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02 spc訓練教材
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02 spc訓練教材

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  • 1. Statistical Process Control 統計製程管制
  • 2. Chapter Outline 概述
    • Statistical Thinking and Statistical Methods
    • 統計思維與統計方法
    • Statistical Process Control (SPC) 統計製程管制
      • Types of data 資料型態
      • Constructing control charts 如何架構管制圖
      • Interpreting control charts 管制圖之說明
      • Process capability 製程能力
    • Acceptance sampling 允收水準
      • Inspection process 檢驗程序
      • Quality measures 品質的量測
      • Sampling vs. screening 抽樣與篩選
  • 3. Process 製程 Variation 變異 Data 資料 Statistical Tools 統計方法 Statistical Thinking 統計思維 Statistical Methods 統計方法 Statistical Thinking and Statistical Methods 統計思維與統計方法
  • 4. Statistical Thinking 統計思維
    • Key Concepts 主要觀念
      • Process and systems thinking 製程與系統的思維
      • Variation 變異
      • Analysis increases knowledge 分析可以增加知識
      • Taking action 可以採取行動
      • Improvement 可以用來改善
    • Role of Data 資料的角色
      • Quantify variation 量化的變異 ( 變動 )
      • Measure effects 量測的效應
  • 5. “ You can’t improve a process that you don’t understand” 你若對製程不懂 , 就無法改善製程 Without a Process View 若無製程的觀點
    • People have problems understanding the problem and their role in its solution (turf). 吾人在其問題的理解與對策執行的角色扮演上會有問題 It is difficult to define the scope of the problem. 難以定義問題範圍
    • It is difficult to get to root causes. 難以找到真正的要因
    • People get blamed when the process is the problem (80/20 Rule). 吾人在當製程是真正問題時 , 會遭到責備
    • Process management is ineffective 製程管理沒有效果
    • Improvement is slowed 改善緩慢
  • 6. Without Understanding Variation 若不了解其變異
    • Management by the last data point 永遠是用最後的資料作管理 ( 永遠在頭痛醫頭 , 腳痛一腳 , 沒有源頭置根本的觀念 )
    • There’s lots of fire fighting 火災不斷
      • Using special cause methods to solve common cause problems 用特別的方法處理共同要因的 ( 一般性 ) 問題
    • Tampering and micromanaging abound
    • 修改與小事的管理老是存在
    • Goals and methods to attain them fail
    • 目標與方法無法達成
    • Understanding the process is handicapped
    • 只知道製程是個問題
      • Learning is slowed 學習慢
    • Process management is ineffective 製程管理沒有效果
    • Improvement is slowed 改善慢
  • 7. Without Data 若是手上沒有資料
    • Everyone is an expert: 每個人都是專家
      • Discussions produce more heat than light 討論不斷
    • Historical memory is poor 歷史的記憶模糊
    • Difficult to get agreement on: 難以得到協議若
      • What the problem is 無法得知問題是什麼
      • What success looks like 無法得知其成果將如何
      • Progress made 或由哪一製程所產出
    • Process management is ineffective 製程管理是無效的
    • Improvement is slowed 改善慢
  • 8. “ Early on, we failed to focus adequately on core work processes and statistics.” 初期若核心工作製程與統計無法適當集中 , 其結果… David Kearns and David Nelder, Xerox Corporation Without Statistical Thinking 若無製程統計的思維
    • Your management and improvement processes are handicappe 吾人的管理與改善將有障礙
    • It’s like 其像
      • Football without a passing attack 足球未經核准即攻擊
      • Growing a lawn without fertilizer 草地未經施肥
      • Doing research without measurements 研究未做量測資料
      • Playing golf without your irons 不用自己的球竿打高爾書球
  • 9. SECURE STORE KIT
    • Load Program
    • Load Pick/Place
    • Load Reflow Profile
    • Load Stencil
    Screen Solder Paste Parts SMT Placement I / R ReFlow Clean PEM Parts (ASIC, ADC, DAC) Placement & Hand Solder Clean
    • Second Level Assy.
