統計基礎及質量統計-預覽頁

　

【正文】 ssed have been for examining the distribution of a single process characteristic. The scatterplot is a graphical tool for examining the relationship between two process characteristics. A scatterplot is an XY 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 characteristics are related to each other (., 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. 6s 60 品質統計圖表 散佈圖 (Scatterplots) Acid Age Etch Rate Acid Age Etch Rate Acid Age Etch Rate 13 13 15 18 30 23 18 19 31 19 7 4 12 25 21 24 29 26 28 20 9 19 6 14 9 9 27 25 30 31 051015202530350 1 2 3 4 5 6Ac i d Ag e6s 61 品質統計圖表 散佈圖 (Scatterplots) In addition 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 6s 62 品質統計圖表 散佈圖 (Scatterplots) 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 NonLinear Relationship 非線性相關 6s 63 品質統計圖表 散佈圖 (Scatterplots) Correlation and Causation We must always take care not to 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. Number of Televisions Number of Traffic Accidents 1970 1990 But is there a causeeffect relationship between the two? ? Did the increase in TV’s cause the number of accidents to go up? (Not likely.) ? Did the increase in traffic accidents cause people to buy more TV’s? (Not likely, either.) 6s 64 練習 6s 65 品質統計圖表 趨勢圖 (Trend Charts) Trend Charts Stability: A process is stable if its mean and standard deviation are constant and predictable over time. A disadvantage of histograms and normal 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 timeordered plots, called Trend charts and Control charts are essential when examining the stability of a distribution over time. A trend 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 6s 66 品質統計圖表 趨勢圖 (Trend Charts) The table below contains average plating thickness measurements taken from 21 lots of product. Below that is a trend chart of the data. Lot Plating Thickness Lot Plating Thickness Lot Plating Thickness 1 8 15 2 9 16 3 10 17 4 11 18 5 12 19 6 13 20 7 14 21 1351401451501551600 5 10 15 20 25L o t N o .6s 67 練習 6s 68 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 mon assumptions is that the data values are independent and that they e from a Normal distribution. This assumption can be violated in several ways: ? Outliers (points that do not fit the rest of the distribution) in the data, ? NonNormalshaped distributions (multimodal or skewed distributions), Data that exhibit these characteristics can be thought of as noisy data. The procedures in this section provide techniques for effective detection and analysis of noisy data. 雜訊 6s 69 品質統計圖表 Noisy Boxplots Trend Chart Histogram Scatterplot Normal Prob. Plot 6s 70 品質統計圖表 Noisy Remended strategy for handling outliers: 1. Identify the outliers using the methods described in the following pages. If possible, find the causes of the outliers. Remove the outliers with identified causes from the data set(找原因 ). 2. If all the outliers can be explained, then analyze the data as usual. 3. However, if there are any outliers that do not have explanations, analyze the data twice: ? including the outliers, ? excluding the outliers. See if and how the analysis results differ. 6s 71 製程能力分析 6s 72 當製程開始產生變異時 ,其統計分佈圖的形狀也開始變化 。 例 :模具尺寸超差。大多數公司是將 SPC用於最終産品 (Y)上 , 而不是用於過程特徵 (X)。 SPC的使用使我們能夠通過失控信號發現特殊原因。 這些限值不應與 顧客規定限值 相比較 。 控制限值是以爲衡量的 Y或 X建立 177。這種措施不能短期或長期保持 。常用的遏制政策是審查或 100%檢查 。該標記使設備停工，以免缺陷繼續發展 。 3) 記住 : 控制限值與顧客規定限值無關 控制上限 中線 樣本均值 6s 88 常用 控制圖類型 (XS) SXLotLotMon i torproc e s sm e a nMon i torproc e s ss ta nd a r ddevi a ti on6s 89 常用 控制圖類型 (XR) RXLotLotMo nit o rpro ce ssm ea nMo nit o rDe v iat ion6s 90 短期 N 30 For control charts with N 30 lots, rather than the usual UCL (upper control limit) and LCL (lower control limit), there are dual sets of control limits: ? Outer Control Limits(3s). ? Inner Control Limits (1s). Lot Nu m be rU C L ( o u t e r )U C L ( i n n e r )L C L ( i n n e r )L C L ( o u t e r )C e n t e r l i n ePr