:如果規(guī)格界限至少離過程均值為6的距離,即Cp 2并且過程偏移小于1.5,即Cp 1.5那么過程缺陷率將小于3.4ppm.664.5什么是六西格瑪品質?-過去.Mikel J Harry 認為過程不同產(chǎn)品批之間的均值將發(fā)生變化平均變化量為1.5 注

38、意:Sigma 能力=f(dpmo)f(dppm)2什么是六西格瑪品質?-現(xiàn)在K=2+1.5K=2+1.5.Capability Analysis with Box-Cox TransformationBox-Cox轉化分析過程能力When the process data are not normal, the Cpk or Ppk indices are not accurate or reliable, because these indices are computed on the basis that the data are normally distributed. 當過程數(shù)據(jù)

39、是非正態(tài)的, 過程能力指數(shù)Cpk or Ppk 是不正確的或可信的,因為這些數(shù)據(jù)是假定數(shù)據(jù)是正態(tài)分布的基礎上.Dppm values associated with the indices will not be near to the actual performance when the normal curve does not model the actual data well.當正態(tài)曲線不能很好的符合實際數(shù)據(jù)時,和指數(shù)相關的DPPM 值不和實際表現(xiàn)相符.If the process data are somewhat bell-shaped but skewed, Box-Cox

40、transformation can be used to make the data normal before we assess the process capability.如果過程數(shù)據(jù)有些鐘型但歪斜的,在我們評估過程能力之前,Box-Cox轉化可幫助將數(shù)據(jù)轉化成正態(tài)Remember to transform the specification limits too before we compute Cpk or Ppk! 記住在計算過程能力指數(shù)前也要將規(guī)格界限進行轉化! Capability Analysis with Box-Cox TransformationBox-Cox轉化

41、分析過程能力.Minitab:Stat Quality Tools Capability Analysis (Normal)Capability Analysis with Box-Cox TransformationBox-Cox轉化分析過程能力.Example 例6Open the file named 01-04.MTW ,Compute the process capability with the specification limits:打開01-04文件,用規(guī)格界限計算過程能力(sample size=1)LSL: 0.1USL: 10Are the data normally

42、distributed?數(shù)據(jù)是正態(tài)分布嗎?Compute the process capability again with Box-Cox transformation.利用Box-Cox轉化計算過程能力Capability Analysis with Box-Cox TransformationBox-Cox轉化分析過程能力.Cpk of 0.41 is reported in the SSAT package. This value is not reliable or accurate if the data are not normal.Data is not normal數(shù)據(jù)不是正

43、態(tài)的Example 6Capability Analysis with Box-Cox TransformationBox-Cox轉化分析過程能力在SSAT 的Cpk 0.41. 如數(shù)據(jù)不是正態(tài)的,此數(shù)據(jù)不是可信的或不正確的.Example 6Cpk has increased from 0.41 to 0.81Capability Analysis with Box-Cox TransformationBox-Cox轉化分析過程能力計算值和此值會有差別.54Assuming Normality.假設正態(tài)USLZ is Normally distributed with Mean = 0 an

44、d SD = 1Z-值平均值為 “0” 標準偏差為 “1”的正態(tài)分布值.LSLZ scoreZ Scores Z-值.55ZLSL, ZUSLUSLLSLZLSLZUSL.多少s 過程USLZ-Score interpretation: How many standard deviations, s or s-hats, is the mean, x-bar, from some specified value, x.Z-值解釋:是一個到平均值有幾個標準偏差的的特定值Lets assume there is only an USL讓我們假設只有只有規(guī)格下限?s0.001ppmUSLTmA Si

45、x Sigma Process25,000ppmUSLTmA Two Sigma Process.Basic Instructions for MinitabComputing Standard Normal Probabilities計算標準正態(tài)概率的MiniTab基本操作.Select “Calc”, “Probability Distributions” and “Normal”.Select “Cumulative Probability”, enter the “Mean” and “Standard Deviation”, click on “Input constant”, en

46、ter the value and click on “OK”.Computing Percent FalloutCumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.8413.Minitab OutputUSL = 12Tm =11A One Sigma ProcessDPPM = (1-0.8413) x 1,000,000 = 158700Cumulative Distribution FunctionNormal

47、with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.8413.Computing Z-Score From Percent FalloutSelect “Inverse Cumulative probability”, set the “Mean” = 0 and “Standard Deviation” =1, click on “Input constant”, enter the total area associated with fallout and click on “OK”. p

48、= 0.8413Inverse Cumulative Distribution FunctionNormal with mean = 0 and standard deviation = 1.00000 P( X = x) x 0.8413 0.9998.s = 1LSL =9USL = 12Tm = 11Determine the DPPMZLSL, ZUSL and the Z scoreExercise.Select “Calc”, “Probability Distributions” and “Normal”.Select “Cumulative probability”, ente