    • Touch-up solder joints
    • Mechanical Installations
    • Staking/Bonding
    Clean Electrical Functional Test Clean Bake Conformal Coat Post Test Inspection Acceptance Test Electrical Controlled Storage Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint
    • Through-hole and Plastic Parts Preparation
    • Tin Components
    • Form & Cut Axial Leads
    Through-hole Component Placement & Hand Solder Clean & Inspection Checkpoint
    • PWB Preparation:
    • Clean
    • Ink Stamp
    • Bake
    Production Operation Inspection Operation Test Operation Material Control Operation KEY Manufacturing Flow Diagram of PWB Assembly PWB 組裝之製造流程圖
  • 10. SECURE STORE KIT
    • Load Program
    • Load Pick/Place
    • Load Reflow Profile
    • Load Stencil
    Screen Solder Paste Parts SMT Placement I / R ReFlow Clean PEM Parts (ASIC, ADC, DAC) Placement & Hand Solder Clean
    • Second Level Assy.
    • Touch-up solder joints
    • Mechanical Installations
    • Staking/Bonding
    Clean Electrical Functional Test Clean Bake Conformal Coat Post Test Inspection Acceptance Test Electrical Controlled Storage Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint Inspection Checkpoint
    • Through-hole and Plastic Parts Preparation
    • Tin Components
    • Form & Cut Axial Leads
    Through-hole Component Placement & Hand Solder Clean & Inspection Checkpoint
    • PWB Preparation:
    • Clean
    • Ink Stamp
    • Bake
    Production Operation Inspection Operation Test Operation Material Control Operation KEY Manufacturing Flow Diagram of PWB Assembly PWB 組裝之製造流程圖
  • 11. Depends on levels of activity and job responsibility. 依據活動的層級與工作執掌 Where we're headed 我們朝何方 Managerial processes to guide us 用管理的程序來指導我們 Where the work gets Done 讓所需的工作被執行完成 Strategic 策略上的 Managerial 管理上的 Operational 作業性的 Executives 高階決策層 Managers 經理階層 Workers 現場員工 Use of Statistical Thinking 運用統計思維
  • 12.
    • Executives use systems approach.
    • 決策者運用系統導向策略
    • Core processes have been flow charted
    • 主要程序已被流程圖表化
    • Strategic direction defined and deployed.
    • 策略方向的訂定與展開
    • Measurement systems in place.
    • 適當的量測系統
    • Employee, customer, and benchmarking studies are used to drive improvement.
    • 是以員工 , 客戶與 benchmarking 的研究被用來主導改善
    • Experimentation is encouraged. 鼓勵實驗
    Statistical Thinking at the Strategic Level 決策者之統計思維
  • 13. .
    • Managers use meeting management techniques
    • 經理利用會議管理技巧
    • Standardized project management systems are in place.
    • 適當的標準化專案管理系統
    • Both project process and results are reviewed.
    • 此專案的流程與結果已被審核
    • Process variation is considered when setting goals.
    • 當設定目標時 , 流程的變異已被考慮
    • Measurement is viewed as a process.
    • 量測點被視為一個流程
    • The number of suppliers is reduced
    • 供應者數目減少
    • A variety of communication media are used.
    • 廣泛的傳訊媒體被採用
    Statistical Thinking at the Managerial Level 經理階層統計思維
  • 14.
    • Work processes are flowcharted & documented
    • 工作程序已被流程圖表化與書面化
    • Key measurements are identified. 主要量測點已被確認
      • Time plots displayed 時間的圖示被展現
    • Process management and improvement utilize:
    • 製程管理與改善採用
      • Knowledge of variation, and 變異觀念的知識及
      • Data analysis 資料分析
    • Improvement activities focus on the process, not blaming employees. 改善工具著重於製程 , 而非責備員工
    Statistical Thinking at the Operational Level 現場員工的統計思維範例
  • 15. Statistical Thinking at the Operational Level 現場員工的統計思維範例
    • A Recent Experience 最近的經驗
    • Huge quantities of data 大量的資料
    • Limited understanding of structure
    • 在有限度理解的結構上
    • Consultants applied artificial neural nets
    • 顧問群運用人工神經網狀系統
    • Didn’t work 但不成功
  • 16. Statistical Thinking at the Operational Level 現場員工的統計思維範例
    • A Recent Experience 最近的經驗
    • Artificial Neural Nets apply nicely in many situations (NIST Examples): 人工神經網狀系統出色地運用於許多領域 :
      • Optical Character Recognition 光學文字辨識系統
      • Finger Printing 指紋辨識
      • Face Printing for the FBI 相貌辨識
    • Example 等案例上
  • 17. … .But, 但
    • Unless you sample the process taking the right amount of the right kind of data (rational subgroups) you will never approach process understanding.
