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1、統計基礎及品質統計,資料數據基礎統計學生產製造環境品質統計圖表製程能力分析SPC統計製程控制,資料及數據,你想瞭解什麽?,資訊源:,分組,離散型,名義型,順序型,間距型,“資料本身並不能提供資訊 必須對資料加以處理以後才能得到資訊,而處理資料的工具就是統計學”.,衡量,連續型,比率型,文字的(A to Z)圖示的 口頭的 數位的(0-9),數據,FAIL,PASS,數量 單價 說明 總價1$10.00$10.003$1.50$4.5010$10.00$10.002$5.00$10.00,裝貨單,離散型資料和連續型資料,電氣電路,溫度,溫度計,連續型,離散型,卡尺,錯誤,$,$,連續資料的優勢,
2、連續的,離散的,信息量少,信息量多,離散型資料(通常)分組/分類是/否,合格/不合格不能計算 離散型資料 分級 很少用 很難加以計算 連續型資料 最常見的尺規 計算時要很小心 連續型資料 比例關係 可應用演算法的多數公式,分類 標簽 第一、第二、第三 相對高度 字母順序 1234溫度計 刻度盤 速度=距離/時間 直尺,衡量工具分類,說明,例子,衡量工具分類,名義型:不相關類,只代表符合條件或不符合條件個體數.順序型:順序類,但沒有各類間隔的資訊.間距型:順序類,兩類之間間隔相等,但沒有絕對零點.比例型:順序類,兩 類之間間隔相等,同時存在絕對零點.,無權使用數位相機,Fred W.Bill S
3、.John D.Sam C.,Bob T.Jim C.Joe W.Diane A.,名義型衡量工具,名義尺規用於不考慮任何特性時，對各元素進行分類。示例中的名義尺規包括魚骨圖上的“原因”,是/否,合格/不合格,等等。,設備,應用,環境,材料,油漆粘附性差,應用表,從每一組中選擇一項國籍婚姻狀態職業,責任人列表,有權使用數位相機,順序型衡量工具,順序尺規根據特性給名義型資料排序(合格或不合格)。順序尺規示例中包括相對高度、Pareto 表、顧客滿意度調查，等等。,例 1:Pareto 表 油漆粘附性檢驗,相對尺寸,準備,順序尺規,原型,油漆類型,應用,濕度,操作者,重要性,例 2:顧客調查,問題
4、:你認爲我們的 服務如何?,非常好很好好還好差,完全同意 有點同意 既不同意也不反對有點反對 完全反對,比預期的稍差 比預期的差得多 最好 較好 中等較差 最差,比預期的好得多 比預期的稍好與預期的一樣,比例尺規範圍舉例 學校裏的五分制(A B C D E)七分制(1 2 3 4 5 6 7)口頭評分(優、好、中、可、差),調查表問卷類型,順序型衡量工具,間距和比例衡量工具,1.移動距離,0,0.10,0.20,2.刻度盤,間距尺規(相對)通常用來表示等距類別的數位資訊，但沒有絕對零點。刻度盤位於表座的頂端，用來作差異對比等。比例尺規 通常用來表示等距類別的數位資訊，但在測量範圍內有絕對零點。
5、卷尺、直尺、在恒定速度下位置相對於時間的值,等等。,間距尺規舉例:(沒有絕對零點),比例尺規舉例:(有絕對零點),3.相對速度,1.直尺,2.恒定速度下位置相對於時間的值,3.將重量作爲以磚塊數量爲變數的函數值,表座,基礎品質統計學,變異(Variation),當我們從一過程中收集數據,會發現數據不會永遠相同,因為變異(Variation)在過程中隨時存在,變異(Variation),我們觀察到的變異,是在過程中各種擾動累積起來的.,變異(Variation),參數,X,X,X,X,X,X,X,X,X,量測值,分佈,多數在此,少數在此,Center均值,Spread散佈,雖然變異是隨機的,但他
6、們的隨機性通常有模式存在,這種模式可用統計上的分佈(Distribution)來形容.如此變異加以統計分析,便可有某種程度的預測性存在並易於被理解或控制.,變異(Variation),中心Center:數據最集中在何處?散佈Spread:數據變異程度及分散狀況如何?形狀Shape:分佈是否對稱?扁平?凹凸?是否有異常區,描述分佈(Distribution),變異(Variation),變異可以是穩定(Stable)或不穩定(Unstable)的.-穩定變異:變化的分佈較具預測性及一致性,對時間而言具可預測性-不穩定變異:對時間而言不具可預測性,PROCESS#1-Stable Variatio
7、n穩定,Part,Thickness,PROCESS#2-Unstable Variation不穩定,Part,Distribution,Distribution,Thickness,變異(Variation),在製造過程中,有變異都是不好.問題是我們能容忍到何種範圍.我們能容忍的變異是具有以下兩項特徵:,STABLE(i.e.,consistent and predictable over time).,CAPABLE(i.e.,small variation compared to the product specifications.),Product Specifications,Pa
8、rameter Distribution,穩定,散佈小,控制變異(Variation),瞭解過程:,使制程更好:,保持穩定並維持高制程能力,過程由時間來看是否穩?制程能力是否能滿足目標規格?,確認並除去不穩定原因 確認並降低變異程度使滿足規格,持續監視及控制過程的變異源,特徵化,改善,控制,因為用抽樣統計,其結果只是估計,和真實可能有差異.適當的抽樣可使統計分析更準確.,Statistics 分佈的數學描述與定義,中心Center:數據最集中在何處?散佈Spread:數據變異程度及分散狀況如何?形狀Shape:分佈是否對稱?扁平?凹凸?是否有異常區,樣本均值,=,X,样本,母體參數和樣本統計量
9、,母體:包含所關心特性的已經製造或將要製造的物件 的全體樣本:在統計研究中實際測量的物件組。樣本通常爲所關心母體的子集,“母體參數”,“樣本統計量”,m=母體均值,s=樣本標準偏差,母體,s=母體標準偏差,均值:一組值的算術平均均值:-反映所有值的影響-受極值影響嚴重 中位數:反應 50%的序一組數排序後居中的數-在計算中不必包含所有值-相對於極值具有“可靠性”眾數值:-在一組資料中最常發生的值,Median,(Mean平均),(Median中數),眾數,Center(中心),50%,50%,全距:在一組資料中，最高值和最低值間的數值距離變異(s2):每個資料點與均值的平均平方偏差標準偏差(s
10、):變異數的平方根.量化變動最常用的量,全距最大值最小值,Spread(散佈),The Rule states how and can be used to describe the entire distribution:Roughly 60-75%of the data are within 1 of.Roughly 90-98%of the data are within 2 of.Roughly 99-100%of the data are within 3 of.,60-75%,90-98%,99-100%,m,m-s,m-2 s,m+s,m+2 s,m+3 s,m-3 s,Spre
