1、OutlinenMinitab功能及視窗介紹n如何繪製圖表n如何分析資料n圖表及分析資料結果的解讀Minitab 功能選單列功能選單列nFile：開啟專案(project)、開啟工作單(worksheet)、匯入外部資 料檔案等等。nEdit：編輯指令如複製、貼上。nData：資料處理相關指令選單。nCalc：數學運算及機率運算相關選單。nStat：統計方法選單。nGraph：各種繪圖選單。nEditor：依目前活動視窗而定之編輯相關指令選單。nTools：工具選單，如 Microsoft Calculator、Notepad等等。nWindows：視窗呈現方式相關的選單。nHelp：只要稍微
2、了解 MINITAB 的作業環境後，就可利用Help 來幫你達成任務。Minitab 視窗類型視窗類型Graph Window圖形視窗圖形視窗 Worksheet資料視窗資料視窗Session Window作業作業(資料輸出資料輸出)視窗視窗Project Manager 專案管理視窗專案管理視窗專案管理視窗專案管理視窗n會話(Session)資料夾：列出專案所有執行統計分析過程，及所使用資料來自那一工件單(.MTW)n繪圖(Graph)資料夾：列出專案所有顯示在繪圖視窗中的統計圖n歷史(History)資料夾：列出專案所有執行過的統計分析指令n報告板(ReportPad)資料夾：將圖表與會話
3、窗之輸出結果存於此處，以利爾後在 Word進行編輯。工作單資料格式工具列工具列nMINITAB 標準工具列 n提供常用指令的捷徑 n活動視窗改變帶來標準工具列按鈕的改變以反映各視窗的功能n把滑鼠指向按鈕，會顯現其簡單功能描述 n專案管理工具列 n提供到達專案管理各檔案的捷徑 n專案管理工具列按鈕不會隨MINITAB的活動視窗而改變 Minitab視窗：資料視窗視窗：資料視窗n在 MINTAB中輸入資料時，程式會把資料讀爲三種格式之一：(1)數值(2)文字(3)日期/時間行的名稱列行的名稱列列的名稱行位於工作單的第一行上方，可輸入中文字型資料登錄箭頭資料登錄箭頭在行號列的最上方有一個資料登錄箭頭
4、，顯示按鍵入鍵後游標移動的方向Minitab視窗：資料視窗（續）視窗：資料視窗（續）n以下資料視窗顯示三個欄位為不同的資料格式文字日期數值File功能列功能列n開啟新檔n開啟舊檔(*.MPJ*.MTW)n儲存檔案n利用資料庫輸入資料檔 與Minitab相容的檔案格式lExcel(xls,xml)lDatabase(DBF)lText(txt,csv,dat)l其他lODBC協定建立表單資料建立表單資料n直接鍵入資料表 n由外部匯入 Minitab:FileOpen Worksheet 在檔案類型在檔案類型 中，選擇 Excel(*.xls)選擇 DATA.xls 選擇 Open 按 開啟開啟(
5、O)確認遺漏值確認遺漏值n查看資料欄是否有長不等遺漏值的情形，避免分析時出現錯誤訊息。n按Project Manager的工具列上的按鈕遺漏值遺漏值數數資料長度資料長度資料堆疊資料堆疊n所有的分析均可用堆疊的資料來執行(也就是利用堆疊資料在 MINITAB 中進行分析一定沒有問題)。Minitab:Data StackColumns12345以圖表表示資料以圖表表示資料Graph功能列功能列確定兩變數間的關係：散佈圖、矩陣圖、邊際圖確認分配：直方圖、點圖、莖葉圖、機率圖、經驗累積分配函數、箱形圖比較變數總結或變數的個別值：箱形圖、區間圖、個別值圖、直條圖、圓形圖確認計數值分配：直條圖、圓形圖描
6、繪資料經過時間的序列：時間序列圖、區域圖、散佈圖確定3個變數間的關係：等高線圖、3D散佈圖、3D曲面圖繪製散佈圖（一）繪製散佈圖（一）Minitab:Graph Scatterplot Simple123外 徑 變 化 量PTF1.21.11.00.90.80.70.654535251504948474645Scatterplot of PTF vs 外徑變化量圖形視窗輸出結果圖形視窗輸出結果繪製散佈圖（二）繪製散佈圖（二）Minitab:Graph Scatterplot With Groups 1234外 徑 變 化 量PTF1.21.11.00.90.80.70.654535251504
7、948474645C3ASTM1ASTM2Scatterplot of PTF vs 外徑變化量圖形視窗輸出結果圖形視窗輸出結果(依群組依群組)繪製直方圖（一）繪製直方圖（一）Minitab:Graph Histogram Simple12ASTM1Frequency6260585654522520151050Histogram of ASTM1圖形視窗輸出結果圖形視窗輸出結果繪製直方圖（二）繪製直方圖（二）Minitab:Graph Histogram With Fit12ASTM1Frequency6260585654522520151050Mean54.98StDev1.940N73Hi
8、stogram of ASTM1Normal 圖形視窗輸出結果圖形視窗輸出結果(配適線配適線)繪製直方圖（三）繪製直方圖（三）Minitab:Graph Histogram With Fit and Groups123圖形視窗輸出結果圖形視窗輸出結果PTF-1Frequency63605754514820151050Mean StDevN54.981.940 7350.761.391 73MethodASTM1ASTM2Histogram of PTF-1Normal 繪製盒形圖（一）繪製盒形圖（一）Minitab:Graph Boxplot One Y,Simple12ASTM1646260
9、5856545250Boxplot of ASTM1圖形視窗輸出結果圖形視窗輸出結果繪製盒形圖（二）繪製盒形圖（二）Minitab:Graph Boxplot One Y,With Groups123MethodPTF-1ASTM2ASTM16560555045Boxplot of PTF-1 vs Method圖形視窗輸出結果圖形視窗輸出結果若盒形圖的部份無重疊，則若盒形圖的部份無重疊，則 X 變動對變動對 Y 有強相關有強相關離群值Max=Q3+1.5IQRMin=Q1-1.5IQR分析資料分析資料顯示敍述統計顯示敍述統計Minitab:Stat Basic Statistics Disp
