工程方法_6sigma_09工序能力分析

1、1流程圖流程圖(Process mapping)C&E矩陣初步分析可能因子矩陣初步分析可能因子FMEA進(jìn)一步分析可能因子進(jìn)一步分析可能因子測(cè)量系統(tǒng)定義測(cè)量系統(tǒng)定義,MSAY 的穩(wěn)定性判定的穩(wěn)定性判定,過(guò)程能力分析過(guò)程能力分析二次二次FMEA可能因子總結(jié)可能因子總結(jié)分析階段分析階段定義階段定義階段魚(yú)骨圖魚(yú)骨圖(Fishbone)21. Process Control vs Process Capability 2. 過(guò)程控制和過(guò)程能力3. Process Capability過(guò)程能力:Specification, Process and Control Limits.規(guī)格,過(guò)程和控制界限

2、Process Potential vs Process Performance過(guò)程潛在的和實(shí)際的表現(xiàn)4. Short-Term vs Long-Term Process Capability5. 短期和長(zhǎng)期過(guò)程能力6. “Six Sigma” Quality ; “ 6Sigma”水平; 7. Introduction to Z-score Z-值介紹8. Process Capability for Non-Normal Data非正態(tài)分布的過(guò)程能力 Cycle-Time (Exponential Distribution)循環(huán)時(shí)間(指數(shù)分布) Reject Rate (Binomial

3、Distribution)不合格(剔除)率(二項(xiàng)式分布) Defect Rate (Poisson Distribution)缺陷率缺陷率(泊松分布泊松分布)31. Process Control過(guò)過(guò)程控制程控制Means the process is operating in statistical control, i.e. common causes are the only source of variation.意味是過(guò)程在穩(wěn)定狀態(tài)下生產(chǎn),也就是說(shuō), 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(guò)程的聲音”,也就是說(shuō),唯一來(lái)源于過(guò)程的數(shù)據(jù)來(lái)判定過(guò)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(shí)間過(guò)去,反饋過(guò)程的表現(xiàn)來(lái)驗(yàn)證它是否來(lái)自

5、于一個(gè)穩(wěn)定的分布,一般地,利用從過(guò)程數(shù)據(jù)計(jì)算控制界限的控制圖來(lái)完成.Just because a process is in control does not necessarily mean it is a good process.僅僅因?yàn)檫^(guò)程受控并不一定說(shuō)它是個(gè)好過(guò)程.42. Process Capability過(guò)過(guò)程能力程能力The “goodness” of a process is measured by process capability過(guò)程的 “好壞”是過(guò)程能力測(cè)量的Compares “voice of the process” with “voice of the cust

6、omer”, which is given in terms of specs. or requirements比較 “過(guò)程聲音”和 “客戶聲音”,哪一個(gè)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(cè)量一個(gè)穩(wěn)定的分布(過(guò)程受控)符合客戶規(guī)格的程度.首先判定過(guò)程穩(wěn)定首先判定過(guò)程穩(wěn)定,確定數(shù)據(jù)分布是正態(tài)的確定數(shù)據(jù)分布是正態(tài)的,再計(jì)算過(guò)程能力和西格碼質(zhì)量水平再計(jì)算過(guò)程能力和西格碼質(zhì)量水平.5When process is under c

7、ontrol, 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(guò)程在受控狀態(tài)下時(shí),客戶要求與過(guò)程表現(xiàn)(產(chǎn)品品質(zhì)或服務(wù)的品質(zhì)變動(dòng)程度)的比值, 如果過(guò)程表現(xiàn)越能滿足客戶要求,則過(guò)程能力越充分,反之則不足.LSLUSL6Process Capability studie

8、s can過(guò)程能力研究可以: indicate the consistency of the process output顯示過(guò)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(guò)程或竟?fàn)帉?duì)手相比較7Process Variation is the inevitable differences among individual measurements or unit

9、s produced by a process.過(guò)程變異是不可避免的差別在單個(gè)測(cè)量或過(guò)程生產(chǎn)單位之間.Sources of Variation變異的來(lái)源: within unit 產(chǎn)品內(nèi) (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 生產(chǎn)線之間(line-line variation) 線-線之間的變異 across time 不同時(shí)間 (time-time vari

10、ation) 時(shí)間-時(shí)間的變異 measurement error 測(cè)量誤差(repeatability & reproducibility) 重復(fù)性和再現(xiàn)性81. Positional Variation位置變異Same process, variation at differing locations simultaneously: 相同的過(guò)程,隨不同位置而產(chǎn)生的變異Temperature variations inside a thermal chamber溫度變異在一個(gè)烘箱中Cavity-to-cavity variations in an injection mold洞坑差別