11、ad(散佈),The shape of a distribution can be described by skewness歪斜(denoted by 1)and by kurtosis凹凸平坦(denoted by 2).,歪斜,凹凸平坦,Shape(形狀),母體均值,樣本均值,母體標準偏差,樣本標準偏差,常用計算公式,母體變異,樣本變異,The most important and useful distribution shape is called the Normal distribution,which is symmetric(對稱),uni-modal(單峰),and fre
12、e of outliers(沒有特異點):,Normal Distribution常態分佈,“常態”分佈是具有某些一致屬性的資料的分佈這些屬性對理解基礎過程（資料從該過程中收集）的特徵非常有用.大多數自然現象和人爲過程都符合常態分配，可以用常態分配表示,故大部份統計都假設是常態分佈。即使在資料不完全符合常態分配時，分析結果也很接近。特別不正常的分佈若假設為常態而去分析則有可能得到誤導結果。有數學技術可將其轉變成常態分佈來作分析。,A Normal probability plot is a cumulative distribution plot where the vertical scal
13、e is changed in such a way that data from a Normal distribution will form a straight line:,Histogram,CumulativeDistribution,NormalProbability Plot,常態概率圖,Normal Distribution常態分佈,第一個屬性:只要知道下面兩項就可以完全描述常態分配:均值標準差,常態分配的好處-簡化,第一個分佈,第二個分佈,第三個分佈,這三個分佈有什麽不同?,常態曲線和其概率,4,3,2,1,0,-,1,-,2,-,3,-,4,40%,30%,20%,10%
14、,0%,99.73%,第二個屬性:曲線下方的面積可以用於估計某“事件”發生的累積概率,95%,68%,樣本值的概率,距離均值的標準偏差數,得到兩值之間的值的累積概率,1,2,0,1,1,0,1,0,0,9,0,8,0,Stat Basic Statistics Display Descriptive StatisticsGraphs Graphical Summary,A2 27.11,描述性統計,圖形分析總結,變數：神秘,中值的95%信賴區間,的95%信賴區間,Anderson-Darling常態測試,P值 0.00,均值 100.00,標準偏差 32.38,變異數 1048.78,偏度 0
15、.01,峰度-1.63,資料量 500.00,最小值 41.77,第一象限 68.69,中值 104.20,第三象限 130.81,最大值 162.82,的95%信賴區間97.5 102.85,s的95%信賴區間30.49 34.53,中值的95%信賴區間 82.78 117.66,資料收集時的重點,How the data are collected affects the statistical appropriateness and analysis of a data set(資料如何收集可影響統計的適切性).Conclusions from properly collected da
16、ta can be applied more generally to the process and output.Inappropriately collected data CANNOT be used to draw valid conclusions about a process.Some aspects of proper data collection that must be accounted for are:The manufacturing environment(製程環境)from which the data are collected.When products
17、are manufactured in batches or lots,the data must be collected from several batches or lots.Randomization(隨機).When the data collection is not randomized,statistical analysis may lead to faulty conclusions.,Continuous Manufacturing(連續)occurs when an operation is performed on one unit of product at a
18、time.An assembly line is typical of a continuous manufacturing environment,where each unit of product is worked on individually and a continuous stream of finished products roll off the line.The automotive industry is one example of Continuous Manufacturing.Other examples of continuously manufacture
19、d product are:television sets,fast food hamburgers,computers.,Lot/Batch Manufacturing(批次)occurs occurs when operations are performed on products in batches,groups,or lots.The final product comes off the line in lots,instead of a stream of individual parts.Product within the same lot are processed to
20、gether,and receive the same treatment while in-process.Lot/Batch Manufacturing is typical of the semiconductor industry and many of its suppliers.Other examples of lot/batch manufactured product include:chemicals,semiconductor packages,cookies.,Manufacturing Environment製造環境,In Continuous Manufacturi