49、r the “Mean” and “Standard Deviation”, click on “Input constant”, enter the value and click on “OK”.Cumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.8413Solution: Minitab.Select “Cumulative probability”, enter the “Mean” and “Standard

50、Deviation”, click on “Input constant”, enter the value and click on “OK”.Cumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 9.0000 0.0228DPPM =( (0.0228) +(1-0.8413) x 1,000,000 = 181500Solution: MinitabZLSL = (9 - 11) / 1.Select “Inverse Cumulati

51、ve probability”, set the “Mean” = 0 and “Standard Deviation” =1, click on “Input constant”, enter the total area associated with fallout and click on “OK”. p = 1-(0.0228) +(1-0.8413) = 1-0.1815 = 0.8185Inverse Cumulative Distribution FunctionNormal with mean = 0 and standard deviation = 1.00000 P( X

52、 = x) x 0.8185 0.9097Solution: Minitab.Process Capability for Non-Normal Data非正態(tài)的過程能力.Process Capability for Non-Normal Data非正態(tài)數(shù)據(jù)的過程能力Not every measured characteristic is normally distributed. Some data follows distributions that are known, and these may be able to have their capability measured acc

53、urately using that knowledge不是所有的測量參數(shù)都是正態(tài)分布的,一些數(shù)據(jù)分布已知,就可以準確地應用自己的過程能力分析方法去測量過程能力Characteristic參數(shù)Distribution分布Cycle Time循環(huán)時間Weibull (Exponential)威布爾(指數(shù))分布Reject Rate不合格率Binomial二項式分布Defect Rate缺陷率Poisson泊松分布.The Weibull Distribution is a general family of distribution with威布爾分布為一個常見的分布,用下式表示:wheresc

54、ale parameter is the value at which CDF=68.17%,andshape parameter determines the shape of the PDF.上式中, 尺度參數(shù)為CDF=68.17%時的值形狀參數(shù)確定了PDF的形狀Process Capability for Cycle Time周期時間的過程能力.At =1,the Weibull Distribution is reduced to當=1,威布爾分布可簡化為: For an Exponential Distribution,對指數(shù)分布,有The Exponential Distribut

55、ion is thus a Weibull Distribution with =1.指數(shù)分布為=1時的威布爾分布.Weibull (x; =1, )Exponential (x; )Process Capability for Cycle Time周期時間的過程能力.Example 4A customer service manager wants to determine the process capability for his department. A primary performance index is the time taken to close a customer c

56、omplaint. The goal for this index is to close a complaint within one calendar week.Performance over the last 400 complaints was reviewed.一位客戶服務經(jīng)理想確定他的部門過程能力,主要評價指標為處理客戶投訴的時間周期,目標為在一周內處理完一單客戶投訴,過去的400%次投訴作為測量數(shù)據(jù).數(shù)據(jù)在此期01-03 Days .Example 4Stat Quality Tools Capability Analysis (Weibull).Example 4.Examp

57、le 4AStat Quality Tools Capability Sixpack (Weibull).Example 4A.Alternatives for Non-Normal Data非正態(tài)數(shù)據(jù)解釋When all other methods fail, it may be necessary to fall back on a simple assessment of the total amount out of specifications. Simply count the number of defective units and divide by the total to

58、 compute the fraction defective. Another standard metric for this is the DPPM.當所有方法失敗,它需要返回到一個評估超出控制界限數(shù)量的簡單方法,簡單地查一下不合格品和全部產(chǎn)品的數(shù)量,然后計算不合格率, 另一個標準刻度也是DPPMIf a Capability Index must be reported, the DPPM can be converted back into a Z value, and then either Ppk = Z/3 or Cpk = Z/3 depending upon whether

59、 the data is long term or short term.如果要得到過程能力指數(shù),DPPM可以轉化為Z-值,然后根據(jù)此數(shù)據(jù)是長期或短期得PPK=Z/3 或Cpk = Z/3 .Process Capability for Reject Rate不合格率的過程能力For a Normal Distribution, the proportion of parts produced beyond a specification limit is對于一個正態(tài)分布,在控制界限下的比例部分.Reject Rate.Thus, for every reject rate there is

60、an accompanying Z-Score,這樣一來,對于每一個不合格率都有一個對應的Z-值Where這里Recall that原先Hence因此Process Capability for Reject Rate不合格率的過程能力.Estimation of Ppk for Reject Rate不合格率Ppk的計算:Determine the long-term reject rate (p)計算長期不合格率(p)Determine the inverse cumulative probability for p, using Calc Probability Distribution