    • 在抽驗的流 ( 製 ) 程裡若你無法取得正確的數量與資料 ( 合理的樣組 ), 你將無法深入了解此一流 ( 製 ) 程
    • Without process understanding, there is no process control.
    • 流 ( 製 ) 程若不了解 , 就無所謂的流 ( 製 ) 程管制
  • 18. Key Learnings from Statistical Thinking Efforts 由統計思維的努力中 , 吾人學到的要點
    • Statisticians don’t understand Statistical Thinking as well as they think they do.
    • 統計的思維不僅要懂而且也要會做
    • Those who do understand it have limited access to managerial and strategic levels.
    • 真正了解統計思維的人 , 在管理與決策上之能力較少受限制
    • There’s much more work to be done.
    • 較多的事能被完成
      • Spread the word 口令的展開
      • Focus on process 著重製程
  • 19.
    • Characteristics for which you
    • focus on defects
    • 其特性著重於缺點
    • Classify products as either ‘good’
    • or ‘bad’, or count # defects
    • 以產品的好 . 壞 , 缺點數量來看
    • e.g., radio works or not
    • 如收音機是否可以播放
    • Categorical or discrete random
    • variables 屬不連續的雖機變數
    Attributes 計數值 Variables 計量值 Quality Characteristics 品質特性
    • Characteristics that you
    • measure, e.g., weight, length
    • 其特性可被量測而得 , 如重量
    • , 長度等
    • May be in whole or in
    • fractional numbers
    • 可以以整數或分數表達
    • Continuous random variables
    • 連續的隨機變數
  • 20. Types Of Data 資料型態
    • Attribute data 計數資料
        • Product characteristic evaluated with a discrete choice
        • 產品資料特性以離散的評估方式選定
          • Good/bad, yes/no 良品 / 不良品 , 好 / 壞
    • Variable data 計量資料
        • Product characteristic that can be measured
        • 產品特性能被量測而得
          • Length, size, weight, height, time, velocity
          • 長度 , 大小 , 重量 , 高度 , 時間 ,, 速度
  • 21. Types of Variations 變異型態
    • Common Cause 共同原因
    • Random 隨機
    • Chronic 長期的
    • Small 影響小
    • System problems 系統問題
    • Mgt controllable 管理上的控制
    • Process improvement 製程改善
    • Process capability 製程能力
    • Special Cause 特殊原因
    • Situational 局部
    • Sporadic 偶而發生
    • Large 影響大
    • Local problems 局部問題
    • Locally controllable 可局部控制
    • Process control 製程管制
    • Process stability 製程的穩定性
  • 22.
    • Statistical technique used to ensure process is making product
    • to standard 統計技術用於確保製程所製出的產品合乎標準
    • All process are subject to variability 所有製程受變異性所支配
    • Natural or Common causes 自然或共同原因 :
    • Random variations 隨機變異如設備損耗
    • Assignable causes 特殊原因
    • Correctable problems 可改善的問題
    • Machine wear, unskilled workers, poor material
    • 如生手 , 材料不良…
    • Objective: Identify assignable causes
    • 目標 : 確認特殊原因
    • Uses process control charts
    • 利用管制圖表
    Statistical Process Control 統計製程管制
  • 23. Causes of Variation 變異的原因
    • Inherent to process 固有製程
    • Random 隨機
    • Cannot be controlled 不可控
    • Cannot be prevented 無法預防
    • Examples 如 :
      • Weather 氣候
      • accuracy of measurements 量測精度
      • capability of machine 設備能力
    • Exogenous to process 外來因子影響製程
    • Not random 非隨機
    • Controllable 可控
    • Preventable 可預防
    • Examples 如
      • tool wear 工具磨耗
      • “ Monday” effect 週一效應
      • poor maintenance 維護差
    Common Causes 共同原因 Assignable Causes 特殊原因 What prevents perfection? Process variation... 何事阻礙完美 ? 製程變異…
  • 24. Product Specification and Process Variation 產品規格與製程變異
    • Product specification 產品規格
    • desired range of product attribute 產品屬性之期望範圍
    • part of product design 產品設計的一部份
    • length, weight, thickness, color, … 長度 , 重量 , 厚度 , 顏色…等
    • nominal specification( 公稱規格 )
    • upper and lower specification limits( 規格上下限 )
    • Process variability 製程變異
    • inherent variation in processes 製程中固有的變異
    • limits what can actually be achieved 其實際能被達成之界限值
    • defines and limits process capability 定義並限制製程能力
    • Process may not be capable of meeting specification!