21、ng the most important variation is between partsIn Lot/Batch Manufacturing,the variation can occur between the parts in a lot and between the lots:Product within the same lot is manufactured together.Product from different lots are manufactured separately.Because of this,each lot has a different dis
22、tribution.This is important because Continuous Manufacturing is a basic assumption for many of the standard statistical methods found in most textbooks or QC handbooks.These methods are not appropriate for Lot/Batch Manufacturing.Different statistical methods need to be used to take into account the
23、 several sources of variation in Lot/Batch Manufacturing.要注意:連續和批量生產所用的統計方法有些不同,With Lot/Batch Manufacturing,each lot has a different mean.Due to random processing fluctuations,these lots will vary even though the process may be stable.This results in several“levels”of distributions,each level with
24、its own variance and mean:A distribution of units of product within the same lot.A distribution of the means of different lots.The total distribution of all units of product across all lots.,The different variances of a Lot/Batch Manufacturing process form a hierarchy called nesting.Data collected f
25、rom such processes usually have what is called a nested data structure.,1,1,2,LOTS,班,2,1,2,Each of the levels in the nested structure corresponds to a single variance.With a nested data set from this process,we need to take each source of variation into account when collecting data to ensure the tot
26、al process variation is represented in our data set:,生產線,2,2,2,2,2,2,2,X,1,2,X,2,2,1,2,1,2,1,;,X,;,X,;,X,X,X,X,+,=,+,=,=,=,=,總,總,總,6原則,變異數可相加,標準差則不能相加輸入變數變異數相加計算輸出中的總變異數,所以,那麽,引起的變異數,輸入變數,引起的變異數,輸入變數,過程輸出的變異數,如果,process has small within-lot variation and large lot-to-lot variation(which is very comm
27、on),data values from the same lot will be highly correlated,while data from different lots will be independent:,品質統計圖表,直方圖(Histograms)方框圖(Boxplots)柏拉圖(Pareto Diagrams)散佈圖(Scatterplots)趨勢圖(Trend Charts),品質統計圖表-直方圖(Histograms),Histograms provide a visual description of the distribution of a set of dat
28、a.A histogram should be used in conjunction with summary statistics such as and s.A histogram can be used to:Display the distribution of the data(現示數據的分佈).Provide a graphical indication of the center,spread,and shape of the data distribution(較定性地顯示數據的均值,散佈及形狀).Clarify any numerical summary statistic
29、s(which sometimes obscure information).(顯示較模糊的統計結果).Look for outliers-data points that do not fit the distribution of the rest of the data.(顯示異常點),:.:.:.:.:.:.:.:.:.:.:.:.-+-+-+-+-+-加侖/分鐘 49.00 49.50 50.00 50.50 51.00,點圖分佈,設想有一個泵流量爲50加侖/分鐘的計量泵。按照節拍對泵的實際流量進行了100次獨立測量。畫出各個點，每點代表一個給定值的輸出“事件”。當點聚集起來時，泵的
30、實際性能狀況可以看作泵流量的“分佈”。,5,1,.,3,5,0,.,8,5,0,.,3,4,9,.,8,4,9,.,3,4,8,.,8,4,0,3,0,2,0,1,0,0,直方圖分佈,還是這些資料，現在設想將其分組後歸入“區間”。泵流量點落入指定區間的次數決定區間條的高度。,頻率,加侖/分鐘,品質統計圖表-直方圖(Histograms),品質統計圖表-直方圖(Histograms),Multi-Modal Shape(雙峰):,Skewed Shape(偏一邊):Data can be right-skewed or left-skewed.This data is right-skewed
