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品質控制 ( 統計製程管制 )

國立中山大學人力資源管理研究所. POM2007. 品質控制 ( 統計製程管制 ). Unit 6. 余德成 國立高雄海洋科技大學運籌管理系 2007.5.13. 大綱. 前言 基本的控制模式 TQC SPC 抽樣方法 品質管制方法 More. 前言. TQM 失敗的原因 管理有兩種 連續改善 基本的控制模式. TQM 失敗的原因. 連續改善. Concepts 如何 連續改善 ? 5-Why 改善工具. Concept-1. Concept-2. 如何 連續改善 ?. 5-Why. ?????. 改善工具. 魚骨圖.

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品質控制 ( 統計製程管制 )

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  1. 國立中山大學人力資源管理研究所 POM2007 品質控制(統計製程管制) Unit 6 余德成 國立高雄海洋科技大學運籌管理系 2007.5.13

  2. 大綱 • 前言 • 基本的控制模式 • TQC • SPC • 抽樣方法 • 品質管制方法 • More

  3. 前言 • TQM 失敗的原因 • 管理有兩種 • 連續改善 • 基本的控制模式

  4. TQM 失敗的原因

  5. 連續改善 • Concepts • 如何連續改善? • 5-Why • 改善工具

  6. Concept-1

  7. Concept-2

  8. 如何連續改善?

  9. 5-Why ?????

  10. 改善工具

  11. 魚骨圖

  12. 基本的控制模式 基本概念

  13. TQC

  14. 戴明獎審查檢點表

  15. SPC • 統計製程管制(Statistical Process Control; SPC) • 統計思維(Statistical Thinking ) • 品質特性(Quality Characteristics) • 資料型態(Types Of Data) • 變異型態(Types of Variations) • 統計方法(Statistical Methods) • 抽樣方法(Sampling Methods)

  16. 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

  17. 品質特性 Variables計量值 Attributes計數值 • 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 • 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

  18. 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

  19. 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

  20. 變異的原因 What prevents perfection? Process variation... 何事阻礙完美?製程變異… Assignable Causes特殊原因 Common Causes共同原因 • 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

  21. 產品規格與品變異 • 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!

  22. 共同原因 Average(平均值) Grams (a) Location

  23. 特殊原因 Average Grams (a) Location

  24. 統計方法 • 統計圖表 • 統計分配 • 管制圖 • 檢定 • 迴歸 • 讓資料說話….Know-why

  25. 常態分配 Mean 平均值 -3s -2s -1s +1s +2s +3s 68.26% 95.44% 99.74% The Normal Distribution • = Standard deviation • =標準差

  26. Theoretical Basis of Control Charts Central Limit Theorem Standard deviation 樣本標準差 Mean平均值

  27. 管制圖 Control Charts UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限 1 2 3 Samples

  28. 管制圖 UCL 管制規格上限 1 2 3 Samples

  29. 管制圖 UCL 管制規格上限 Nominal 中心線 LCL 管制規格下限 Assignable causes likely 可能的特殊原因 1 2 3 Samples

  30. 製程管制的三種顯示型態 • 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 Frequency Lower control limit 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 Size Weight, length, speed, etc.

  31. 群體與樣本間之關係 Three population distributions群體分配 Distribution of sample means樣本平均值分配 Beta Standard deviation of the sample means Normal Uniform (mean)

  32. 機遇原因之觀察 At a fixed point in time 固定時間 Over time 連續時間 Target Time Target 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

  33. 製程管制圖 Process Control Charts

  34. 管制圖型態 Control Charts Variables Attributes Charts Charts Continuous 連續的 Numerical Data Categorical or Discrete 離散的 Numerical Data 計量 計數

  35. 管制圖的選定 Quality Characteristic variable attribute defective defect no n>1? x and MR constant sampling unit? yes constant sample size? yes p or np no n>=10 or computer? x and R yes no no yes p-chart with variable sample size c u x and s

  36. Statistical Process Control Steps No Produce Good Start Provide Service Assign. Take Sample Causes? Yes Inspect Sample Stop Process Create Find Out Why Control Chart

  37. 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

  38. X Chart 平均值管制圖 • 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 • 間控製程平均數 • 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

  39. 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 m estimated as the average of the sample means (the grand mean or nominal value)假設製程平均值m與樣本平均值相同 • process standard deviation s estimated by:製程標準差s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/d2, where或樣本平均值/ d2 • sample range R = (Rmax-Rmin), d2 = value from look-up table, 全距為R, d2可由查表得知,

  40. X-bar vs. R charts • 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)

  41. 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

  42. Type 1 and Type 2 Error Alarm No Alarm In-Control 管制內 Out-of-Control 失控

  43. 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

  44. Type 1 Errors for these Tests Test Probability Type 1 Error 1/1 2(0.00135) 0.0027 2/3 0.0052 7/7 (0.5)7 0.0078 10/11 0.00586 16/20 0.0059

  45. Type 2 Error • Suppose m1 > m • Type 2 Error = • where F(z) denotes the the cumulative probability of a standard normal variate at z • Power = 1- Type 2 Error. Power increases as … • n increases, as (m1-m) increases, and as s decreases. • Extension to m1 < m is straightforward

  46. X Chart Control Limits From Table Sample Range at Time i Sample Mean at Time i # Samples

  47. 管制圖之係數表

  48. R Chart全距管制圖 • 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

  49. R Chart Control Limits From Table查表 Sample Range at Time i 某時間間隔之全距 Samples size 樣本大小

  50. 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

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