How to become a Six Sigma Company － An executive briefing for global business.ppt

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How to become a Six Sigma Company – An executive briefing for global business Eden . Chen CTI Group, USA Six Sigma Academy 29 August 2002 Hong Kong 內容大綱 品質管理演進 什麼是6  6  的發展歷史 為什麼 6 很重要 6 的宗旨、目標、效益、成果 6 的行動步驟 6 的流程關係式 6 的特質 如何推動6 ，6從那裡下手 不適合導入6的企業 推動6高階主管的責任 6組織架構 6功能職掌 6 的訓練程序與基本需求及培訓要點 6 的成功關鍵 廿一世紀贏家必備的三原則 品質管理的演進 年代 品質歷史 品質觀念 品質制度 檢查方式 管理方式 檢查規則 作業員的品管 OQC 領班的品管 FQC 檢驗員的品管 IQC 統計的品管 SQC 品質保證QA 全面品質管制 TQC 全面品質保證 TQA 全面品質管理 TQM 品質是檢驗出來的 品質是製造出來的 品質是設計出來的 品質是管理出來的 品質是習慣出來的 QI QC TQC TQM QA TQA 判別式檢查 資訊式檢查 源流式檢查 危機管理 例外管理 目標管理 第三者 下游 下工程 1900 1920 1940 1960 1980 1990 2000 品質可以預防的 6 Sigma 流程品質管理 參變數控制 流程管理 製程管理 什麼是6  品質目標：控制所有流程、產品或服務達到6σ品質水準，意即將缺點或失誤降至為以下 工作哲學：6σ就是要求全面品質保證，所有員工必須建立減少變異及瑕疵之工作態度及思維模式 衡量標準：σ代表標準差，是全世界通用之品質管制方法，σ愈大變異愈小，則其品質愈佳；而6σ要求為良品率達% 公司策略：6σ是有系統的運用及整合品質改善工具，是企業產品品質升級標竿 顧客滿意：6σ設計在於使產品或服務能以數據和量測作確認是否完全符合顧客需求 「品質」是企業生存和發展最有效的途徑 什麼是6 (續) 它是公司的政策 -- 這是對顧客的品質進步的承諾。 這是對公司的品質改善的承諾。 它是改善的工具 -- 這是在訓練和執行改善專案，減 少變異和不良的一個很好用的統 計工具，也是非常有系統的方法 Sigma DPMO 在統計學上 6 Sigma 就是 每百萬個機會僅 允許個不良 2 3 4 5 6 308,537 66,807 6,210 233 美國一般企業水準 我們的目標 6是一個可以獲取、維持和擴大企業成功的彈性系統 6  的前世今生 PDCA SPC 品管七手法 新品管七手法 6  6  VOC DOE BPR 5S QCD 6  的發展歷史(一) 1980年代早期摩托羅拉總裁Bob Galvin在帶領摩托羅拉進行一場品質革命。該公司的可靠度工程師Bill Smith，寫下了最原始的Six Sigma報告並對Galvin簡報。 Galvin正面回應了Bill Smith的熱烈的簡報 摩托羅拉花費超過1億7000萬美元在6  訓練 Galvin個人也全程參與訓練課程 摩托羅拉在美國創辦了第一個6 專案。 6  的發展歷史(二) 摩托羅拉證實在品質與流程方面有重大的改善，使得摩托羅拉成為全球性的公司 Bill Smith和他的同事Mike Harry瞭解到，僅是使用統計工具要達到6  是很困難的。因此他們加入了設計生產化的概念，以健全設計建議規劃。 發現由下而上的訓練績效不彰，因此由摩托羅拉大學接手由上而下的教育訓練。 Harry離開摩托羅拉在Arizona創辦6  學會， 6  因而推展開來。 6  的發展歷史(三) 鑑於摩托羅拉公司的成功案例，奇異公司總裁Jack Welch亦於1996年1月初向五百名高階主管宣佈，要全面執行6σ計畫。 為了落實6σ 推動決心， Jack Welch更於1997年5月發佈命令，將 6σ的「帶」列入奇異主管升遷條件之一。 摩托羅拉與奇異於執行6σ主要差異： 摩托羅拉是局部的，偏重最終產品(End Product) 奇異則是全面的，注重過程(Process) 為什麼 6 很重要 滿足顧客『高品質及低成本』  擁有較小風險  接收高品質的產品  能夠提高顧客最好和最快 的低成本高利益的服務 公司可以獲得『最好的回收』  公司可以維持世界性生產水準  公司可以較佳而且穩定的收入  公司可以被其他共事的公司承認在所 有主要市場具備世界性的領先地位 對中衛廠商提供『成功的新工具』  可以被其他公司承認此中衛體系在 所有主要市場具備世界性的領先地位  提升自己改善自己的產品或服務的 能力  提升自己改善自己的生產力及獲利力 的能力 帶給員工『榮耀與工作機會』  擁有生產高品質產品或服務所需的工 具和資源  擁有擴展自己技術與領導力的機會  能更有條理的處理工作並減少重施工  能擁有在世界一流公司服務的榮耀  能獲得更好的利益 6 Sigma讓每個人都成為贏家 6 的宗旨 真正以客為尊。 管理依據資料與事實而調整更新。 以流程為主，強調管理與改善。 預防管理。 團隊合作。 追求完美，容忍失敗。 6 的目標 全面消除變異與浪費 增進顧客滿足 持續的檢測流程 改善製程能力 降低不良 改變企業文化 建全公司體質 增加收益與提高市場佔有率 以持續改善驅動獲利增加達到永續經營 6 的目標(續) Goal Problem Statement Thought Process Map “Line of Sight” Analyze Improve Control Start Define Measure Critical x’s in Control subject measurement interpretation actions SIPOC Process Map Lean Intro to Variation Quality Concepts FMEA Voice of the Process MSE DOE Results Identify Customers Identify Right Y’s Identify Suppliers Identify Inputs Identify right y’s Identify right x’s Classify x’s Identify Value Add Eliminate Waste Qualify Demand Identify Y Variation Centrality Dispersion Y Capability Z Score Cp, Cpk Prioritize Y Z Score RT Yield Identify Y Failure Modes Failure Effects Assign Severity Identify (x) Causes Assign Occurrence Identify Controls Assign Detection Prioritize Action State of Control in control out of control Detect Components of Variation (Subgrouping) Measurement Variation understood MSE KAPPA INTRACLASS Components detected Identify critical x’s mean sigma Empirical model Control Plans 6 的效益 短期間 頭痛的問題立即解決 鎖定已經存在的問題 鑑定問題對成本的影響 長期間 找出潛在問題 預防潛在問題發生 鑑別潛在的改善機會 投入階層越高與主官的參與越多效果越瘋狂 6 現有成果 Motorola公司 1990年創先發展6  推動四年節省了22億美元 存貨周轉率到2000年增加4倍達到30次 GE公司 1996年投入2億美元，1997年投入3億美元 1998年營運獲利高達%為80年代的兩倍 2001年成為全面6 公司 Honeywell公司 1994年開始推動6  直接由6 產生之成本收益每年約5億美元 6 現有成果(續) 金寶電子公司 1994年組團赴摩托羅拉接受6σ的訓練 預計2002年品質目標達6σ 台証公司 2000年8月開始執行第一個DOE至今，已有效降低電費達35%及縮短開戶時間約46% 榮鋼科技公司 2000年引進6 成果已經開始反應在財報上 漢翔公司發動事業部 1999年至今(2001年)已完成3個Waves訓練 服務水準在2000年內由50%提升到100% 6 的行動步驟 D M A I C QCD P D C A 6 的流程關係式 基本原則：Y 代表產出(outputs)，它可以是策略目標、顧客要求、獲利、顧客滿意度、不良率…等；而 x代表產出(inputs)，它可以是流程變數、行動方案、品質變異及5M1E…等 滿足顧客需求目標 找到真正影響的變數X，並精進改善工作流程 Y = f(x) Y x 6 的流程關係式(續) 如果有效的控制變異 Xi 並需不斷地檢測 Y Y = F( X1, X2, X3,……, Xn) X1, X2, X3,……, Xn Y 隸屬的，相關的 輸出量 結果 徵狀 監督 獨立的 輸入過程 原因 問題 控制 DMAIC Define 界定 界定什麼是最重要的 Measure 量測 量測現在表現如何 Analysis 分析 分析那裡出問題了 Improve 改善 改善錯誤解決問題 Control 控制 控制確保改善成果能持續 DMAIC執行步驟 Define 界定 Measure 量測 Analysis 分析 Improve 改善 Control 控制 正確的問題 正確的人 步驟一：尋找改善機會 步驟二：建立改善團隊設立目標 正確的流程 步驟三：分析量測正確流程的表現 步驟四：訂定流程改善的期望目標 正確的展現 效能 步驟五：找出根本肇因提出改善方案 步驟六：排序、規劃並測試改善方案 步驟七：精進並實現改善方案 再做一次 步驟八：量測進度並維持成效 步驟九：感謝團隊並發表成果 DMAIC常用工具 Define 界定 Measure 量測 Analysis 分析 Improve 改善 Control 控制 圖表 SIPOC 概念流程圖 作業流程圖 柏拉圖 統計上的變異與標準差 前面所用的工具和 製程能力分析 Cp & Cpk 失效模式分析(FMEA) 前面所用的工具和 量測系統評估(MSE) 實驗計畫法(DOE) 回歸分析 魚骨圖 親合圖 風險評估 圓餅圖 前面所用的工具和 管制計畫(SPC) 管制圖 DMADV Define 界定 界定什麼是最重要的 Measure 量測 量測現在表現如何 Analysis 分析 分析怎樣可以表現最好 Design 設計 設計新產品或新流程 Verify 鑑定 進行鑑定驗證改進 如何決定使用DMAIC或DMADV 界定 是否有 現成 流程 量測 連續資料 資料扭曲 量測 鑑定 設計 分析 分析 製程能力 是否良好 控制 改善 DMADV BPR Y N Y N N Y N Y DMAIC DFSS DMAIC及DMADV關係 無 法 控 制 可 以 控 制 製程能力不佳 製程能力良好 DMADV DMADV DMAIC Six Sigma Performance DMAIC及DMADV的異同 DMADV 以顧客滿意為主軸 結合品質關鍵要素 引進新流程或新產品 現有流程可能支離破碎 聚焦在預防產生不良 影響程度不易計量 DMAIC 以顧客滿意為主軸 結合品質關鍵要素 重點在現有流程控制 現有流程有製程能力 聚焦在減少或預防產生不良 影響程度容易計量 6 的特質 全面性 專業性 獨立性 知識性 關聯性 一致性 團隊合作無間 --全面展開 --各專業製程與流程分別展開 --各改善專案可獨立進行 --需隨時補充改善創意新知 --改善成果互相關聯到公司整體表現 --文件管理、表達方式與溝通一致 如何推動6  由上而下逐步建立6 的觀念 成立推動組織 進行一波波的綠帶訓練 建立以6 工具的溝通方式 建立6 的工作環境 培養黑帶團隊 以自己的黑帶培訓現場作業人員 以自己的黑帶持續培訓綠帶 改變企業文化成為一個6 的公司 6從那裡下手 企業轉型 當企業工作模式有了重大改變。 