31、the right tail is longer than the left tail.,Outliers:特異點,練習,品質統計圖表-方框圖(Boxplots),Boxplots are a graphical tool valuable for comparing the distributions of two or more groups(e.g.,different lots,shifts,operators,etc.).Each distribution on this chart consists of the following:A“box”representing the m
32、iddle 50%of the data values.The length of the“box”is called the“Interquartile Range”(IQR).Inside the“box”is a line representing the median(50th percentile)of the data.Two“tails”which extend out to the minimum and maximum data values(assuming there are no outliers in the data).If the distance between
33、 the a data point and the nearer quartile is greater than 1.5xIQR,the data point is labeled as an outlier,and the“tail”on that side of the boxplot is shortened to the outermost data value within 1.5xIQR from the quartile.,品質統計圖表-方框圖(Boxplots),Median,MaximumData Value,75thPercentile,25thPercentile,Ou
34、termostdata valueswithin 1.5xIQRof the 75th and25th Percentiles.,Outlier,NO OUTLIERS,IQR,OUTLIERS,MinimumData Value,Outlier,1.5xIQR,品質統計圖表-方框圖(Boxplots),EXAMPLE:Creating a BoxplotThe figure below is a boxplot of the 100 plating thickness measurements.The histogram for the same data set is displayed
35、for comparison.,品質統計圖表-方框圖(Boxplots),Plating thickness measurements collected from 7 lots of product.,品質統計圖表-方框圖(Boxplots),Multi-Modal Shape:,Skewed Shape:,Outliers:,練習,品質統計圖表-柏拉圖(Pareto Diagrams),While histograms are used to display the distribution of a set of continuous(measured)data,Pareto diagr
36、ams are used to display the distribution of discrete(counted)data,such as different types of defects.Pareto diagrams can also be used with continuous(measured)data,particularly in displaying variance components analysis results,as we will see later in this course.Pareto diagrams are a useful tool fo
37、r determining which problems or types of problems are most severe or occur most frequently,hence should be given high priority for process improvement efforts.Pareto diagrams separate the significant vital few problems from the trivial many to help determine which problems to address first(and which
38、 to address later).重點中找重點!,Pareto圖分析,Pareto 圖根據 frequency 欄的內容判斷各個缺陷影響的大小，並按從大到小的次序排列。最後一組總是標有“其他”，並以默認方式包括所有缺陷的分類計算，這幾類缺陷非常少，它們占總缺陷的 5%以下。該圖右側 Y 軸表示占總缺陷的百分比，左側 Y 軸表示缺陷數。紅線(在螢幕上可以看到)表示累積百分比，而直方圖表示每類缺陷的頻率(占總量的百分比)。在圖的下方列出所有的值,百分比,缺陷的Pareto圖,計數,缺陷 計數 274 59 43 19 10 18百分比 64.8 13.9 10.2 4.5 2.4 4.3累積百
39、分比 64.8 78.7 88.9 93.4 93.4 100.0,螺釘丟失,夹子丢失,襯墊泄漏,外殼有缺陷,零件不完整,其他,400300200100 0,100806040200,百分比（%）,品質統計圖表-柏拉圖(Pareto Diagrams),Pareto圖分析:創建一個加權的 Pareto圖,通過指定金額/缺陷或用其他的加權方法，可以給次數加權。列在C1中的缺陷發生次數的價格列在 C3(value)中，價格乘以次數等於這類缺陷的費用(c4)。繪製費用（cost）曲線圖，而不是繪製次數（count）圖，這樣可以更好地說明每個缺陷對業務的影響。,品質統計圖表-柏拉圖(Pareto Di
40、agrams),層別Pareto圖:解釋分組資料,上圖使用了一個 By Variable（從屬變數），所有的圖都在一頁上。下圖使用同樣的命令，沒有從屬變數。當選擇每頁一張圖時，所有的圖的計數(左軸)刻度相同。右側的百分比只反映該圖占總體的百分比。這些圖表明，70%的記錄缺陷是刮傷和剝落的(下部)，約有一半的缺陷是夜班人員記錄的(上右圖)。此外，記錄缺陷是刮傷和剝落的比例，對白班和夜班的 來說似乎也差不多。然而，晚班和周末班出現的缺陷樣式是不同的。,裂紋Pareto圖,白班,晚班,夜班,周末班,刮傷剝落其他污點,151050,151050,151050,151050,裂紋Pareto圖,4030