11、在一個(gè)注塑模中2. Cyclical Variation重復(fù)誤差Sequential repetitions of a process over fairly short time, say, less than 15 mins: 在一定短的時(shí)間內(nèi)某過(guò)程的連續(xù)重復(fù),比方說(shuō), 少于15分鐘:Variations between consecutive batches of a process同一過(guò)程的連續(xù)批次之間的變異Differences from lot to lot of raw materials不同批次原材料之間的差別3. Temporal Variation時(shí)間的變異Variatio

12、ns over longer periods of time, such a several hours, days or weeks. 長(zhǎng)期的變異, 例如幾個(gè)小時(shí),幾天或幾個(gè)星期.9Inherent 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(jié)果A process operating with only chance causes of variation present is said to be “in statist

13、ical control” 如果一個(gè)過(guò)程運(yùn)行時(shí)只存在固有原因變異的作用,就說(shuō)它處在“統(tǒng)計(jì)控制狀態(tài)”.一般原因一般原因10Special or Assignable Variation特殊的可特殊的可查查明的明的變變異異May be due to可能歸因與 : a) improperly adjusted machine 不正確的調(diào)機(jī) b) operator error 員工錯(cuò)誤 c) defective raw material 有缺陷的原材料A process operating in the presence of assignable causes of variation is sai

14、d to be “out-of-control”.如果一個(gè)過(guò)程運(yùn)行時(shí)存在可指出原因變異,則稱該過(guò)程“失控異常原因異常原因11a)b)c)a) Process is highly capableb) Process is marginally capablec) Process is not capablea)過(guò)程能力高b)過(guò)程能力一般c)過(guò)程能力差12Specification Limits (LSL and USL) created by design engineering in response to customer requirements to specify the tolera

15、nce for a products characteristicProcess Limits (LPL and UPL)measures the variation of a processthe natural 6 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(shè)計(jì)工程部門(mén)根據(jù)客戶要求確定的產(chǎn)品性能公差。過(guò)程界限(L

16、PL and UPL) 用來(lái)測(cè)量過(guò)程的變異為所測(cè)量特性的自然公差(六倍標(biāo)準(zhǔn)差(6)界限控制界限(LCL and UCL)用來(lái)測(cè)量樣本統(tǒng)計(jì)量的變異(均值，方差比例等)13Distribution ofIndividual Values (x)Distribution ofSample Averages (x) 單值分布樣本均值分布14Two measures of process capability:過(guò)程能力的兩種測(cè)量Process Potential過(guò)程潛力CpProcess Performance過(guò)程表現(xiàn)CpuCplCpk15The Cp index assesses whether th

17、e natural tolerance (6) of a process is within the specification limits. 工序能力指數(shù)Cp用以評(píng)價(jià)是否一個(gè)過(guò)程的自然公差(6)處于規(guī)格界限以內(nèi).6LSLUSLToleranceNaturalTolerancegEngineerinCp6LSLUSLCp自然公差工程公差16Traditionally, a Cp of 1.0 indicates that a process is judged to be “capable”.if the process is centered within its engineering

18、tolerance, 0.27% of parts produced will be beyond specification limits. Cp Reject Rate1.000.270 %1.330.007 %1.506.8 ppm2.002.0 ppb一般地: Cp等于1.0代表該過(guò)程被判斷為有能力的.-比如,如果過(guò)程中心與規(guī)格中心重合,此時(shí)該過(guò)程有0.27%的產(chǎn)品出現(xiàn)在規(guī)格以外.供參考供參考17a)b)c)a) Process is highly capable (Cp2)b) Process is capable (Cp=1 to 2)c) Process is not capab

19、le (Cp2)b)過(guò)程能力尚可(Cp=1 to 2)c)過(guò)程能力差(Cp1.5)b) Process is capable (Cpk=1 to 1.5)c) Process is not capable (Cpk1)a)Cp = 2Cpk = 2b)Cp = 2Cpk = 1c)Cp = 2Cpk 1.5)b)過(guò)程績(jī)效 一般(Cpk=1 to 1.5)c)過(guò)程績(jī)效差(Cpk1)22Specification Limits規(guī)格界限:4 to 16 gMachine機(jī)器Mean平均值Std Dev標(biāo)準(zhǔn)偏差(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the c