    • 製程是有可能無法達到規格的要求 !
  • 25. Grams (a) Location Average ( 平均值 ) Common Causes 共同原因
  • 26. (a) Location Grams Average Assignable Causes 特殊原因
  • 27.
    • = Standard deviation
    • = 標準差
    The Norma l Distribution 常態分配 -3  -2  -1  +1  +2  +3  Mean 平均值 68.26% 95.44% 99.74%
  • 28. Mean 平均值 Central Limit Theorem Standard deviation 樣本標準差 Theoretical Basis of Control Charts
  • 29. UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限 1 2 3 Samples Control Charts 管制圖
  • 30. 1 2 3 Samples Control Charts 管制圖 UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限
  • 31. Assignable causes likely 可能的特殊原因 1 2 3 Samples Control Charts 管制圖 UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限
  • 32. Process Control: Three Types of Process Outputs 製程管制的三種顯示型態 Frequency Lower control limit Size Weight, length, speed, etc. Upper control limit (b) In statistical control, but not capable of producing within control limits. A process in control (only natural causes of variation are present) but not capable of producing within the specified control limits; 共同原因變異 and (c) Out of control. A process out of control having assignable causes of variation. 特殊原因變異
    • In statistical control and capable of producing within control limits. A process with only natural causes of variation and capable of producing within the specified control limits. 正常型
  • 33. The Relationship Between Population and Sampling Distributions 群體與樣本間之關係 Uniform Normal Beta Distribution of sample means 樣本平均值分配 Standard deviation of the sample means (mean) Three population distributions 群體分配
  • 34. Visualizing Chance Causes 機遇原因之觀察 Target At a fixed point in time 固定時間 Time Target Over time 連續時間 Think of a manufacturing process producing distinct parts with measurable characteristics. These measurements vary because of materials, machines, operators, etc. These sources make up chance causes of variation. 製造各零件之量測特性會因 4M 等機遇原因而發生變異
  • 35. Process Control Charts 製程管制圖
  • 36. Control Chart Types 管制圖型態 計量 計數 Control Charts Variables Charts Attributes Charts Continuous 連續的 Numerical Data Categorical or Discrete 離散的 Numerical Data
  • 37. Control Chart Selection 管制圖的選定 Quality Characteristic variable attribute n>1? n>=10 or computer? x and MR no yes x and s x and R no yes defective defect constant sample size? p-chart with variable sample size no p or np yes constant sampling unit? c u yes no
  • 38. Produce Good Provide Service Stop Process Yes No Assign. Causes? Take Sample Inspect Sample Find Out Why Create Control Chart Start Statistical Process Control Steps 統計製程管制控制步驟
  • 39. Statistical Thinking is a philosophy of learning and Action based on the following fundamental principles: 統計思維哲學之學習與行動基於以下原則
    • All work occurs in a system of interconnected processes,
    • Variation exists in all processes, and
    • Understanding and reducing variation are keys to success.
    • 所有工作的產生源於系統互相連結之製程 , 而變異存在於所有製程 , 了解並降低製程的變異是成功的關鍵
  • 40. Using Control Charts 如何使用管制圖 1) Select the process to be charted 選擇需要被圖表化之製程 2) Get 20 - 25 groups of samples 選擇樣組及樣本大小 (usually 5-20 per group for X and R-chart or n≥50 for p-chart) 3) Construct the Control Chart 建立管制圖 4) Analyze the data relative to the control limits. Points outside of the limits should be explained 分析關聯於管制界線之資料 , 點超出界限需能被解釋 5) Once they are explained, eliminate them from the data and recalculate the control chart 一旦澄清 , 消除異常點及原因 , 並重算管制圖資料 6) Use the chart for new data, but DO NOT recalculate the control limits 利用此新資料 , 但無須重算管制界限
  • 41.