41、20100,100806040200,缺陷計數 15 13 6 6百分比 37.5 32.5 15.0 15.0 累積百分比 35.5 70.0 85.0 100.0,刮伤,拨落,其他,污点,計數,計數,計數,計數,計數,百分比（%）,品質統計圖表-柏拉圖(Pareto Diagrams),練習,品質統計圖表-散佈圖(Scatterplots),Until now,all the graphical tools weve discussed have been for examining the distribution of a single process characteristic.T
42、he scatterplot is a graphical tool for examining the relationship between two process characteristics.A scatterplot is an X-Y plot of one variable versus another.Each unit of product usually has many characteristics,process input variables,etc.One objective might be to see whether two variables or c
43、haracteristics are related to each other(i.e.,to see what happens to one of the variables when the other variable changes).This relationship between two variables is called correlation.Scatterplots can help us answer this type of question.,品質統計圖表-散佈圖(Scatterplots),品質統計圖表-散佈圖(Scatterplots),In additio
44、n to telling us whether or not two variables are related,scatterplots can tell us how they are related,and the strength of the relationship:,Strong Positive Correlation強正相關,No Correlation無關,Weak Negative Correlation弱負相關,Weak Positive Correlation弱正相關,Strong Negative Correlation強負相關,品質統計圖表-散佈圖(Scatter
45、plots),In addition,scatterplots are an excellent tool for determining the type of relationship between the two variables,as well as looking for outliers:,Linear Relationship線性相關,Outliers 特異,Non-Linear Relationship非線性相關,品質統計圖表-散佈圖(Scatterplots),Correlation and CausationWe must always take care not to
46、 confuse correlation with causation.The fact that two characteristics are correlated does not prove that one causes the other.Both may be related to some other factor which is the true root cause.,But is there a cause-effect relationship between the two?Did the increase in TVs cause the number of ac
47、cidents to go up?(Not likely.)Did the increase in traffic accidents cause people to buy more TVs?(Not likely,either.),練習,品質統計圖表-趨勢圖(Trend Charts),Trend ChartsStability:A process is stable if its mean and standard deviation are constant and predictable over time.A disadvantage of histograms and norma
48、l probability plots is that they cannot be used to determine whether the process is stable over time.A plot of the data in time order will allow us to do that.These time-ordered plots,called Trend charts and Control charts are essential when examining the stability of a distribution over time.A tren
49、d chart or a control chart can detect instability if it exists.Control charts,which are a special kind of trend chart,are discussed in detail separately in a later course module.可看出穩定性及預測性,品質統計圖表-趨勢圖(Trend Charts),The table below contains average plating thickness measurements taken from 21 lots of
50、product.Below that is a trend chart of the data.,練習,品質統計圖表-Noisy,The results of a statistical analysis can be seriously affected by the failure of the data to meet certain required assumptions.One of the most common assumptions is that the data values are independent and that they come from a Normal
