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Six-Sigma Training Book

Six-Sigma Training Book. Six-Sigma. 數据分布. 數据分布. Continuous Distributions. Normal Exponential Weibull Lognormal t c 2 f. Sampling Distributions. 正態分布. The most widely used model for the distribution of continuous random variable.

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Six-Sigma Training Book

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  1. Six-Sigma Training Book Six-Sigma BPTL Confidential

  2. 數据分布 BPTL Confidential

  3. 數据分布 Continuous Distributions Normal Exponential Weibull Lognormal t c2 f Sampling Distributions BPTL Confidential

  4. 正態分布 The most widely used model for the distribution of continuous random variable. Arises in the study of numerous physical phenomena, such as the velocity of molecules. Plot is known as Probability Density Function of X BPTL Confidential

  5. 正態分布 • Many natural phenomena and man-made processes are observed to have normal distributions, or can be closely represented as normally distributed. • For example, the length of a machined part is observed to vary about its mean due to: • temperature drift, humidity change, vibrations, cutting angle variations, cutting tool wear, bearing wear, rotational speed variations, fixturing variations, raw material changes and contamination level changes • If these sources of variation are small, independent and equally likely to be positive or negative, the length will closely approximate a normal distribution. BPTL Confidential

  6. 正態分布 - 歷程表 • First introduced by French mathematician Abraham DeMoivre in 1733. • Made famous in 1809 by German mathematician K.F. Gauss when he also developed a normal distribution independently and used it in his study of astronomy. • As a result, it is also known as the Gaussian distribution. • During mid to late nineteenth century, many statisticians believed that it was “normal” for most well-behaved data to follow this curve. Karl Friedrich Gauss BPTL Confidential

  7. 正態分布 • 正態分布易于理解, 具有特性, 統計學提供了許多基于正態分布的強有力的分析方法來幫助人們做決定. • 因此, 我們通常會試圖用正態分布去近似模擬其它分布 (如可能) 或轉化數据以“使”它遵從正態分布. • 它是分析過程能力的首選分布形式. BPTL Confidential

  8. Distribution One Distribution Two Distribution Three 正態分布的一些特性 1 • A normal distribution can be completely described by knowing only the: • Mean (m) • Variance (s2) X ~ N(m, s2) What is the difference between the 3 normal distributions? BPTL Confidential

  9. A~Normal(A,A²) B~Normal(B,B²) A~Normal(A,A²) B~Normal(B,B²) B~Normal(B,B²) A~Normal(A,A²) 正態分布的一些特性 What is the difference between process A & B for each case? BPTL Confidential

  10. µ - ¥ + ¥ 正態分布的一些特性 2 • The mean, median and mode all coincide at the same value - m. There is perfect symmetry. If a set of observations is arranged in an increasing order of magnitude (ranked data), the middle value is called the median. • If the number of observations is odd, the median is the value of the middle number. • If the number of observations is even, there are 2 middle numbers, and the median is the average of the 2 values. The mean represents the arithmetic average of all observations in a data set. The mode is the observation that occurs most frequently in the sample. Mean Median Mode BPTL Confidential

  11. 正態分布的一些特性 3 • The area under sections of the curve can be used to estimate the cumulative probability of a certain “event” occurring: µ Point of Inflection m +/- 3s is often referred to as the width of a normal distribution 1s + ¥ - ¥ 68.27% 95.45% BPTL Confidential 99.73%

  12. - ¥ - ¥ - ¥ + ¥ + ¥ + ¥ 正態分布的一些特性 Let’s compute the cumulative probabilities of the following distributions: m = 16.6 s = 2.8 m = 3.5 s = 0.6 20.0 1.8 m = -1.5 s = 0.9 BPTL Confidential -2.8 0.5

  13. 正態分布的一些特性 MiniTab: Calc ð Probability Distributions ð Normal... Enter m value Enter s value Enter x value BPTL Confidential

  14. ? ? 什么是 6σ ? BPTL Confidential

  15. 6σ簡介 BPTL Confidential

  16. The Focus of Six Sigma • Identifying criticalaspects of the business with problems or opportunities for improvement. • Targeting those critical areas and designating improvement efforts as Six Sigma Black Belt projects. • Selecting top people to work on the projects--full time. • Ensuring these people have the time, tools, and resources they need to succeed. BPTL Confidential