20、orresponding Cp and Cpk for each machine.計(jì)算每一臺(tái)機(jī)器相應(yīng)的Cp and Cpk 23 5 . 0464166LSLUSLCp 5 . 043410;431016Min3LSL;3USLMinCpk24 0 . 1264166LSLUSLCp 0 . 123410;231016Min3LSL;3USLMinCpk25 0 . 1264166LSLUSLCp 5 . 02347;23716Min3LSL;3USLMinCpk26 0 . 2164166LSLUSLCp 0 . 113413;131316Min3LSL;3USLMinCpk27For a

21、normally distributed characteristic, the defective rate F(x) may be estimated via the following:對(duì)于服從正態(tài)分布的特性,缺陷率F(x)可以通過(guò)下式求得For characteristics with only one specification limit:對(duì)于只存在單邊規(guī)格的特性,缺陷率計(jì)算如下:a)LSL onlyb)USL only USLxPrLSLxPrxFUSL1LSLUSLLSLZ1ZLSLUSL LSLZLSLxPrxF USLZ1USLxPrxF28Specification Li

22、mits規(guī)格界限:4 to 16 gMachine機(jī)器Mean平均值Std Dev標(biāo)準(zhǔn)偏差(a) 10 4(b) 10 2(c) 7 2(d) 13 1Determine the defective rate for each machine.試計(jì)算每一機(jī)器的不合格品率29Mean 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 -9.03.0 0 1,350 1,350Lower Sp

23、ec Limit = 4 gUpper Spec Limit = 16 g30Of 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 deviation?在1000個(gè)同一機(jī)器生產(chǎn)的產(chǎn)品中,248個(gè)長(zhǎng)度大于10.27c

24、m(客戶規(guī)格), 如產(chǎn)品的長(zhǎng)度是平均值為10.10cm,問(wèn)其標(biāo)準(zhǔn)偏差是多少?31(a) Poor Process Potential (b) Poor Process PerformanceLSLUSLLSLUSLExperimental Design to reduce variationExperimental Design to center mean to reduce variation(a) 差的過(guò)程潛力( b) 差的過(guò)程能力試驗(yàn)設(shè)計(jì)降低變異試驗(yàn)設(shè)計(jì)均值對(duì)中降低變異322ppmT1CCProcess capability statistics measure process var

25、iation relative to specification limits. 過(guò)程能力統(tǒng)計(jì)量用以測(cè)量過(guò)程輸出相對(duì)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(jì)量比較設(shè)計(jì)公差和過(guò)程自然變異.The Cpk statistic takes into account the location of the process relative to the midpoint between specifications. If the pro

26、cess target is not centered between specifications, the Cpm statistic is preferred.Cpk統(tǒng)計(jì)量考慮了過(guò)程位置相對(duì)于規(guī)格中心的變化.如果過(guò)程目標(biāo)不是規(guī)格中心,選用Cpm統(tǒng)計(jì)量更適用33A process is stable if the distribution of measurements made on the given feature is consistent over time.當(dāng)一個(gè)過(guò)程的某個(gè)給定的特性在一段時(shí)間內(nèi)測(cè)量結(jié)果的分布呈現(xiàn)一致的特性,則說(shuō)該過(guò)程是穩(wěn)定的.TimeStable Proces

27、s穩(wěn)定過(guò)程TimeUnstable Process不穩(wěn)定過(guò)程ucllclucllcl34Within Capability (previously called short-term capability) shows the inherent variability of a machine/process operating within a brief period of time.內(nèi)部能力(又叫短期能力)代表了一個(gè)過(guò)程或設(shè)備在短期內(nèi)的固有變異.Overall Capability (previously called long-term capability) shows the va

28、riability of a machine/process operating over a period of time. It includes sources of variation in addition to the short-term variability.總體能力(又叫長(zhǎng)期能力)代表了一個(gè)過(guò)程或設(shè)備在經(jīng)過(guò)長(zhǎng)時(shí)間運(yùn)行后的變異.它包含了除短期變異之外的變異來(lái)源.35WithinOverallSample Size 30 50 units 100 unitsNumber of Lots single lot several lotsPeriod of Time hours or

29、 daysweeks or monthsNumber of Operators single operatordifferent operatorsProcess Potential Cp PpProcess Performance Cpk Ppk內(nèi)容總體樣本容量30-50個(gè)100個(gè) 批數(shù)單批多批時(shí)間周期數(shù)小時(shí)數(shù)天數(shù)周到數(shù)月作業(yè)人數(shù)單個(gè)作業(yè)員多個(gè)作業(yè)員過(guò)程潛力CpPp過(guò)程能力CpkPpk供參考供參考36Within CapabilityOverall CapabilityThe key difference between the two sets of indices lies in the