企業策略 改善企業的關鍵策略或營運弱點。 解決問題 企業內的成本、流程改善或問題的解決預防。 跨入6之前的準備工作 評估企業的現況與未來展望--不要太樂觀 公司的策略課題是否明確？ 您知道貴公司在市場上所扮演的角色與價值嗎？ 您知道貴公司所處產業的市場與科技等的變遷驅趨勢嗎？ 公司有可達成的財務與成長目標嗎？ 您知道貴公司的財務是否夠健全？ 公司的願景能被充分的理解與持續傳頌嗎？ 公司內的組織對變動能快速有效的反應嗎？ 公司如何快速反應市場或顧客的需求變動？ 公司內的創新與改善能使公司持續維持競爭優勢嗎？ 公司的前景如何？公司有必要改變嗎？ 6 在維繫及確保企業的成長與競爭優勢。 跨入6之前的準備工作(續) 評估企業當前的績效與處境 公司的整體成效如何？ 您知道貴公司達到獲利及銷售目標了嗎？ 您知道貴公司的良率水準嗎？ 公司能有效重視並滿足顧客需求嗎？ 您知道貴公司瞭解顧客的程度到那個水準嗎？ 公司的服務與產品品質能匹配嗎？ 公司內的營運效率有多好？ 公司常常在忙於解決問題與救火嗎？ 公司內的單位成本有競爭優勢嗎？ 公司的支援流程可以增加公司的附加價值嗎？ 公司有足夠的改善空間讓6  大展身手嗎？ 公司對顧客的認識與衡量系統能有效執行嗎？ 跨入6之前的準備工作(續) 評估企業當前的改善與創新能力 公司的變革管理成效如何？ 您知道貴公司改善措施能相互聯結嗎？ 貴公司有足夠資訊可衡量改善前後的成果嗎？ 公司跨組織功能的流程順暢嗎？ 您知道貴公司同仁都能瞭解整個流程嗎？ 公司對顧客新要求或更嚴格的規範的調適有多快？ 公司內的部門間互動是否良好？ 公司內的現有變革措施能與6 搭配嗎？ 公司現有的創新、改善與變革是否占用了員工心力？ 公司內的現有解決問題方案比6 好嗎？ 公司現有的改善系統，是否足夠用來維持公司的成長與競爭優勢？ 推動6高階主管的責任 先找到強而有力的邏輯依據，要能先說服自己。 不可推諉，規劃並積極參與執行。 營造企業願景並努力當推手。 目標明確，強力推薦，共擔責任。 確實執行衡量，確保落實改善成果。 成效發表與激勵。 6組織架構 6功能職掌 推行委員會--企業負責人與主官(管) 設立基本設施與環境。 檢討並協助專案進展。 協助量化評估對公司的影響。 找出工作中的強弱勢。 排除小組障礙，提供必要資源。 分享作業典範。 6功能職掌(續) 主官(管)或負責人(Sponsor) 設立改善範圍。 核准改善專案。 協助找尋資源。 參與專案會議，管理推展進度。 排除小組障礙，化解跨部門紛爭。 將獲得的知識運用於日常管理上。 6功能職掌(續) 執行領導人(Project Leader) 支援上階領導入，參與溝通。 選定改善專案，領導改善專案。 確認小組成員，尋求外部支援。 支援、激勵與執行，推展專案進度。 安排小組成員訓練，記錄推動活動情況。 執行改善措施與『內部行銷』。 6功能職掌(續) 教練與師傅(Mentor) 參與上下左右的溝通，處理組員爭端。 協助選定改善專案主題與衡量方式。 處理抗拒與不合作人員。 評估成效並驗證成員。 協助小組提供整體效益。 流程擁有人(Process Owner) 提供並管理作業流程。 組員(Team Member) 執行流程的衡量，分析與改進。 6 的訓練程序與基本需求 首重高階主官的決心 + 毅力 現場作業人員訓練 安排一至三天的訓練 主要使大家都能瞭解什麼是6 ？如何善加 利用6 的工具 綠帶訓練 Green Belt (GB) 四週至三個月訓練 教導熟練的在企業內應用6 的改善工具 使授訓者具備初級領導才能與溝通技巧 黑帶訓練 Black Belt (BB) 三至六個月訓練 建立突破性改善的強力領導軍團 建立6 生根內化的種子團隊 6 培訓要點 強調實務--讓企業內人人皆能現學現賣。 案例要結合公司現況。 知 識能不斷累積--先建構一個主要原則與基礎觀念，循序漸進。 多樣化趣味性學習。 學習不只是為了學習--要能創造獲利。 讓培訓成為常態工作。 6 的成功關鍵 6 以與顧客關係密切程度及競爭力聯結關係制定企業策略與優先順序。 6 當成改進管理的方法。 保持訊息簡單與明確。 將6 發展成有自我特色的改善工具。 同時重視短期效應與長期成效。 最高領導階層要負責，公開結果、承認挫敗、記取教訓。 睿智使用工具，投資使它見效。 使學習成為一種常態。 羅溫吉布森-----預思未來 一項不變原則 *永遠保持領先 二項改變原則 *不斷修正 *不斷改善 三項創新原則 *創造新市場 *創造新產品 *改寫產業競爭法則 廿一世紀贏家必備的三原則 報告完畢 敬請指教 If you are interested, please visit our website at The Definition of Quality has Changed Quality was Conformance to Physical Specifications Quality is Exceeding Customer Expectations and Demands Focusing on Manufacturing Control. Responsibility Assigned to Quality Control Departments The Fundamental Pre-requisite to Achieve Customer Satisfaction Core Value and Contribution to the Success of the Entire Company Quality as a Value Market Share Quality -- Reliability -- Durability “Typical” Bathtub Curve Early Failures Fit/Finish Windnoise Water Leaks STR, etc. Warranty Customer Dissatisfiers Fundamentals of Variation Statistical Thinking is Not Terribly Complicated 1. All Things Vary 2. Variation is Measured Using 2 Methods: Variable - Specific Measurement Attribute - Good or Bad 3. Types of Variation Common Cause - Part of the Process Special Cause - Assignable Fundamentals of Variation 4. Common Cause Uniform Pattern Special Cause No Pattern 5. The Output of a System or Process is the Result of Both Common and Special Cause Variation. The Inherent Variation in a Process. What Is “Common Cause” Variation? UCL LCL CL Stable Process What Type of Variation Would You Expect to Find Between the Control Limits? What Are Some Examples of Common Cause Variation? Is it More Difficult to Eliminate Common or Special Cause Variation? How Would You Reduce “Common Cause” Variation? Where Are the Specification Limits? UCL LCL CL Output Results Variation That is Not Part of the Original System, but Which Represents a Change. What Is “Special Cause” Variation? UCL LCL CL Special Cause Problem 6. People can Only Affect What They can Control! Operators Only Influence Their Portion of the Process. 7. Management is Responsible to Make Improvements on Common Cause Variation! Workers are Responsible to Make Improvements to the Special Cause. 8. Reducing Common Cause Variation Requires Different Action than Reducing Special Cause Variation Fundamentals of Variation (Continued) Fundamentals of Variation (Continued) 9. Workers and Managers Alike Want to do a Better Job, they Simply Need to Understand Which Part of the System they can Affect. 10. Data Collected and Presented Using Control Charts is a Basis for Action on the System. Managers Must Know What Action to Take Based on the Variation Patterns. There are Three Kinds of Variation: Common Cause Variation Special Cause Variation Management Variation “Central Tendency” (“Clumping” Tendency) “Dispersion” (“Spreading” Tendency) Values Frequency “SKEWED” DISTRIBUTION “NORMAL” DISTRIBUTION Characteristics of Variation Measures of Central Tendency MEAN = TOTAL OF ALL VALUES NUMBER OF VALUES MEDIAN -- MIDDLEMOST VALUE MODE -- MOST FREQUENT VALUE STANDARD DEVIATION IS- A MEASURE OF DISPERSION THAT USES MORE VALUES THAN DOES THE RANGE. SIX STANDARD DEVIATIONS, THREE IN EITHER DIRECTION FROM THE PROCESS MEAN, WILL ACCOUNT FOR 99-100% OF MOST STABLE PROCESSES. Measures of Dispersion RANGE -- DISTANCE BETWEEN MAXIMUM AND MINIMUM VALUE MAX MIN MEAN Process Dispersion = 6 Standard Deviations = 6s Capability -- the Dispersion of a Process 6s Comparing Dispersion to the Width of a Specification Lower Spec Limit (LSL) Upper Spec Limit (USL) Process Dispersion = 6 Standard Deviations = 6s Specification Width = USL-LSL CR = Capability Ratio = 6s/USL-LSL Cp = Capability Index = USL-LSL/6s PR = Performance Ratio = 6s/USL-LSL Pp = Performance Index = USL-LSL/6s Capability Ratio and Index Describe Stable Processes and May be Used for Prediction; Performance Ratio and Index are Used for Historical Comparisons A Limitation of Ratios and Indices According to These Measures, Process B is as “Good” as Process A! Process A Process B Lower Spec Limit (LSL) Upper Spec Limit (USL) Measures Relating Dispersion and Centering to Spec Limits Lower Spec Limit (LSL) Upper Spec Limit (USL) X - Process Dispersion = 6 Standard Deviations = 6s = Process Mean Cpk, Ppk = Lesser value of USL - X or X - LSL - - 3s 3s THE SEVEN TOOLS OF QUALITY “SEVEN OLD TOOLS” Cause & Effect Diagram Relates causes and effects within a process. Flowchart Displays how a process works Histogram Graphically summarizes variation within a set of data for one characteristic. Scatter Diagram Displays relationship between two variables Control Chart Identifies stability, capability and central tendency of a process Check Sheet Records data on a form that readily allows interpretation of results from the form itself Pareto Chart Displays frequency or cost of events to assist in determining importance X X X X X X X X X X X X X X X X X X X X DECISION PROCESS STEP STOP START 19 4 3 0 5 10 15 20 HOOD ROOF D/L FENDER DOOR 4 4 Operator Machine Number A B 1 2 3 4 Month 7 8 9 Assembly nonconformity Changes in time taken Control error Others Special Cause vs. Common Cause (Assignable & Normal Variation) “Special Cause” “Spill” Not Predictable Some One Thing Changed (Almost Always) “Common Cause” Normal Variation Very Predictable Range of Performance UCL IPTV LCL ~ ~ } } 影響品質最大的敵人是什麼? 減少變異，向目標靠攏是我們努力的方向 變異 VARIATION Aerospace Industrial Development Corporation 6研究討論的是什麼? 如果有效的控制變異 Xi 何需不斷地檢測 Y Y = F( X1, X2, X3,……, Xn) X1, X2, X3,……, Xn Y 隸屬的，相關的 輸出量 結果 徵狀 監督 獨立的 輸入過程 原因 問題 控制 Normal Distribution Normal Distribution (expressed as parts per million) z Z+ Z- ppm Z ppm (area) Z ppm (area) Z ppm (area) Z ppm (area) Z ppm (area) 1,000,000 999,912 894,350 105,650 1,000,000 999,892 884,930 96,801 1,000,000 999,869 874,928 88,508 1,000,000 999,841 864,334 80,757 1,000,000 999,807 853,141 73,529 1,000,000 999,767 841,345 66,807 1,000,000 999,720 828,944 60,571 1,000,000 999,663 815,940 54,799 1,000,000 999,596 802,338 49,471 1,000,000 999,517 788,145 44,565 1,000,000 999,423 773,373 40,059 1,000,000 999,313 758,036 35,930 1,000,000 999,184 742,154 32,157 1,000,000 999,032 725,747 28,716 1,000,000 998,856 708,840 25,588 1,000,000 998,650 691,462 22,750 1,000,000 998,411 673,645 20,182 1,000,000 998,134 655,422 17,864 1,000,000 997,814 636,831 15,778 1,000,000 997,445 617,911 13,903 1,000,000 997,020 598,706 12,224 1,000,000 996,533 579,260 10,724 1,000,000 995,975 559,618 9,387 1,000,000 995,339 539,828 8,198 1,000,000 994,614 519,939 7,143 1,000,000 993,790 500,000 6,210 1,000,000 992,857 480,061 5,386 1,000,000 991,802 460,172 4,661 999,999 990,613 440,382 4,025 999,999 989,276 420,740 3,467 999,999 987,776 401,294 2,980 999,999 986,097 382,089 2,555 999,998 984,222 363,169 2,186 999,998 982,136 344,578 1,866 999,997 979,818 326,355 1,589 999,997 977,250 308,538 1,350 999,996 974,412 291,160 1,144 999,995 971,284 274,253 968 999,993 967,843 257,846 816 999,991 964,070 241,964 687 999,989 959,941 226,627 577 999,987 955,435 211,855 483 999,983 950,529 197,662 404 999,979 945,201 184,060 337 999,974 939,429 171,056 280 999,968 933,193 158,655 233 999,961 926,471 146,859 193 999,952 919,243 135,666 159 999,941 911,492 125,072 131 999,928 903,199 115,070 108 In Excel: ppm = (1-normsdist(Z))*1,000,000 Z=normsinv(1-ppm/1,000,000) Six Sigma Successes at GE From GE Stockholder Report 1998 Estimate SIX SIGMA BREAKTHROUGH IMPROVEMENT TRADITIONAL CONTINUOUS IMPROVEMENT TIME IMPROVEMENT RATE SIX SIGMA VERSUS CONTINUOUS IPROVEMENTS Key Drivers Basic Issues 1. Basic Organizational Capabilities 2. Manufacturing Process Variations 3. Business Process Variations 4. Customer requirements 5. Quality of Specifications 6. Supplier Capabilities Skill-sets and tools required to implement process improvements in businesses are lacking. Lack of product manufacturing process capabilities result in high COPQ (.. Rework, scrap, field failure). Transition of market demands to engineering is poor. Product cost estimation is often wrong resulting in poor financial performance and incorrect manufacturing decisions. Front-end customer definitions/requirements inadequate. Engineering systems and processes for design and documentation are often inadequate and wrong. Specifications sent to suppliers/subcontractors very considerably in their quality, resulting in poor quality parts. Poor capture of design intent. Lack of mature supply base management (.. qualification of suppliers & certification of parts) results in poor quality parts/services, late deliveries, higher part/service costs. Process Input: Business Goals and Targets Select the Right Projects Select and Train the Right People Plan and Implement 6σ Improvement Program Manage for Excellence Sustain the Gains 營收目標為32億 產品成本降低10% Time Delivery Reduction Delivery Inventory Quality Productivity Cost 交貨達成率 >95% 採購成本 降低5% 報廢率 降低5% 製造費 降低10% 實質用人費 降低20% Project 焦距對準Y’s Project Leader 管理階層& Break Belt Process Owner 6σOffice 主計室 審核估算 Saving Project Approval 登錄到6σ system 自動給ID Saving 計算及進度控管 提 供 資 料 提供資料 確認saving金額及彙整報告 審核 確認project完成 確認無其他成本 績效維持否 矯正 追蹤 NO 差異分析報表 Initiate Project Closure 追蹤一年 (每季一次) Project Process Map 8-blocker 估計Saving Project 彙整 Project Approval Team Charter Problem Statement Specific Numeric Goals Time to Complete Potential Barriers Team Members Rule #1: No two objects are alike, therefore, variation exists everywhere! Product performance Service quality Process outputs (y’s) Concept of Variation The philosophy of Six Sigma is to reduce variation. Rule #2: Variation exists in two states of control: Controlled: referred to as common cause, is a stable or consistent pattern of variation over time (predictable) Uncontrolled: referred to as special cause, is a pattern that changes overtime (unpredictable) Rule #3: To control and reduce variation you must first understand, quantify, AND interpret variation in a data set. Statistics to Understand Variation How do we understand and quantify variation? We use the science of statistics. What is statistics? Statistics is the science of collecting, analyzing, presenting, and interpreting data. How statistics help in understanding and quantifying variation? Statistical methods and tools are used to effectively determine Y=f(x): 1) Transform data from a state of random & miscellaneous nature to orderly and cumulative knowledge. Quantify Y’s 2) Quantify cause & effect relationships. Quantify x’s on Y’s 3) Inferential measuring tool. Confidence in the influence of the x’s over time Concepts of Data Data are observations made upon our environment. Examples: individuals, customers, processes, products, services, times, events. (Note: Data described in terms of numbers eliminates ambiguity.) Data are raw material used to interpret reality and must be in context. Contains at least 2 values (also known as variables) Defined and interpreted equally by all observers Able to take action on data Data is classified into two categories: qualitative quantitative What are data? Data is a key source of information. Qualitative Data Qualitative data characteristics: A minimum of 2 variable values or representation of 2 variables exist. Examples: Can assume a finite number of variable values. Usually exists in integer form. Representation of variables can be ranked or non-ranked. Examples: No meaningful information exists between variables. Qualitative data is commonly referred to as attribute data. 1,0 Pass/Fail on product tests Win/Loss on marketing process Agree/Disagree on customer survey Number of product defects Number of customer requirements Numerical (1to 5, -1 to 1-, 0 to 100) Ranked: On product performance: excellent, very good, good, fair, poor Salsa taste test: Mild, Hot, Very Hot, MMS (makes me suffer) Customer survey: strong agree, agree, disagree, strongly disagree Non-Ranked: In a company: Dept A, Dept B, Dept C In a shop: Machine 1, Machine 2, Machine 3 Types of transportation: boat, train, plane Data: Quantitative Quantitative data characteristics: Data can potentially take on any value. Examples: Numeric values have equal units of measure. Examples: Meaningful information exists between variables. Dimension of time Length of feature Interest rates , 1/4. 20, , 1,000,000 Fahrenheit and Celsius for temperature Calendar years Program task calendar Length in inches Minutes for time duration Frequency count like defects per unit Percentage number as in market share Quantitative data is commonly referred to as continuous data. Data Summary Data Qualitative (attribute) Quantitative (continuous) Minimum of 2 variable values Finite number of variable values No information between variable values Potentially any value Values have equal units Information exists between variables Quantitative (continuous) data yield the most information. Project Information Continuum Low High Data Impact on Project The lack of data is a failure mode in project completion success. Without data, decision for actions to implement are at risk: Makes situation worse Incurs unnecessary cost Decreases customer satisfaction If you cannot collect data, and money cannot be spent to collect data, the value of the project is in question. Data Set Evaluation Begin by asking three simple questions: What variable value occurs most? What variable is the midpoint? What is the spread of the variable values? How do you extract knowledge from a data set ? To answer the questions, look at the frequency distribution, which is a count of how frequently a variable value occurs within a data set. Frequency Table A frequency table is used to condense and summarize a set of data. The table contains the elements of class interval, midpoint, frequency, and relative frequency. Class Interval is range of variable values used to tally the count or frequency of occurrence. The number and size of the class intervals are dependent on: Number of Classes - Generally between 5 and 20 classes are used Note: Rules to create interval classes include : 1) Easy for reader to interpret 2) Narrow enough to reveal interesting detail 3) Wide enough to show data “pile up” 