【正文】 LSL)/3Precision精密度Capability準(zhǔn)確度83 Meanings of Cpk Measures Cpk 量測之意義量測之意義Cpk = negative numberCpk = zeroCpk = between 0 and 1Cpk = 1Cpk 184 Statistical Process Control – Identify and Reduce Process Variability統(tǒng)計製程管制統(tǒng)計製程管制 確認(rèn)並降低製程變異確認(rèn)並降低製程變異Lower specification limitUpper specification limit(a) Acceptance sampling(b) Statistical process control(c) cpk 185 Quality Control Approaches品質(zhì)管制方法品質(zhì)管制方法n Statistical process control (SPC)統(tǒng)計製程管制統(tǒng)計製程管制 n Monitors production process to prevent poor quality 監(jiān)控產(chǎn)品製程以預(yù)防不良品質(zhì)監(jiān)控產(chǎn)品製程以預(yù)防不良品質(zhì) n Acceptance sampling允收抽樣允收抽樣 n Inspects random sample of product or materials to determine if a lot is acceptable隨機抽樣檢驗產(chǎn)品或物料以決定此批是否隨機抽樣檢驗產(chǎn)品或物料以決定此批是否允收允收86 Sampling vs. Screening抽樣與篩選抽樣與篩選n Sampling抽樣抽樣 n When you inspect a subset of the population n 群體批中檢查小批群體批中檢查小批 n Screening n When you inspect the whole population n 群體批中檢查全數(shù)群體批中檢查全數(shù) n The costs consideration n 成本的考量成本的考量 ,經(jīng)濟(jì)的原則經(jīng)濟(jì)的原則Acceptance Sampling允收抽樣允收抽樣n Accept/reject entire lot based on sample results 整個允收整個允收 /拒收是樣品結(jié)果為基礎(chǔ)拒收是樣品結(jié)果為基礎(chǔ) n Not consistent with TQM of Zero Defects 與與 TQM的零缺點不同的零缺點不同 n Measures quality in percent defective 以缺點百分率測量品質(zhì)以缺點百分率測量品質(zhì)Sampling Plan抽樣計劃抽樣計劃n Guidelines for accepting lot允收批之指導(dǎo)作允收批之指導(dǎo)作業(yè)業(yè) n Single sampling plan單一抽樣計劃單一抽樣計劃n N = lot size批量批量 n n = sample size (random)樣本大小樣本大小n c = acceptance number允收數(shù)允收數(shù)n d = number of defective items in sample樣本不良項目之樣本不良項目之?dāng)?shù)目數(shù)目n If d = c, accept lot。Capable 168。 , Nominal value 800 1000 1200 HoursUpper specification Lower specificationProcess distribution(a) Process is capable78 Process Capability製程能力製程能力 Lower specificationMeanUpper specification Two sigma181。 6 consecutive points increasing or decreasing 168。 Establish regions A, B, and C as one, two, and three s 168。 Now it appears that shift 15 is outofcontrol. 168。 It appears that shifts 4, 7 and 12 were out of control. 168。 168。 They obtain the following data:67 168。 Upper Control Limit =UCLLCL60 Ex: Control “Commuting times” Step 1 Commuting Times (min.) .WEEKMinutesXbar =R =Step 2 Step 3X = R = 36 n = 5UCLL = X + A2*R = + (.58)*(36) = LCLL= X A2*R = = UCLR = D4*R = ()*() = LCLR = D3*R = 061 Control “Commuting times” (cont.)step 4 Commuting times .UCL = Xbarbar = LCL = Xbar Chart1 102 3 4 5 6 7 8 95010075R Chart UCL = Rbar = LCL = 01 102 3 4 5 6 7 8 97553562 Figurep Chart不良率管制圖不良率管制圖n Type of attributes control chart 計數(shù)管制圖計數(shù)管制圖 n Nominally scaled categorical data 以絕對資料分類以絕對資料分類 n ., goodbad 如好如好 ,壞壞 n Shows % of nonconforming items 顯示不合格項目顯示不合格項目 % n Example: Count defective chairs divide by total chairs inspected。 How can we tell if the variability is in control?59 RChart168。 