30、 estimates for Within and Overall .評(píng)估內(nèi)部能力和總體能力的主要區(qū)別在于評(píng)估所用的標(biāo)準(zhǔn)差有區(qū)別 within and overallWithinp6LSLUSLCWithinpl3LSLCWithinpu3USLCWithinpk3NSLCOverallp6LSLUSLPOverallpl3LSLPOverallpu3USLPOverallpk3NSLP37Consider the following observations from a control chart:從一個(gè)控制圖中考慮以下觀測(cè)值: S/NX1X2 XkMeanRangeStd Dev1x1,

31、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(biāo)準(zhǔn)差Overall 的估計(jì)可用以下公式1nxxc11nxc12m1ik1jij42m1ik1jij4Overall 38The within variation Within may be estimated by one ofthe following methods:內(nèi)部標(biāo)準(zhǔn)差Overall 可按下列方法中的一種進(jìn)行評(píng)價(jià)(a) R-bar

32、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(biāo)準(zhǔn)偏差方法In MiniTab, the Pooled Standard Deviation is the default method.在MiniTab 中,pooled Standard Deviation 方法為默認(rèn)方法.2WithindR4Wit

33、hincS 1n1n1nS1nS1nS1nc1m212mm2222114Within39In 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(shí),使用移動(dòng)極差方法(Moving Range Method), The within variation Within is then estimated using either短期標(biāo)準(zhǔn)差 Within 可用下式中的一個(gè)可用下式中的一個(gè)計(jì)計(jì)算算a) the Average Movi

34、ng Range :方法移動(dòng)極差平均值b) the Median Moving Range : 移動(dòng)極差中位數(shù):1iiiXXMR2WithindMR2WithindMR40The 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 suppliers. Assess the process

35、 capability for this supplier.“The data is available in “01-03”. Data are collected in subgroups of 5 each.某汽車(chē)發(fā)動(dòng)機(jī)的凸輪軸長(zhǎng)度規(guī)格為6002mm.控制該長(zhǎng)度可以避免報(bào)廢和返工,每個(gè)子組收集5個(gè)長(zhǎng)度數(shù)據(jù),該軸由外部供應(yīng)商供應(yīng),請(qǐng)?jiān)u估該供應(yīng)商的過(guò)程能力.數(shù)據(jù)存儲(chǔ)在“01-03”中.實(shí)際操作實(shí)際操作MiniTab41Histogram of the camshaft length suggests mixed populations. Further investigation revea

36、led 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(zhǎng)度為幾個(gè)總體的混合數(shù)據(jù).進(jìn)一步調(diào)查顯示有兩個(gè)供應(yīng)商向公司供應(yīng)該凸輪軸.數(shù)據(jù)來(lái)源于

37、兩家供應(yīng)商的產(chǎn)品.該兩家供應(yīng)商的過(guò)程能力相同嗎?如果不同,你推薦使用哪一家的產(chǎn)品?實(shí)際操作實(shí)際操作MiniTab42MiniTab:Stat Quality Tools Capability Sixpack(Normal)4320100600.5600.0599.5599.0Xbar and R ChartSubgrMeanMean=599.5UCL=600.3LCL=598.83210RangeR=1.341UCL=2.835LCL=020100Last 20 Subgroups601600599598Subgroup NumberValues602T598Capability PlotPr

38、ocess ToleranceIIIIIIIIISpecificationsWithinOverall601.0599.5598.0Normal Prob Plot601.0599.5598.0Capability HistogramWithinStDev:Cp:Cpk:0.5764291.160.90OverallStDev:Pp:Ppk:Cpm:0.6208651.070.830.87Process Capability for Camshaft Length (Supplier A)4420100604602600598Xbar and R ChartSubgrMean11Mean=60

39、0.2UCL=602.5LCL=598.07.55.02.50.0RangeR=3.890UCL=8.225LCL=020100Last 20 Subgroups603.5601.0598.5596.0Subgroup NumberValues602598Capability PlotProcess ToleranceIIIIIIIISpecificationsWithinOverall605600595Normal Prob Plot605600595Capability HistogramWithinStDev:Cp:Cpk:1.672310.400.35OverallStDev:Pp:P