4) Coincide data with interval midpoint Boundary Values - where “no-overlapping occurs” of variable values Width of Each Class - choose the same width for each class. The choice of number of classes and the width are dependant. Approx. Class Width =Max. Data - Min Data Number of classes Brigade Field Exercise Data of 50 Shots (Inches) EXAMPLE 12 classes chosen Decimal values from to to prevent overlap Width of class set at 1 inch Frequency Table (cont.) Midpoint is the middle of the class interval. Frequency is the count of occurrences within the class interval. (Note: frequency should sum to total data set) Brigade Field Exercise Data of 50 Shots (Inches) EXAMPLE Midpoints are 102,103, etc… The number of times values fall within interval are counted and listed. The Rf is calculated based on a total quantity of 50. Relative frequency (Rf) is the occurrence as compared to the entire set of class intervals. R f = Frequency Qty in Data set (Note: Rf always sums to ) Frequency Table (cont.) Brigade Field Exercise Data of 50 Shots General Rules to Form Table 1) Determine the largest and smallest numbers and find the difference between the two numbers. 2) Divide the difference found in step 1 into a convenient number of class intervals. (Note: Usually between 5 & 20, try to coincide midpoint values to reduce assignment errors.) 3) Check to make sure boundary values do not coincide (overlap) with data set values. 4) Assign frequency of occurrences to the intervals using a tally or score sheet. Compare totals as a check. 5) Calculate Relative frequency. Method The Histogram A histogram is the graphical representation of a Frequency Distribution. Brigade Field Exercise Data of 50 Shots Histograms show general shapes: > Symmetry > Clusters > Spreads > Gaps > Outliers Are used to graph counts, frequency, and/or relative frequency data (Usually on the vertical (y) axis) Show possible data values as class intervals. (Usually on the horizontal (x) axis) Help facilitate class interval sizing appropriateness. Shows for each bar the frequency at which the data set value falls within the interval. Frequency Distribution Shapes Poisson Normal Skewed Normal Exponential Uniform 5 COMMON SHAPES Each distribution has a mathematical definition. Matching data sets to shapes is key to analysis. Most data sets fall within a normal shape. This module focuses on Normal Distributions. Measures of Central Tendency Measures of Central Tendency are a common set of measures that describe the location or “clustering” of the variable values. They answers the question: Where does the average or location of the population “tend to center?” The three common measurements of central tendency are: Mode Median Mean The Mode The mode is the data set value(s) that occurs with the greatest frequency. Attributes and Uses Useful for Qualitative type data. Quick look for cluster. > Unimodal > Bimodal > Multimodal Limited properties for additional analysis. Brigade Raw Data MODE EXAMPLE When the data are arranged from the highest to lowest value, the median is the midpoint value in the data set. The Median Attributes and Uses Good estimator when extreme data set value exists. Works for undetermined values. Limited properties for additional analysis. 1) Data sorted from low to high 2) Since data set qty is 50 (even) 25th & 26th values selected 3) The median is: The sum of the values 2 = 107 EXAMPLE Brigade Raw Data If the data set contains an odd quantity of values, the median is the value of the middle variable If the data set contains an even quantity of values, the median is the average value of the two middle variables The Mean The mean, is the sum the of values, divided by the quantity of variables in the data set. Sample Mean = X = X i  i = 1 n n Attributes and Uses Accounts for all numerical values in data set Sum of distances above mean equal sum of distances below mean Susceptible to extreme outliers in data sets Basic building block for statistical analysis The Sum of The Values Total Quantity Of Values = 5351 X = 50 = EXAMPLE Brigade Raw Data n = quantity of observations in the data set xi = ith data value Measures of Dispersion Dispersion has three common measures: Range Variance Standard deviation Dispersion is the degree to which the data tend to spread about the mean. Dispersion answer the question: What is the “spread of the data set”? Spread Range Range= R = Xmax - Xmin Attributes and Uses Simplest measure of dispersion or variation. Does not account for each numerical value. Most affected by extreme scores. Affected by sample size, validity strongest for small data sets (fewer than ten.) Simple to calculate (no need for calculator or Excel.) Provides “rough” estimate of variation. Range is the difference between the largest and smallest data set values. 