  17. Customer Focus: A Model For Success What purpose is Six-sigma ? People Processes Processes People Technology Organization Technology Organization Capability Capability • 商務上的生存競爭有賴于我們多大程度上讓我們的客戶滿意. • 客戶滿意才能体現品質, 价格, 和貨期的意義. • 品質,成本, 准時走貨無不依耐于工序能力. BPTL Confidential

  18. Six Sigma Vision What purpose is Six-sigma ? The Vision of Six Sigma is to delight customers by delivering world-class quality products through the achievement of Six Sigma levels of performance in everything we do. Six Sigma Philosophy The philosophy of Six Sigma is to apply a structured, systematic approach to achieve breakthrough improvement across all areas of our business. BPTL Confidential

  19. Six Sigma - Aggressive Goal What purpose is Six-sigma ?  PPM Process Capability Defects per Million Opp. BPTL Confidential

  20. Statistical Definition of n-Sigma s - n s +n This is the so-called n-sigma m o scale Process Width Design Width Sigma is a statistical unit of measure that reflects process capability. The sigma scale of measure is perfectly correlated to such characteristics as defects-per-unit, parts-per million defective, and the probability of a failure/error. scale LSL T USL LSL T USL scale BPTL Confidential LSL T USL LSL T USL

  21. s - 6 st s - 3 st Statistical Definition of 6σ s + 6 st This is the six- sigma we said m o s + 3 st scale Process Width Design Width scale LSL T USL LSL T USL .001 ppm < LSL .001 ppm > USL scale BPTL Confidential LSL T USL LSL T USL

  22. 6σ - Performance Target Sigma Long-Term Yield Standard 3 Sigma 93.32 % Historical 4 Sigma 99.379 % Current 5 Sigma 99.9767 % Intermediate 6 Sigma 99.99966 % Long-Run BPTL Confidential

  23. The Strategy USL LSL • Characterize • Optimize • Breakthrough T USL LSL T USL LSL T BPTL Confidential LSL’ USL’

  24. Breakthrough Strategy Phase 4: Control The Breakthrough Phases Phase 1: Measurement Characterization Phase 2: Analysis Phase 3: Improvement Optimization BPTL Confidential

  25. The Breakthrough PhasesAnalysis tool and method Dot plot , Box plot, Histogram chart, Pareto chart Capability study ( Cpk) Phase 2: Analysis GR& R study Cause&effect analysis Fishbone and C&E matrix BPTL Confidential

  26. The Breakthrough PhasesImprovement tool and method Set up process Map Improvement Set up FMEA and control Analysis rolled throughput yield …………. BPTL Confidential

  27. 工 序 能 力 分 析 BPTL Confidential

  28. 學 習 目 標 • 工序控制与工序能力 • 工序能力: • 規格, 工藝和控制的界限 • 工序潛力与工序表現 • 短期与長期工序能力 • “6σ” 品質 BPTL Confidential

  29. 工序控制与工序能力 1. 工序控制 • 意即工序運作處于統計控制狀態 , 換言之,普遍的原因是變化的僅有來源. • 鑒于 “用事實說話”,即一個人僅需要用源于工序的數据 來判定工序是處于受控狀態. • 過程的跟蹤表現來証實它是否建立了長時間穩定的數据分布表現,典型地, 用帶有“僅從工序中的數据計算出的”控制圖表 . • “而且一個工序在受控” 并不一定意味著它是一個好工序 . BPTL Confidential

  30. 工序控制与工序能力 2. 工序能力 • “好處” 是工序能力可被度量 • 比較 “工序的現狀” 与 “客戶的要求”, 均須以規格為依据 • 度量一個穩定的工序狀態(受控制)在多大程度上能滿足客戶的規格 . BPTL Confidential

  31. 變化的類型 固有的或定值的變化 • 許多微小又不可避免的原因導致的累積效果 • 只有微小的机會導致變化的運作工序稱為“統計控制” BPTL Confidential

  32. 變化的類型 特定或確定的變化 • 可能由于 a) 不正確的調机 b) 操作者錯誤 c) 有缺陷的原材料 • 一個工序如果出現上面的變化則稱為“失控” . BPTL Confidential