40、pk:1.878610.350.31Process Capability for Camshaft Length (Supplier B)45Motorola 的原始定義:如果規(guī)格界限至少離過(guò)程均值為6的距離,即Cp 2并且過(guò)程偏移小于1.5,即Cp 1.5那么過(guò)程缺陷率將小于3.4ppm.664.5什么是六西格瑪品質(zhì)?-過(guò)去46Mikel J Harry 認(rèn)為過(guò)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 注意:Sigma 能力=f(dpmo)f(dppm)2什么是六西格瑪品質(zhì)?-現(xiàn)在K=2+1.5K=2+1.547When the process data are not norma

41、l, 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(dāng)過(guò)程數(shù)據(jù)是非正態(tài)的, 過(guò)程能力指數(shù)Cpk or Ppk 是不正確的或可信的,因?yàn)檫@些數(shù)據(jù)是假定數(shù)據(jù)是正態(tài)分布的基礎(chǔ)上.Dppm values associated with the indices will not be near to the actual performance when the norm

42、al curve does not model the actual data well.當(dāng)正態(tài)曲線不能很好的符合實(shí)際數(shù)據(jù)時(shí),和指數(shù)相關(guān)的DPPM 值不和實(shí)際表現(xiàn)相符.48If the process data are somewhat bell-shaped but skewed, Box-Cox transformation can be used to make the data normal before we assess the process capability.如果過(guò)程數(shù)據(jù)有些鐘型但歪斜的,在我們?cè)u(píng)估過(guò)程能力之前,Box-Cox轉(zhuǎn)化可幫助將數(shù)據(jù)轉(zhuǎn)化成正態(tài)Remember to

43、 transform the specification limits too before we compute Cpk or Ppk! 記住在計(jì)算過(guò)程能力指數(shù)前也要將規(guī)格界限進(jìn)行轉(zhuǎn)化! 49Minitab:Stat Quality Tools Capability Analysis (Normal)50Example 例例6Open the file named 01-04.MTW ,Compute the process capability with the specification limits:打開(kāi)01-04文件,用規(guī)格界限計(jì)算過(guò)程能力(sample size=1)LSL: 0.

44、1USL: 10Are the data normally 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(zhuǎn)化計(jì)算過(guò)程能力511086420-2USLLSLProcess Capability Analysis for DimensionPPM TotalPPM USLPPM USLPPM USLPPM USLPPM USLPPM USLPPM LSLPpkPPLPPUPpCpmCpkCPLCPUCpStDev (Overall)StDev (With

45、in)Sample NMeanLSLTargetUSL12352.05 1486.4110865.64 8685.19 876.04 7809.1510000.00 0.0010000.000.770.770.990.88 *0.810.811.040.920.09904330.09401751000.999990.77268 *1.29420Exp. Overall PerformanceExp. Within PerformanceObserved PerformanceOverall CapabilityPotential (Within) CapabilityProcess DataW

46、ithinOverallCpk has increased from 0.41 to 0.81計(jì)算值和此值會(huì)有差別計(jì)算值和此值會(huì)有差別5354Assuming Normality.假設(shè)正態(tài)假設(shè)正態(tài)sxXZUSLpsxUSLZsxLSLPsxUSLsxXsxLSLPUSLXLSLPpzZPUSLXPZ is Normally distributed with Mean = 0 and SD = 1Z-值平均值為 “0” 標(biāo)準(zhǔn)偏差為 “1”的正態(tài)分布值.LSLLSLXPZ score55USLpsxUSLZsxLSLPsxUSLsxXsxLSLPUSLXLSLPUSLXPLSLLSLXPZLSLZ

47、USLUSLsxUSLscoreZZ-Score interpretation: How many standard deviations, s or s-hats, is the mean, x-bar, from some specified value, x.Z-值解釋值解釋:是一個(gè)到平均值有幾個(gè)標(biāo)準(zhǔn)偏差的的特定值是一個(gè)到平均值有幾個(gè)標(biāo)準(zhǔn)偏差的的特定值xLets assume there is only an USL讓我們假設(shè)只有只有規(guī)格下限?s0.001ppmUSLTA Six Sigma Process25,000ppmUSLTA Two Sigma Process57 Select

48、 “Calc”, “Probability Distributions” and “Normal”. Select “Cumulative Probability”, enter 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

49、0.84131587. 08413. 011USLXPUSLXP58USL = 12T 11A One Sigma ProcessDPPM = (1-0.8413) x 1,000,000 = 15870011 11-12 sxUSLsxxZscoreZUSLCumulative Distribution FunctionNormal with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.841359 Select “Inverse Cumulative probability”, set the