10、lay Descriptive Statistics12345作業視窗輸出結果作業視窗輸出結果圖形視窗輸出結果圖形視窗輸出結果PTF-1Frequency636057545148302520151050636057545148ASTM1ASTM2Histogram of PTF-1 by MethodPanel variable:MethodPTF-1Frequency636057545148302520151050636057545148ASTM1ASTM2ASTM150.76StDev1.391N73Mean54.98StDev1.940N73ASTM2MeanHistogram(with
11、 Normal Curve)of PTF-1 by MethodPanel variable:MethodMethodPTF-1ASTM2ASTM16560555045Individual Value Plot of PTF-1 vs MethodMethodPTF-1ASTM2ASTM16560555045Boxplot of PTF-1 by Method顯示圖形總結顯示圖形總結123Minitab:Stat Basic Statistics Graphical Summary可選擇可選擇輸入輸入或或空白空白圖形視窗輸出結果圖形視窗輸出結果(依變數依變數)636057545148Media
12、nMean55.5055.2555.0054.7554.50Anderson-Darling Normality TestVariance3.763Skewness2.01848Kurtosis7.64834N73Minimum51.020A-Squared1st Quartile53.825Median54.8203rd Quartile55.735Maximum63.40095%Confidence Interval for Mean54.5252.4655.43195%Confidence Interval for Median54.51955.09595%Confidence Inte
13、rval for StDev1.6682.318P-Value 0.005Mean54.978StDev1.94095%Confidence IntervalsSummary for PTF-1Method=ASTM1636057545148MedianMean51.1551.0050.8550.7050.5550.40Anderson-Darling Normality TestVariance1.934Skewness1.83161Kurtosis7.32882N73Minimum47.280A-Squared1st Quartile49.905Median50.6403rd Quarti
14、le51.295Maximum56.61095%Confidence Interval for Mean50.4312.2451.08095%Confidence Interval for Median50.33450.95095%Confidence Interval for StDev1.1961.662P-Value 0.005Mean50.755StDev1.39195%Confidence IntervalsSummary for PTF-1Method=ASTM2圖形視窗輸出結果圖形視窗輸出結果(空白空白)636057545148MedianMean53.553.052.552.0
15、51.5Anderson-Darling Normality TestVariance7.317Skewness0.78110Kurtosis1.28311N146Minimum47.280A-Squared1st Quartile50.638Median52.7203rd Quartile54.923Maximum63.40095%Confidence Interval for Mean52.4242.3353.30995%Confidence Interval for Median51.58053.62095%Confidence Interval for StDev2.4263.057P
16、-Value Basic Statistics Normality Test12圖形視窗輸出結果圖形視窗輸出結果ASTM1Percent646260585654525099.99995908070605040302010510.1Mean Probability Plot Single12圖形視窗輸出結果圖形視窗輸出結果ASTM1Percent6560555099.99995908070605040302010510.1Mean Time Series Plot Simple12圖形視窗輸出結果圖形視窗輸出結果Index相 對 密 度250225200175150125100755025110
17、110099989796Time Series Plot of 相對密度有任何想法嗎？可提供什麼資訊嗎？有任何想法嗎？可提供什麼資訊嗎？繪製管制圖（一）繪製管制圖（一）Minitab:Stat Control Charts Variables Charts for Subgroups Xbar-R123圖形視窗輸出結果圖形視窗輸出結果SampleSample Mean6054484236302418126199.599.098.598.097.5_X=98.509UCL=99.358LCL=97.660SampleSample Range605448423630241812613210_R=1
18、.166UCL=2.660LCL=01111111Xbar-R Chart of 相對密度表示有不尋表示有不尋常結果存在常結果存在的界限的界限繪製管制圖（二）繪製管制圖（二）Minitab:Stat Control Charts Variables Charts for Individuals I-MR12圖形視窗輸出結果圖形視窗輸出結果ObservationIndividual Value2502252001751501251007550251101100999897_X=98.509UCL=100.005LCL=97.013ObservationMoving Range2502252001