  33. 工序能力 工序能力 研究能: • 顯示工序輸出的恒定性 • 顯示輸出符合規格的程度 • 用于和另一工序或競爭對手比較 BPTL Confidential

  34. b) a) c) 工序能力與規格极限 a) 工序能力高 b)工序能力能夠滿足 c)工序能力不足夠 BPTL Confidential

  35. 三種极限類型 規格极限 (LSL and USL) • created by design engineering in response to customer requirements to specify the tolerance for a product’s characteristic 工序极限 (LPL and UPL) • measures the variation of a process • the natural 6 limits of the measured characteristic 控制极限 (LCL and UCL) • measures the variation of a sample statistic (mean, variance, proportion, etc) BPTL Confidential

  36. 工序能力指數 工序能力的兩种度量: • 工序潛力 • Cp • 工序表現 • Cpu • Cpl • Cpk BPTL Confidential

  37. 工序潛力 Cp指標顯示實際工差 (6)是否超出規格. 公式 BPTL Confidential

  38. 工序潛力 傳統上, Cp有 1.0 時顯示工序能力被判為“有能力考核成績”. • 若數据集中于工程工差內, 將僅有0.27% 的工件會超差. Cp拒貨率 1.00 0.270 % 1.33 0.007 % 1.50 6.8 ppm 2.00 2.0 ppb BPTL Confidential

  39. b) a) c) 工序潛力 a) 工序能力高 (Cp>2) b) 工序能力可 (Cp=1 to 2) c) 工序能力差 (Cp<1) BPTL Confidential

  40. Process is centered Process is not centered 工序潛力 The Cp index compares the allowable spread (USL-LSL) against the process spread (6). It fails to take into account if the process is centered between the specification limits. BPTL Confidential

  41. 工序表現 The Cpk index relates the scaled distance between the process mean and the nearest specification limit. BPTL Confidential

  42. 工序表現 Cpk不良率 1.0 0.13 – 0.27 % 1.1 0.05 – 0.10 % 1.2 0.02 – 0.03 % 1.3 48.1 – 96.2 ppm 1.4 13.4 – 26.7 ppm 1.5 3.4 – 6.8 ppm 1.6 794 – 1589 ppb 1.7 170 – 340 ppb 1.8 33 – 67 ppb 1.9 6 – 12 ppb 2.0 1 – 2 ppb BPTL Confidential

  43. a) b) Cp = 2 Cpk = 1 Cp = 2 Cpk = 2 c) Cp = 2 Cpk < 1 工序表現 a)工序能力高(Cpk>1.5) b)工序能力可(Cpk=1 to 1.5) c)工序能力差(Cpk<1) BPTL Confidential

  44. USL USL LSL LSL 工序潛力与工序表現 (a) Poor Process Potential (b) Poor Process Performance • Experimental Design • to reduce variation • Experimental Design • to center mean • to reduce variation BPTL Confidential

  45. a) b) Cp = 2 Cpk = 1 Cp = 2 Cpk = 2 c) Cp = 2 Cpk < 1 工序潛力与工序表現 BPTL Confidential

  46. ucl ucl lcl lcl 工序穩定性 A process is stable if the distribution of measurements made on the given feature is consistent over time. Stable Process Time Unstable Process Time BPTL Confidential

  47. 短期工序能力与長期工序能力 短期工序能力(previously called short-term capability) shows the inherent variability of a machine/process operating within a brief period of time. 長期工序能力(previously called long-term capability) shows the variability of a machine/process operating over a period of time. It includes sources of variation in addition to the short-term variability. BPTL Confidential

  48. 短期工序能力与長期工序能力 Within Overall Sample Size 30 – 50 units  100 units Number of Lots single lot several lots Period of Time hours or days weeks or months Number of Operators single operator different operators Process Potential Cp Pp Process Performance Cpk Ppk BPTL Confidential

  49. 實戰演練 The length of a camshaft for an automobile engine is specified at 600 ±2 mm. Control of the length of the camshaft is critical to avoid scrap/rework. The camshaft is provided by external suppliers. Assess the process capability for this supplier. The data is available in Camshaft.MTW. Data are collected in subgroups of 5 each. BPTL Confidential

  50. Example 4 Minitab: Stat  Quality Tools  Capability Analysis (Normal) BPTL Confidential

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