XBar管制圖監(jiān)控中心管制圖監(jiān)控中心 (一旦一旦 R管制圖處於管制狀管制圖處於管制狀態(tài)態(tài) ):平均值於爭個製程是否穩(wěn)定平均值於爭個製程是否穩(wěn)定 ? Bring the Rchart under control, then look at the xbar chart(先看先看 R圖圖 ,再看再看 Xbar圖圖 ) 46 How to Construct a Control Chart如何建立管制圖如何建立管制圖 1. Take samples and measure 2. For each subgroup, calculate the sample average and range. 每個群組每個群組 ,計算平均值與全距計算平均值與全距 3. Set trial center line and control 圖之中心線與管制界限圖之中心線與管制界限 4. Plot the R chart. Remove outofcontrol points and revise control R圖圖 ,移除異常點移除異常點 ,再修正管制界再修正管制界限限 5. Plot xbar chart. Remove outofcontrol points and revise control R圖圖 ,移除異常點移除異常點 ,再修正管制界再修正管制界限限 6. Implement sample and plot points at standard intervals. Monitor the ,於標(biāo)準(zhǔn)間於標(biāo)準(zhǔn)間隔時間取樣隔時間取樣 ,監(jiān)控此管制圖監(jiān)控此管制圖 47 Type 1 and Type 2 Error第一種與第二種錯誤第一種與第二種錯誤 Alarm No AlarmInControl 管制內(nèi) OutofControl 失控 48 Common Tests to Determine if the Process is Out of Control管制圖異常之判定管制圖異常之判定 n One point outside of either control limit n 一點超出管制界線一點超出管制界線 n 2 out of 3 points beyond UCL 2 sigma n 3點有點有 2點在點在 2個標(biāo)準(zhǔn)差或以外個標(biāo)準(zhǔn)差或以外 n 7 successive points on same side of the central line n 連續(xù)連續(xù) 7點在中心線之同一側(cè)點在中心線之同一側(cè) n of 11 successive points, at least 10 on the same side of the central line n 連續(xù)連續(xù) 11點有點有 10點在中心線之同一側(cè)點在中心線之同一側(cè) n of 20 successive points, at least 16 on the same side of the central line n 連續(xù)連續(xù) 20點有點有 16點在中心線之同一側(cè)點在中心線之同一側(cè) 49 Type 1 Errors for these Tests 第一種錯誤第一種錯誤 Test Probability Type 1 Error2/37/710/1116/201/1 2() ()7 50 Type 2 Error第二種錯誤第二種錯誤 Suppose m1 m Type 2 Error = where F(z) denotes the the cumulative probability of a standard normal variate at z ? Power = 1 Type 2 Error. Power increases as … n increases, as (m1m) increases, and as s decreases. ? Extension to m1 m is straightforward51 `X Chart Control LimitsSample Range at Time i SamplesSample Mean at Time iFrom Table52 Factors for Computing Control Chart Limits管制圖之係數(shù)表管制圖之係數(shù)表TableR Chart全距管制圖全距管制圖 n Type of variables control chart計量管制圖計量管制圖 n Interval or ratio scaled numerical data n 間距或比率量測數(shù)字資料間距或比率量測數(shù)字資料 n Shows sample ranges over time n Difference between smallest largest values in inspection sample樣本中最大值與最小值之差樣本中最大值與最小值之差 n Monitors variability in process間控製程變異性間控製程變異性 n Example: Calculate Range of samples of solder paste。 Plot 如計算錫膏厚度之平均值如計算錫膏厚度之平均值 ,再點圖再點圖43 Basic Probabilities Concerning the Distribution of Sample Means有關(guān)樣本平均數(shù)之機率分佈有關(guān)樣本平均數(shù)之機率分佈 Std. dev. of the sample means 樣本平均數(shù)標(biāo)準(zhǔn)差 : 44 Estimation of Mean and Std. Dev. of the Underlying Process在製程控制之下之平均值與標(biāo)準(zhǔn)差估計在製程控制之下之平均值與標(biāo)準(zhǔn)差估計 n use historical data taken from the process when it was “known” to be in control 當(dāng)製程穩(wěn)定時當(dāng)製程穩(wěn)定時 ,利用過去所產(chǎn)生之歷史資料利用過去所產(chǎn)生之歷史資料 n usually data is in the form of samples