1) Data sorted from low to high 2) Select lowest value 3) Select highest value 4) Calculate: Range = r = 113 - 102 = 11 EXAMPLE Brigade Raw Data The variance is the sum of the difference between each data set value and the mean divided by the number in the sample minus 1. Uses Used to compare the amount of dispersion in two data sets. Large variance = more dispersion. Determine “critical x’s” for Y’s. The Variance Where :  (Xi - X)2 = Deviation for each data set value n - 1= Total data set size - 1 NOTE: For values of n> 30, use the value of n. EXAMPLE s 2 = Brigade Raw Data The Variance (cont.) STATAPULT “A” STATAPULT “B” Statapult A’s variance is smaller than Statapult B’s. Standard deviation is the positive square root of the variance. Recall that the sample variance for the data is The standard deviation = s = inches Taking the square root of the variance, the inches2 unit is converted to inches. This makes the units the same as the original data making more sense and making it easier to compare. The Standard Deviation Brigade Raw Data EXAMPLE s = s = ( X i - X ) 2 S i = 1 n n - 1 Standard Deviation, known as the standard measure of dispersion, is approximately the average distance a data set is from the mean. ^ s = inches 2 2 ^ ^ The Standard Deviation (cont.) In practical terms the standard deviation answers the questions: 1) What is the spread of the data? 2) How does this data set compare with other data sets? Activity Breakout For the data noted below, find the elements of centrality and dispersion. MODE: _______ MEDIAN: _______ MEAN: _______ RANGE: _______ STD DEV: _______ VARIANCE: _______ Calculate Centrality and Dispersion Normal Distributions and Z-Score The Normal Distribution % of the time, a normal random variable assumes a value within plus or minus 1 standard deviation of its mean. % of the time, a normal random variable assumes a value within plus or minus 2 standard deviations of its mean. % of the time, a normal random variable assumes a value within plus or minus 3 standard deviations of the mean. The normal distribution is a symmetric, continuous distribution with the mean at the center. Attributes of Normal Distribution Precise mathematical definition Applies to most data sets Area under curve represents probability of random variable Point of Inflection* 1s +5 +6 +2 +3 +1 +4 -1 -5 -4 -6 -3 -2 - ¥ + ¥ Total area under the curve =100 % * Slope change in curve % % % m Applying Normal Distributions Using a theoretical normal distribution and knowing that the area under the curve represents 100% of the observations, we can answer the questions: 1) What percentage of observations will occur for any value ? 2) What is the relative location of an observed value? For instance, where does a specification value lie with respect to the distribution? Data sets all have different values of variables, means and standard deviations.  A s = 34 s=3 B Z - Score is a simple method that transforms the data into a single numeric value. Z-Score A method that expresses a variable as a number of standard deviations from the data set mean. Z = Observed variable minus the mean value Standard Deviation of the values Z = s Xi - µ s= m 0 1 m s EXAMPLE Attributes Has  = 0 and s = 1 Locate any variable relative position Area symmetric around the mean A (+) Z is above (to the right of) Mean A (-) Z is below (to the left of) Mean Standard tables for probabilities Compare scores of different distributions Determine defects with customer specifications From the Brigade Data The target for the exercise was set at 111 +/- 1 inches. What is the Z-Score for the the minimum spec value and target? FOR minimum Xi = 110,m = ,s = Z distribution Z = 110 - = FOR Target Xi = 111,m = ,s = Z = 111 - = 110 111 Z-Score or or s ^ Xi - X Xi - X S Applying Z-Score The practical implication of the Z-Score is the relationship to what the customer may see! m s Customer Upper Spec Value acceptable DEFECT EXAMPLE: Let’s assume that the two Z-Scores calculated in the last example represent the two different customer upper specification values. What would be the approximate probability of defects (p[d]) for the two Z-Scores? For Z= the p(d) approximately 159,000 PPM For Z= the p(d) approximately 66,000 PPM Data Spread / Centering Large Spread Desired Current Situation LSL USL T Accurate but not precise Data exhibit three types of problems which can impact performance: 1) Large Spread; 2) Not Centered; and 3) Large Spread and Not Centered. Current Situation Desired Not Centered LSL USL T Precise but not accurate EXAMPLE For the exercise, the specification for the 50 shots was set for 109 +/- 3 inches. LSL USL T s= m 109 106 112 From the Brigade Data What problems need to be addressed? Time Impact on Variation Studies show that over time, variation increases +/- due to shifts of the mean. The shift results from changes of inputs (x’s) over time. Action Determine the short or long term by considering: s The length of time in the data set Number of set ups/methods Changes in material Different manpower Different machines Measurement changes Mother nature changes Sustained Capability of the Process LSL USL T Long-Term Performance Short-Term Performance Dynamic Mean Time 1 Time 2 Time 3 Time 4 Process Capability Ratios Cp Compares the width of the data set variation to the width of the specification. Cpk The minimum calculated value when comparing the data mean and standard deviation to the specification upper and lower values. Both the Cp and Cpk ratios should be calculated and reported. However, indicators to understanding the capability can be acquired using only the Cpk ratio. Process capability ratios compare the data set variation