19、7515012510075502513210_MR=0.563UCL=1.838LCL=011111111111111111I-MR Chart of 相對密度背景背景n“資料如果沒有以背景來描述的話，就無法讀出他的意義”Donald J.Wheeler PhDn瞭解資料最佳的方式是將資料以時間序列放置，如果能選擇適當的管制圖會更好。開始試著將您的資料與有意義的 背景資料來放置確認不穩定性確認不穩定性圖形視窗輸出結果圖形視窗輸出結果ObservationIndividual Value2502252001751501251007550251101100999897_X=98.509UCL=10
20、0.005LCL=97.013ObservationMoving Range25022520017515012510075502513210_MR=0.563UCL=1.838LCL=011111111111111111I-MR Chart of 相對密度ObservationIndividual Value2502252001751501251007550251101100999897_X=98.509UCL=100.005LCL=97.013ObservationMoving Range25022520017515012510075502513210_MR=0.563UCL=1.838LC
21、L=0222111221221111222222222222222111122222222122221111I-MR Chart of 相對密度繪製柏拉圖繪製柏拉圖Minitab:Stat Quality Tools Pareto Chart1234圖形視窗輸出結果圖形視窗輸出結果CountPercent報廢項目Count29.715.214.54.84.1Cum%31.761.476.691.04695.9100.043222176Percent31.7OtherUT條狀亮紋目視亮點（非D）孔洞密度目視亮點（非A）160140120100806040200100806040200Pareto
22、 Chart of 報廢項目製程能力分析（一）製程能力分析（一）Minitab:Stat Quality Tools Capability AnalysisNormal12345圖形視窗輸出結果圖形視窗輸出結果5452504846LSLUSLProcess DataSample N67StDev(Within)1.01568StDev(Overall)1.82456LSL45.00000Target*USL55.00000Sample Mean48.64694Potential(Within)CapabilityCCpk1.64Overall CapabilityPp0.91PPL0.67PP
23、U1.16PpkCp0.67Cpm*1.64CPL1.20CPU2.08Cpk1.20Observed PerformancePPM USL0.00PPM Total0.00Exp.Within PerformancePPM USL0.00PPM Total164.93Exp.Overall PerformancePPM USL248.87PPM Total23063.80WithinOverallProcess Capability of PTF資料轉換資料轉換Minitab:Stat Control Charts Box-Cox Transformation123圖形視窗輸出結果圖形視窗輸
24、出結果LambdaStDev5.02.50.0-2.5-5.01.1501.1251.1001.0751.050Upper CLLimitLambda-4.99769(using 95.0%confidence)Estimate-4.99769Lower CL*Upper CL0.69561Best ValueBox-Cox Plot of ASTM1資料轉換後之製程能力分析資料轉換後之製程能力分析123463605754514845LSLUSLProcess DataSample N73StDev(Within)1.08267StDev(Overall)1.94656LSL45.00000T
25、arget*USL55.00000Sample Mean54.97795Potential(Within)CapabilityCCpk1.54Overall CapabilityPp0.86PPL1.71PPU0.00PpkCp0.00Cpm*1.54CPL3.07CPU0.01Cpk0.01Observed PerformancePPM USL438356.16PPM Total438356.16Exp.Within PerformancePPM USL491873.80PPM Total491873.80Exp.Overall PerformancePPM USL495480.03PPM
26、Total495480.18WithinOverallProcess Capability of ASTM1圖形視窗輸出結果圖形視窗輸出結果5.4000E-094.8000E-094.2000E-093.6000E-093.0000E-092.4000E-091.8000E-091.2000E-09LSL*USL*transformed dataProcess DataSample N73StDev(Within)1.08267StDev(Overall)1.94656After TransformationLSL*0.00000Target*LSL*USL*0.00000Sample Mea
27、n*0.00000StDev(Within)*0.00000StDev(Overall)*0.0000045.00000Target*USL55.00000Sample Mean54.97795Potential(Within)CapabilityCCpk 2.99Overall CapabilityPp1.84PPL3.64PPU0.04PpkCp0.04Cpm*2.99CPL5.92CPU0.06Cpk0.06Observed PerformancePPM USL438356.16PPM Total438356.16Exp.Within PerformancePPM LSL*0.00PPM