50、“Mean” = 0 and “Standard Deviation” =1, click on “Input constant”, enter the total area associated with fallout and click on “OK”. p = 0.84139998. 08413. 09998. 08413. 0scoreZZPzZPInverse Cumulative Distribution FunctionNormal with mean = 0 and standard deviation = 1.00000 P( X = x) x 0.8413 0.99986

51、0 1LSL =9USL = 12T 11Determine the DPPMZLSL, ZUSL and the Z score61 Select “Calc”, “Probability Distributions” and “Normal”. Select “Cumulative probability”, enter the “Mean” and “Standard Deviation”, click on “Input constant”, enter the value and click on “OK”.Cumulative Distribution FunctionNormal

52、 with mean = 11.0000 and standard deviation = 1.00000 x P( X = x) 12.0000 0.841311 11-12 sxUSLsxxZUSL62 Select “Cumulative probability”, enter the “Mean” and “Standard Deviation”, click on “Input constant”, enter the value and click on “OK”.Cumulative Distribution FunctionNormal with mean = 11.0000

53、and standard deviation = 1.00000 x P( X = x) 9.0000 0.0228DPPM =( (0.0228) +(1-0.8413) x 1,000,000 = 181500ZLSL = (9 - 11) / 163 Select “Inverse Cumulative probability”, set the “Mean” = 0 and “Standard Deviation” =1, click on “Input constant”, enter the total area associated with fallout and click

54、on “OK”. p = 1-(0.0228) +(1-0.8413) = 1-0.1815 = 0.81859097. 08185. 09097. 08185. 0scoreZZPzZPInverse Cumulative Distribution FunctionNormal with mean = 0 and standard deviation = 1.00000 P( X USLPPM USLPPM LSLPpkPPLPPUPpScaleShapeSample NMeanLSLTargetUSL122970.80122970.80 * 75000.00 75000.00 *0.39

55、*0.39 *3.341.004003.34 * *7.00Expected LT PerformanceObserved LT PerformanceOverall (LT) CapabilityProcess Data71Stat Quality Tools Capability Sixpack (Weibull)724003002001000241680Individual and MR ChartObser.Individual ValueMean=3.34UCL=10.46LCL=-3.779241680Mov.RangeR=2.677UCL=8.746LCL=0400390380L

56、ast 25 Observations9630Observation NumberValues7Overall (LT)Shape: 1.00Scale: 3.34Pp: *Ppk: 0.39Capability PlotProcess ToleranceSpecificationsIIII10.001.000.100.01Weibull Prob Plot20100Capability HistogramProcess Capability for Complaint Closure73When all other methods fail, it may be necessary to f

57、all 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 compute the fraction defective. Another standard metric for this is the DPPM.當(dāng)所有方法失敗,它需要返回到一個(gè)評(píng)估超出控制界限數(shù)量的簡(jiǎn)單方法,簡(jiǎn)單地查一下不合格品和全部產(chǎn)品的數(shù)量,然后計(jì)算不合格率, 另一個(gè)標(biāo)準(zhǔn)刻度也是DPPMIf a

58、 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 the data is long term or short term.如果要得到過(guò)程能力指數(shù),DPPM可以轉(zhuǎn)化為Z-值,然后根據(jù)此數(shù)據(jù)是長(zhǎng)期或短期得PPK=Z/3 或Cpk = Z/3 74For a Normal Distribution, the proportion of parts produced

59、 beyond a specification limit is對(duì)于一個(gè)正態(tài)分布,在控制界限下的比例部分. )Z(F1USLZPr1USLZPrUSLXPrReject Rate75Thus, for every reject rate there is an accompanying Z-Score,這樣一來(lái),對(duì)于每一個(gè)不合格率都有一個(gè)對(duì)應(yīng)的Z-值Where這里Recall that原先Hence因此3,3USLLSLMinPpkLimitSpecScoreZ3ScoreZPpk76Estimation of Ppk for Reject Rate不合格率不合格率Ppk的計(jì)算的計(jì)算:Dete

60、rmine the long-term reject rate (p)計(jì)算長(zhǎng)期不合格率(p)Determine the inverse cumulative probability for p, using Calc Probability Distribution Normal計(jì)算相反的累計(jì)概率p, 點(diǎn)擊 Calc Probability Distribution NormalZ-Score is the magnitude of the returned valueZ-值是反推值的多少.Ppk is one-third of the Z-ScorePpk 是 Z-值的三分之一.77A sales mana