【正文】 統(tǒng)計 69 Jason Lee 2023/07/04 過程改善及控制圖 過程 衡量系統(tǒng) 輸入 輸出 1. 發(fā)現(xiàn)可指定的原因 4. 驗證結(jié)果 2. 確定根本原因 統(tǒng)計 70 Jason Lee 2023/07/04 控制圖的益處 用於提高生産率的已證實的技術 有效防範缺陷 防止不必要的過程調(diào)整 提供診斷資訊 提 供 關於過程能力的資訊 統(tǒng)計 71 Jason Lee 2023/07/04 控制圖類型 控制圖有許多類型，但是它們的根本原理是相同的 利用 SPC和過程目標方面的知識選擇正確的類型 根據(jù)以下幾方面選擇控制圖類型 ： 資料類型 : 屬性還是變數(shù) ? 採樣容易：樣本同質(zhì)性 資料分佈 : 正常或非正常 ? 分組大小 : 不變的或變化的 ? 其他考慮 統(tǒng)計 72 Jason Lee 2023/07/04 控制圖的組成 KVOP的 X均值圖 2 0 1 0 0 6 1 5 6 0 5 5 9 5 5 8 5 樣本數(shù) X = 5 9 9 . 1 U C L = 6 1 3 . 6 L C L = 5 8 4 . 6 控制下限 UCL = m +ks 中線 = m LCL = m k s 其中 m = 樣本均值 s = 樣本標準偏差 k = 控制限制距中線的差值 (通常爲 177。 控制限值是以爲衡量的 Y或 X建立 177。當控制圖表出現(xiàn)非隨機型式信號時，我們就可以知道特殊原因引起的變動改變了過程。 這些限值不應與 顧客規(guī)定限值 相比較 。 控制圖表是在統(tǒng)計上從時間上跟蹤過程和産品參數(shù)的方法。 SPC的使用使我們能夠通過失控信號發(fā)現(xiàn)特殊原因。然而，只有我們將重點放在控制輸入 (X),而不是控制輸出 (Y)時 , 我們才能認識到我們在提高質(zhì)量、生産率及降低成本上的努力收效有多大 。大多數(shù)公司是將 SPC用於最終産品 (Y)上 , 而不是用於過程特徵 (X)。 作管制時加入規(guī)格上下線 , 超出規(guī)格則視為不良如下圖 : 統(tǒng)計 62 Jason Lee 2023/07/04 製程能力好 ,中心值在目標上且分佈均在規(guī)格內(nèi) 製程能力尚可 ,中心值在目標上 ,分佈均在規(guī)格內(nèi)但稍微太分散 製程能力尚可 ,中心值有漂移 ,但分佈尚在規(guī)格內(nèi) 製程能力不好 ,中心值雖在目標 ,但分佈超出規(guī)格外 製程能力不好 ,中心值不在目標 ,分佈雖集中但超出規(guī)格外 製程能力最差 ,中心值不在目標 ,分佈不集中且超出規(guī)格外 統(tǒng)計 63 Jason Lee 2023/07/04 計算 Ca,Cp,Cpk公式 規(guī)格中心 m LSL + 3 s 3 s 製 程寬度 6 s 規(guī)格 寬度 T USL Su SL ? ?1nxxn1i2i2?????snnn nxx??? 1Ca: Capability of Accuracy準確度 : 實際中心 Ca = X m (T/2) X m X Ca只對雙邊規(guī)格適用 . 分級標準如下 : 等級 Ca 值 A │Ca│≦ % B % │Ca│≦ 25% C 25% │Ca│≦ 50% D │Ca│50% 主值 統(tǒng)計 64 Jason Lee 2023/07/04 計算 Ca,Cp,Cpk公式 規(guī)格中心 m LSL + 3 s 3 s 製 程寬度 6 s 規(guī)格 寬度 T USL Su SL ? ?1nxxn1i2i2?????snnn nxx??? 1Cp: Capability of Precision精確度 : 實際中心 X m X 當僅有下限時 :Cp = ( SL)/(3σ) 對雙邊規(guī)格 : Cp = T/(6σ) 當僅有上限時 : Cp = (Su )/(3σ) X X 等級 Cp值 A Cp≧ B ≦ Cp C ≦ Cp D Cp 分級標準如下 : 主值 統(tǒng)計 65 Jason Lee 2023/07/04 計算 Ca,Cp,Cpk公式 Cpk: 指制程能力參數(shù) , 是 Cp和 Ca的綜合 . 對雙邊規(guī)格 : Cpk=(1│Ca│)*Cp= Min[(Su )/(3σ), ( SL)/(3σ)] 對單邊規(guī)格 , 可以認為 T為 ∞, 則 Ca= ( μ)/ (T/2)= 0 Cpk= (1│Ca│)*Cp= Cp 等級 Cpk值 評價 A Cpk≧ 理想 B ≦ Cpk 正常 C Cpk 不足 分級標準如下 : X X X 統(tǒng)計 66 Jason Lee 2023/07/04 SPC介紹 SPC是用於研究變動的一種基本工具 ,它使用統(tǒng)計信號監(jiān)測並改善過程績效。 例 :模具尺寸超差。 例 :每日生產(chǎn)參數(shù)設定漂移 。ve discussed 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. 統(tǒng)計 50 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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 e統(tǒng)計 51 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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 統(tǒng)計 52 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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 統(tǒng)計 53 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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.) 統(tǒng)計 54 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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(wěn)定性及預測性 統(tǒng)計 55 Jason Lee 2023/07/04 品質(zhì)統(tǒng)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 dat