28、 LSL*0.00PPM Quality Tools Capability SixpackNormal12345Individual Value635649423528211471514845_X=48.647UCL=51.694LCL=45.600Moving Range635649423528211471420_MR=1.146UCL=3.743LCL=0ObservationValues65605550455451485250484655504540WithinOverallSpecsWithinStDev1.01568Cp1.64Cpk1.20CCpk1.64OverallStDev1
29、.82456Pp0.91Ppk0.67Cpm*111111Process Capability Sixpack of PTFI ChartMoving Range ChartLast 25 ObservationsCapability HistogramNormal Prob PlotAD:0.335,P:0.503Capability Plot圖形視窗輸出結果圖形視窗輸出結果判斷資料穩定性判斷資料穩定性資料是否有規律性資料是否有規律性判斷資料常態性判斷資料常態性製程能力指標製程能力指標假設檢定假設檢定n描述我們想要檢定的事項為假設 -設備工程師有5個新參數，它們是否比現在的參數好？-兩種不同
30、方法的實驗結果是否有差異？-不同操作人員的產出是否有差異？n我們可以比較一個群組的資料平均值、中位數與標準差和標準的比較，或針對多群組的資料比較它們的平均數、中位數和標準差。假設檢定路徑圖假設檢定路徑圖確認資料具有代表性確認資料具有代表性（Control Charts)是否為常態？是否為常態？單水準單水準2水準水準2+水準水準單水準單水準2水準水準2+水準水準變異是否相等？變異是否相等？2水準水準2+水準水準檢定平均數：檢定平均數：1-sample T1-sample Z檢定標準差：檢定標準差：Descriptive Statistics檢定中位數：檢定中位數：1-sample Wilcoxo
31、n檢定平均數：檢定平均數：2-sample T1-way ANOVA檢定平均數：檢定平均數：1-way ANOVA檢定平均數：檢定平均數：2-sample T檢定中位數：檢定中位數：Kruskal-WallisMoods Median檢定中位數：檢定中位數：Kruskal-WallisMoods Median檢定中位數：檢定中位數：Mann-WhitneyYNYN變異數相等檢定變異數相等檢定Minitab:Stat ANOVA Test for Equal Variances123視窗輸出結果視窗輸出結果Method95%Bonferroni Confidence Intervals for
32、StDevsASTM2ASTM12.42.22.01.81.61.41.21.0MethodPTF-1ASTM2ASTM16560555045F-Test0.124Test Statistic1.95P-Value0.005Levenes TestTest Statistic2.39P-ValueTest for Equal Variances for PTF-1資料為常態分配資料為常態分配時看時看F-Test；非；非常態分配時看常態分配時看Levenes Test2-Sample t檢定檢定Minitab:Stat Basic Statistics 2-Sample t1234視窗輸出結果視
33、窗輸出結果中位數檢定中位數檢定Minitab:Stat Nonparametrics Mann-Whitney123視窗輸出結果視窗輸出結果MSA路徑圖路徑圖資料型態？資料型態？Crossed GRRNested GRRAttribute GRR計量值計量值計數值計數值同一樣本同一樣本多人量測多人量測YN計量值計量值MSAMinitab:Stat Quality Tools Gage Study Gage R&R Study(Crossed)12345視窗輸出結果視窗輸出結果量測系統能辨別製程資料間的群組數量。量測系統能辨別製程資料間的群組數量。Imagine you measured 10
34、different parts,and Minitab reported that your measurement system could discern 3 distinct categories.This means that some of those 10 parts are not different enough to be discerned as being different by your measurement system.If you want to distinguish a higher number of distinct categories,you ne
35、ed a more precise gage.組成變異的貢獻度：組成變異的貢獻度：87.74%100%12.26%0.51%11.75%10.39%1.37%分析結果的判定標準分析結果的判定標準%Study Variation%ContributionNumber of Distinct CategoriesGoodBelow 15%Below 2%Above 10Caution15 to 30%2 to 7.7%5 to 10DangerAbove 30%Above7.7%Below 5%Study Variation的組成為兩種標準差的比率%Contribution的組成為兩種變異的比率視
36、窗輸出結果視窗輸出結果PercentPart-to-PartReprodRepeatGage R&R100500%Contribution%Study VarSample Range0.0160.0080.000_R=0.00435UCL=0.01120LCL=0ABCSample Mean7.327.267.20_X=7.2679UCL=7.2723LCL=7.2634ABCpart109876543217.327.267.20operatorCBA7.327.267.20partAverage10 9 8 7 6 5 4 3 2 17.327.267.20operatorABCGage n