to a set of specifications. Cp and Cpk are two statistics used to define process capability. Compares the width of the data set variation to the specification width. Cp = USL - LSL 6 Cp - Process Capability Ratios LSL Process Width Specification Width USL T +3  -3  X Attributes Assumes process mean on specification target Cp= industry standard 6 Sigma goal Cp = Cp The minimum calculated value when comparing the data mean and standard deviation to the specification upper and lower values. Cpk - Process Capability Ratios LSL USL T s X Attributes Cpk < considered poor 6 Sigma goal: Cpk = for short term data Demonstrated sustained long term Cpk values > , consider eliminating measurement min (USL - X, X - LSL) Cpk = 3 Cpk Process Capability Ratio Table Most data tables have Sigma shift LSL USL T s= m 109 106 112 Activity Breakout Process Capability Ratios For the figure above: 1) Calculate the Z-Score and capability ratios. 2) Approximate the probable defects Z-Score ________ Cp ________ Cpk ________ Defects: __________ From the Brigade Data Summary No two objects are alike. Therefore, variation exists everywhere. To control and reduce variation, you must first understand, quantify and interpret variation in a data set. Data exist in two types: qualitative data, usually referred to as attribute; and quantitative, usually referred to as continuous.. Linkage of data is the key to success of a project. Measures of centrality and dispersion quantify data sets. Z-Score is a measure that quantifies the impact of customer specifications and provides insight into the probability of defects. Studies show that over time, variation increases +/-  due to changes in process inputs. The variation increase results in changes over time. Cp and Cpk are measures that quantify the impact of customer specifications and provide insight into the probability of defects. The next step on your path is to identify the “state of control” for a data set. (See rule #2 in Concepts of Variation). In Quality Concepts you will learn how to work with qualitative data and integrate with Z-Scores from continuous data. In Voice of the Process (Control Charts) you will continue to discover the influence of time and it’s relationship to centrality, of dispersion and control. Defects per Unit (DPU) allows you to compare defects from different samples, failure modes or process steps. Defects Per Unit (DPU) and TDU TDU = DPU1 + DPU2 + DPU3 + ... Total Defects per Unit (TDU) is the sum of all DPUs for all parts in an assembly, or all steps in a process flow diagram. DPU = Number of Defects Number of Units at the Beginning of the Process or Process Step Yield represents the units that emerge from a process step without incurring a defect. Yield Yield can also be calculated directly from DPU. Yield is also referred to as percent yield. Yield = Number of Satisfactory Units Total Number of Units % Yield = Yield * 100 Yield = 1 - DPU Rolled Throughput Yield (RTY) is the probability that a product will pass through the entire process without rework and without any defects. RTY= Y1 x Y2 . . . Yn (n = number of process steps) The M&M Exercise: Form Chocolates Coat Pieces Stamp M’s Start Bag & Ship Y1= ______ Y2= ______ Y3= ______ RTY = Y1 x Y2 x Y3 = ______x______x______ = _______ Rolled Throughput Yield (RTY) An action during a process step Cutting material in a machining operation Filling out a data form Making a handoff A specific feature A part dimension is in or out of spec A failure mode has or hasn’t occurred A field of information is or is not completed correctly Examples of opportunities: Opportunities An opportunity is any chance to create a defect. Some guidelines for counting opportunities: Understand how the information will be used Who will see the information? What will they do with it? Be consistent Agree on a standard method for counting opportunities early in the process, and use the same method over time to track improvement. Document the method, and be prepared to defend it. Opportunity counting is subjective: Internally, you may see many opportunities for creating defects. An external customer will see only one opportunity for a defective part, product or process. WARNING! Different counting methods will result in different s’s. Issues in Counting Opportunities DPMO allows defect data from products and processes of varying complexity to be compared against one another. Overall Process Quality Metrics Defects Per Million Opportunities (DPMO) DPMO can be calculated from DPU: DPMO = # of Defects # of Opportunities X 1,000,000 DPMO = DPU X 1,000,000 # of Opportunities/Unit where m is the process mean s is the process standard deviation m USL ZUs LSL s ZLs DPMO DPMO Sigma Score(Z) The Sigma Score (or Z-Score) is the number of standard deviations between the mean and the closest specification limit. Sigma Score (Z) vs. DPMO Conversion Table Note: This table includes a shift for all listed values of Sigma (., represents short-term Sigma & long term DPMO) Also, DPMO assumes a single-sided test. Sigma Score (Z) vs. DPMO Conversion Table Note: This table includes a shift for all listed values of Sigma (., represents short-term Sigma & long term DPMO) Also, DPMO assumes a single-sided test. Why