    • Type of variables control chart 計量管制圖
    • Interval or ratio scaled numerical data
    • 間距或比率量測數字資料
    • Shows sample means over time
    算出樣本平均值
    • Monitors process average
    監控製程平均數
    • Example: Measure 5 samples of solder paste &
    • compute means of samples; Plot
    如計算錫膏厚度之平均值 , 再點圖  X Chart 平均值管制圖
  • 42. Basic Probabilities Concerning the Distribution of Sample Means 有關樣本平均數之機率分佈 Std. dev. of the sample means 樣本平均數標準差 :
  • 43. Estimation of Mean and Std. Dev. of the Underlying Process 在製程控制之下之平均值與標準差估計
    • use historical data taken from the process when it was “known” to be in control 當製程穩定時 , 利用過去所產生之歷史資料
    • usually data is in the form of samples (preferably with fixed sample size) taken at regular intervals 樣本資料是在一定間隔的時間裡取得
    • process mean  estimated as the average of the sample means (the grand mean or nominal value) 假設製程平均值 與樣本平均值相同
    • process standard deviation  estimated by: 製程標準差 估算由
        • standard deviation of all individual samples 所有個別值樣本之標準差
        • OR mean of sample range R/d 2 , where 或樣本平均值 / d 2
        • sample range R = (Rmax-Rmin), d 2 = value from look-up table, 全距為 R, d 2 可由查表得知 ,
  • 44. X-bar vs. R charts 平均值 VS 全距管制圖
    • R charts monitor variability: Is the variability of the process stable over time? Do the items come from one distribution?
    • R 管制圖監控變異性 , 是否整個製程處於安定狀態 ? 有項目超出此一分配嗎 ?
    • X-bar charts monitor centering (once the R chart is in control): Is the mean stable over time?
    • X-Bar 管制圖監控中心 ( 一旦 R 管制圖處於管制狀態 ): 平均值於爭個製程是否穩定 ?
    • >> Bring the R-chart under control, then look
    • at the x-bar chart( 先看 R 圖 , 再看 Xbar 圖 )
  • 45. How to Construct a Control Chart 如何建立管制圖 1. Take samples and measure them. 取樣量測 2. For each subgroup, calculate the sample average and range. 每個群組 , 計算平均值與全距 3. Set trial center line and control limits. 製作解析用管制圖之中心線與管制界限 4. Plot the R chart. Remove out-of-control points and revise control limits. 畫 R 圖 , 移除異常點 , 再修正管制界限 5. Plot x-bar chart. Remove out-of-control points and revise control limits. 畫 R 圖 , 移除異常點 , 再修正管制界限 6. Implement - sample and plot points at standard intervals. Monitor the chart. 管制用管制圖 , 於標準間隔時間取樣 , 監控此管制圖
  • 46. Type 1 and Type 2 Error 第一種與第二種錯誤 Alarm No Alarm In-Control 管制內 Out-of-Control 失控
  • 47. Common Tests to Determine if the Process is Out of Control 管制圖異常之判定
    • One point outside of either control limit
    • 一點超出管制界線
    • 2 out of 3 points beyond UCL - 2 sigma
    • 3 點有 2 點在 2 個標準差或以外
    • 7 successive points on same side of the central line
    • 連續 7 點在中心線之同一側
    • of 11 successive points, at least 10 on the same side of the central line
    • 連續 11 點有 10 點在中心線之同一側
    • of 20 successive points, at least 16 on the same side of the central line
    • 連續 20 點有 16 點在中心線之同一側
  • 48. Type 1 Errors for these Tests 第一種錯誤 Test Probability Type 1 Error 2/3 7/7 10/11 16/20 1/1 2(0.00135) 0.0027 0.0052 (0.5) 7 0.0078 0.00586 0.0059
  • 49. Type 2 Error 第二種錯誤 Suppose  1 >  Type 2 Error =
    • where  (z) denotes the the cumulative probability of a standard normal variate at z
    • Power = 1- Type 2 Error. Power increases as …
    • n increases, as (    ) increases, and as  decreases.
    • Extension to    is straightforward
  • 50.  X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i From Table
  • 51. Factors for Computing Control Chart Limits 管制圖之係數表 Table
  • 52.
    • Type of variables control chart 計量管制圖
    • Interval or ratio scaled numerical data
    • 間距或比率量測數字資料
    • Shows sample ranges over time
      • Difference between smallest & largest values in inspection
      • sample 樣本中最大值與最小值之差
    • Monitors variability in process 間控製程變異性
    • Example: Calculate Range of samples of solder paste;
    • Plot 計算全距並點圖
    R Chart 全距管制圖
  • 53. Sample Range at Time i 某時間間隔之全距 Samples size 樣本大小 From Table 查表 R Chart Control Limits R 管制圖管制界限公式
  • 54. Setting up a X-BAR R Chart 建立 X-bar R 管制圖
    • Take about 20-25 sample groups (n) of the process result.