37、ame:Date of study:Reported by:Tolerance:Misc:Components of VariationR Chart by operatorXbar Chart by operatordata by partdata by operator operator*part InteractionGage R&R(ANOVA)for data變異的組成變異的組成The percent contribution from Part-To-Part is larger than that of Total Gage R&R,telling you that much o
38、f the variation is due to differences between parts;however,more than 10%of the variation is due to the measurement system.瞭解實際數據的變異組成瞭解實際數據的變異組成PercentPart-to-PartReprodRepeatGage R&R100806040200%Contribution%Study VarGage name:Date of study:Reported by:Tolerance:Misc:Components of VariationGage R&
39、R(ANOVA)for data應期待零件間（應期待零件間（Part to Part）較大）較大 Gage R&R 較小較小Range ChartSample Range0.0150.0100.0050.000_R=0.00435UCL=0.01120LCL=0ABCSample Mean7.307.257.207.15_X=7.2679UCL=7.2723LCL=7.2634ABCGage name:Date of study:Reported by:Tolerance:Misc:R Chart by operatorXbar Chart by operatorGage R&R(ANOVA)
40、for dataMost of the points in the R chart are inside the control limits,indicating variation is mainly due to differences between parts.確認資料收集情境是穩定的確認資料收集情境是穩定的 1.所有點都應落在管制界限內所有點都應落在管制界限內2.若所有點超出管制界限，則該方法是可疑的。若所有點超出管制界限，則該方法是可疑的。3.若有一名操作員超出管制界限，若有一名操作員超出管制界限，則該名操作員的方法是可疑的。則該名操作員的方法是可疑的。4.若所有若所有range
41、 values=0，則該鑑別力是可疑的。，則該鑑別力是可疑的。Xbar ChartSample Range0.0150.0100.0050.000_R=0.00435UCL=0.01120LCL=0ABCSample Mean7.307.257.207.15_X=7.2679UCL=7.2723LCL=7.2634ABCGage name:Date of study:Reported by:Tolerance:Misc:R Chart by operatorXbar Chart by operatorGage R&R(ANOVA)for dataMost of the points in th
42、e Xbar chart are outside the control limits,indicating variation is mainly due to differences between parts.確認操作一致性確認操作一致性 1.所有點都應超出管制界限內。所有點都應超出管制界限內。2.界限來自於重複性。界限來自於重複性。3.我們希望變異來自不同零件，因此所有點都應落在管我們希望變異來自不同零件，因此所有點都應落在管 制界限外。制界限外。4.若所有樣本都在管制界限內，則樣本取樣有問題若所有樣本都在管制界限內，則樣本取樣有問題part109876543217.3257.3007
43、.2757.2507.2257.2007.1757.150Gage name:Date of study:Reported by:Tolerance:Misc:data by partGage R&R(ANOVA)for data依零件別依零件別There are not large differences between parts,as shown by the non-level line.確認樣本特性是否存在確認樣本特性是否存在SOP內內 1.每一零件的各點應相聚集。每一零件的各點應相聚集。2.各平均值間應有明顯的差異以各平均值間應有明顯的差異以辨別不同的零件。辨別不同的零件。oper
44、atorCBA7.3257.3007.2757.2507.2257.2007.1757.150Gage name:Date of study:Reported by:Tolerance:Misc:data by operatorGage R&R(ANOVA)for data依操作員別依操作員別There are small differences between operators,as shown by the nearly level line.沒有資訊的圖沒有資訊的圖操作員與零件交互作用操作員與零件交互作用Indicating a significant interaction betw
45、een each Part and Operator.partAverage10 9 8 7 6 5 4 3 2 17.3257.3007.2757.2507.2257.2007.1757.150operatorABCGage name:Date of study:Reported by:Tolerance:Misc:operator*part InteractionGage R&R(ANOVA)for data1.尋找平行線段，非平行線段表示有問題存在。尋找平行線段，非平行線段表示有問題存在。2.最佳情況：所有線重合或呈平行。最佳情況：所有線重合或呈平行。nGarbage in,garbage out.n重點在於如何解釋您的分析結果。n刀不磨不亮，記得常使用它。結語結語