    • Each sample should contain 4 or 5 observations.
    • For each sample calculate the average and the range.
    • Average all the sample averages = X-BAR.
    • Average all the sample ranges = R-BAR.
    • Calculate the upper & lower control limit for X-BAR
    • Calculate the upper & lower control limit for R-BAR
  • 55. Using an s-Chart Instead of an R-Chart 利用標準差圖取代 R 管制圖
    • S-Charts are used when:
    • Tight control of process variation is essential.
    • Sample size equals 10 or more.
      • a computer can be used to simplify & speed up calculations.
    • Formulas:
    Control Limits for s-Chart Control Limits for X-bar Chart
  • 56. Example: The first 20 days samples are as follows:
  • 57. UCL LCL X-bar Chart
    • Is the process in control?
    • Are the specifications being met?
    • How can we tell if the variability is in control?
  • 58. R-Chart
    • The R chart measures the change in the spread over time.
    • Plot R, the range for each sample.
    • Lower Control Limit =
    • Upper Control Limit =
    UCL LCL
  • 59. Ex: Control “Commuting times” Step 1 Commuting Times (min.) - A.M. WEEK Minutes Xbar = R = Step 2 Step 3 X = 74.6 R = 36 n = 5 UCL L = X + A 2 *R = 74.6 + (.58)*(36) = 95.48 LCL L = X - A 2 *R = 74.6 - 20.88 = 53.72 UCL R = D 4 *R = (2.11)*(36.0) = 75.96 LCL R = D 3 *R = 0
  • 60. Control “Commuting times” (cont.) step 4 Commuting times - A.M. UCL = 95.48 Xbarbar = 74.6 LCL = 53.72 Xbar Chart 1 10 2 3 4 5 6 7 8 9 50 100 75 R Chart UCL = 75.96 Rbar = 36.0 LCL = 0 1 10 2 3 4 5 6 7 8 9 75 5 35
  • 61. Figure
  • 62.
    • Type of attributes control chart 計數管制圖
    • Nominally scaled categorical data 以絕對資料分類
    • e.g., good-bad 如好 , 壞
    • Shows % of nonconforming items 顯示不合格項目 %
    • Example: Count # defective chairs & divide by
    • total chairs inspected; Plot 計算椅子的不良數
    • 除以椅子總檢驗數 , 點圖
      • Chair is either defective or not defective 椅子只有好
      • 與壞兩種
    p Chart 不良率管制圖
  • 63. Setting up a p Chart 建立 p 管制圖
    • Take about 20-25 samples of the process result. Each
    • sample should be large enough to contain AT LEAST 1
    • bad observation. Often for P-Charts samples sizes are
    • in excess of 100.
    • For each sample calculate the percentage of bad units.
    • Average all the sample percentages together, this is P-BAR.
    • Calculate the upper & lower control limit for the P-BAR chart
    • using the following formulas :
  • 64. p Chart Control Limits 不良率管制圖管制界限 # Defective Items in Sample i Size of sample i
    • If individual samples are within 25% of the average sample size then control limits can be calculated using the average sample size :
    • z = 2 for 95.5% limits;
    • z = 3 for 99.7% limits
    • If sample sizes vary by more than 25% of the average sample size then control limits should be computed for each sample.
  • 65. Example: p-Chart
    • M&M Mars wants to institute a statistical process control on a new candy bar. In order to do so, every shift they sample 50 bars and determine the number of defective ones.
    • They obtain the following data:
  • 66.
    • 20 groups of 50 = 1000 samples
    • Total defective = 170
    • p-bar = 0.17
    • UCL = 0.17 + 3 x 0.053 = 0.329
    • LCL = 0.17 - 3 x 0.053 = 0.010
    • Plotting the % defective shows:
  • 67. Identifying Special Causes 確認特殊要因
    • It appears that shifts 4, 7 and 12 were out of control.
    • Upon further inspection it appears that too much water was added to the process in shifts 4 and 7 and that in shift 12 a new operator started.
    • Since each of the out of control points have assignable causes, we eliminate them from the data.
    • The new control chart is then:
  • 68.
    • Now it appears that shift 15 is out-of-control.
    • Further checking shows that the temperature was set too high during this shift.
    • Therefore, we want to eliminate this point so that in subsequent tests we can identify when this occurs.
    • If we eliminate this point the new control chart is:
    Identifying Special Causes
  • 69. Final p Chart
    • UCL = 0.122 + 3 x 0.046 = 0.260
    • LCL = 0.122 - 3 x 0.046 = -0.016 = 0.0
      • (negative control limits should be set to 0)
    • Now they should use this chart for all subsequent sampling until the process changes
  • 70. Determining if Your Process is “Out of Control” 決定你的製程是否在穩定狀態
    • Establish regions A, B, and C as one, two, and three 
    • One or more points fall outside the control limits.
    • 2 out of 3 consecutive points fall in the same region A
    • 4 out of 5 consecutive points fall in the same region A or B
    • 6 consecutive points increasing or decreasing
    • 9 consecutive points on the same side of the average.
    • 14 consecutive points alternating up and down
    • 15 consecutive points within region C.
    A B C A B C
  • 71. Using an np Chart 建立不良數管制圖
    • Np charts for number of nonconforming units. 以不合格品之數統計
    • Converted from basic p-chart 由 p 管制圖演變而來
    • Multiply p by sample size (n). 不良率乘以樣本大小
    • Formulas:
  • 72. Setting up a c chart 建立缺點數管制圖
    • Take about 20-25 samples from the process.
    • Each sample contains 1 unit.
    • For each unit count the number of occurrences for the
    • observation of interest.
    • Calculate the average number of occurrences per unit.
    • This is C-BAR.
    • Calculate the upper & lower control limit for the C-BAR chart
    • using the following formulas:
  • 73. Using an u Chart 建立單位缺點犐赯 ?/span>
    • A u chart is used when the unit size inspected for defects
    • is not constant. In these cases the unit is often referred to
    • as an area of opportunity (n i ).
    • The average occurrence per area of opportunity
    • (i.e. the center line) is calculated as:
    • The same 25% variation rule discussed for p-charts
    • applies here as well. Control limits are calculated as:
  • 74. Figure
  • 75. 425 Grams Mean 平均值 Process Distribution 製程分配 Distribution of sample means 樣本平均值分配 Sample Means and the Process Distribution 樣本平均值與製程分配
  • 76. Process Capability 製程能力 µ , Nominal value 800 1000 1200 Hours Upper specification Lower specification Process distribution (a) Process is capable
  • 77. Process Capability 製程能力 Lower specification Mean Upper specification Two sigma µ , Nominal value
  • 78. Process Capability 製程能力 Lower specification Mean Upper specification Four sigma Two sigma µ , Nominal value
  • 79. Process Capability 製程能力 Lower specification Mean Upper specification Six sigma Four sigma Two sigma µ , Nominal value
  • 80. Process Capability 製程能力
    • Capable
    • Very capable
    • Not capable
    Process variation LSL USL Spec
  • 81. Process Capability C pk 製程能力指數
    • Assumes that the process is:
      • under control
      • normally distributed
    • 假設製程為穩定且為常態分配
    • C pk =min(C pu , C pl )
    • C pu =(USL-µ)/3
    • C pl =(µ-LSL)/3
    Precision 精密度 Capability 準確度
  • 82. Meanings of C pk Measures C pk 量測之意義 C pk = negative number C pk = zero C pk = between 0 and 1 C pk = 1 C pk > 1
  • 83. Statistical Process Control – Identify and Reduce Process Variability 統計製程管制 - 確認並降低製程變異 Lower specification limit Upper specification limit (a) Acceptance sampling (b) Statistical process control (c) c pk >1
  • 84. Quality Control Approaches 品質管制方法
    • Statistical process control (SPC) 統計製程管制
      • Monitors production process to prevent poor quality
      • 監控產品製程以預防不良品質
    • Acceptance sampling 允收抽樣
      • Inspects random sample of product or materials to determine if a lot is acceptable 隨機抽樣檢驗產品或物料以決定此批是否允收
  • 85. Sampling vs. Screening 抽樣與篩選
    • Sampling 抽樣
      • When you inspect a subset of the population
      • 群體批中檢查小批
    • Screening
      • When you inspect the whole population
      • 群體批中檢查全數
    • The costs consideration
    • 成本的考量 , 經濟的原則
  • 86. Acceptance Sampling 允收抽樣
    • Accept/reject entire lot based on sample results
    整個允收 / 拒收是樣品結果為基礎
    • Not consistent with TQM of Zero Defects
    與 TQM 的零缺點不同
    • Measures quality in percent defective
    以缺點百分率測量品質
  • 87. Sampling Plan 抽樣計劃
    • Guidelines for accepting lot 允收批之指導作業
    • Single sampling plan 單一抽樣計劃
    • N = lot size 批量
    • n = sample size (random) 樣本大小
    • c = acceptance number 允收數
    • d = number of defective items in sample 樣本不良項目
    • 之數目
    • If d <= c, accept lot; else reject
    若 d <= c, 允收此批 , 其他則批退
  • 88. Producer’s & Consumer’s Risk 生產者與消費者冒險率
    • TYPE I ERROR = P(reject good lot)
    •  or producer’s risk, too nervous
    • 5% is common
      • 第一種錯誤 = 將好批判成壞批的機率 , 緊張忙亂的錯誤
    • TYPE II ERROR = P(accept bad lot)
    •  or consumer’s risk, absent- minded
    • 10% is typical value
      • 第二種錯誤 = 將壞批判成好批的機率 , 心不在焉的錯誤
  • 89. Quality Definitions 品質的定義
    • Acceptance quality level (AQL)
    允收水準
    • Acceptable fraction defective in a lot
    允許一批中不良的比例
    • Lot tolerance percent defective (LTPD)
    拒收水準 , 批容許不良率
    • Maximum fraction defective accepted in a lot
    允許一批中最大不良的比例
  • 90. Operating Characteristic (OC) Curve 作業特性曲線
    • Shows probability of lot acceptance
    顯示批允收的機率
    • Based on 是基於 :
    • sampling plan 抽樣計劃
    • quality level of lot 批品質的等級
    • Indicates discriminating power of plan
    顯示不同計劃的差異性
  • 91. Operating Characteristic Curve OC 曲線 允 收 機 率 AQL LTPD  = 0.10  = 0.05 Probability of acceptance, P a { 0.60 0.40 0.20 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 0.18 0.20 0.80 { Proportion defective 不良比例 1.00 OC curve for n and c 樣本大小與 c 允收數
  • 92. Average Outgoing Quality (AOQ) 平均出廠品質
    • Expected number of defective items
    • passed to customer
    期望通過客戶之不良項目數
    • Average outgoing quality limit (AOQL) is
    maximum point on AOQ curve 平均出廠品質界限是 AOQ 曲線的最大值
  • 93. AOQ Curve 平均出廠品質曲線 0.015 0.010 0.005 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 AOQL Average Outgoing Quality (Incoming) Percent Defective AQL LTPD
  • 94. Double Sampling Plans 雙次抽樣計劃
    • Take small initial sample
    抽取少量之原始樣本
    • If # defective < lower limit, accept
    • If # defective > upper limit, reject
    • If # defective between limits, take second sample
    • 若不良數 < 下界限 , 允收
    • 若不良數 > 上界限 , 拒收
    • 若不良數界於界限內 , 第二次抽樣
    • Accept or reject based on 2 samples
    允收與拒收是站在此二抽樣樣本上
    • Less costly than single-sampling plans
    比單次抽樣成本低
  • 95. Multiple (Sequential) Sampling Plans 多重 ( 連續 ) 抽樣計劃
    • Uses smaller sample sizes 使用較小的樣本大小
    • Take initial sample 取出原始樣本
    • If # defective < lower limit, accept
    若不良數 < 下界限 , 允收
    • If # defective > upper limit, reject
    若不良數 > 上界限 , 拒收
    • If # defective between limits, resample
    若不良數界於界限內 , 重新抽樣
    • Continue sampling until accept or reject lot based on all sample data
    連續抽樣必需站在所有的樣本資料以決定允收或拒收
  • 96. Choosing A Sampling Method 如何選擇抽樣之方法
    • An economic decision 經濟的考量
    • Single sampling plans 單次抽樣計劃
    • high sampling costs 高抽樣成本
    • Double/Multiple sampling plans
    雙次 / 連續抽樣計劃
    • low sampling costs 低抽樣成本
  • 97.  
  • 98.  
  • 99.  
  • 100.