Six Sigma is the Goal For complex products and systems, 6s is necessary to produce and perform defect-free more than 90% of the time. Impact of Complexity on Rolled Throughput Yield 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 Number of Parts/Process Steps Rolled Throughput Yield 4s 5s 6s There is an optimum quality level beyond which the costs of quality improvement exceed the expected cost savings from a reduced number of defects. Answers will vary for individual processes Product Scorecard is only one tool used to make this decision Business models, customer needs and cost must also be considered Cost Sigma Optimum Impact of Quality Level on Cost Determining a Desired Sigma for Your Process * * * * Quality is a value, more than a thing -- a value by which we operate. Quality underlies all of the following: Organizational focus Leadership Responsibility Focus on the Customer Corporate Wide Effort Global Reputation Stretch Targets Market Share Revenue Growth * Quality is fundamentally very simple. It consists of: * working on the right problems * using the right tools to work on those problems Quality, Reliability and Durability are Three Distinctly Different Phases of Quality. QUICK EXERCISE: The Assembly Plant has the Most Influence on (Circle One) A. Quality B. Reliability C. Durability D. All Three Remedial Engineering has the Most Influence On (Circle One) A. Quality B. Reliability C. Durability FTQ Gates are a Measure of (Circle One) A. Quality B. Reliability C. Durability * NOTES * A stable process will tend to generate a distribution with a uniform pattern. Often that pattern is the “bell shape” of the Normal Distribution. Sometimes, as with ranges and with most attribute data, the pattern may not be symmetrical. The key point is that a stable process, one in statistical control, will generate distributions with a relatively consistent pattern, whatever it may look like. * All things vary, so all processes have variation. Common cause variation is due to random differences or fluctuations in the major process variables. Thus, ambient temperature and humidity, part orientation, presence of small “burrs” in fastener threads, air tool orientation, air pressure, time to perform an operation, and the like all may contribute to measurable differences in the quality characteristics of a part, subsystem, or vehicle. * Variation characteristic of a stable process allows for prediction. If variation indicates a stable process, then judgement can be made on whether to change the process to meet requirements. Data from a stable process forms a baseline against which later data can be compared to judge the success of “breakthrough” process improvement efforts. If a process is not stable then a prediction can not be made (except for some processes whose cyclical behavior is caused by known special causes). You are at at the mercy of the process and react. The process manages the person instead of the person managing the process. STABILITY IS NOT A FUNCTION OF CAPABILITY DON’T CONFUSE STABILITY AND CAPABILITY * Dr. Deming claimed that a stable process was an “achievement”. It is stated that 95% of industrial processes are out-of-control -- not stable, due to the operation of one or more “special causes”. Special causes are changes from the usual operation of a process. They are generally unpredictable. The variation from special causes is not part of the predictable pattern of variation in a process. Although a system affected by common cause variation only can be expected to maintain a predictable variation pattern, it is usual for a process to become subject to special causes. This is why a stable process is an “achievement”. * NOTES * NOTES * Poor Management decisions result from not understanding the source of variation. Probably the most common management inappropriate action is tampering with the system. * NOTES * This chart displays two distributions of data for a particular characteristic. The characteristic could be human height, fender-to-hood gaps, the number of spelling errors made in a standard report, etc. Each “block” represents a different measured value of the characteristic. Going towards the right of the chart the values -- heights, shoe sizes, numbers of mistakes made, etc. -- increase. Frequency is indicated by the number of “blocks” in a particular column -- the “height” of the column. The more “blocks” in a column, the greater the height of the column in the overall distribution, the more cases of that particular measurement in the distribution. Data tends to differ. Data tends to “spread out” from a “center of gravity”. The “spreading tendency” is termed “dispersion”, and the “gravitational tendency” is named “central tendency”. The distribution formed by these two tendencies is so often a symmetrical “bell-shape” that is labeled “Bell Curve” or “Normal Distribution”. This is particularly common for many distributions generated by variable data. Attribute data often forms distributions in which the pattern is not a mirror-image “bell”, but the pattern is “skewed” to one side or the other. The slope of one “tail” is more gradual, more like the “bunny run” on a ski slope than the steep slope of the bell curve. For some distributions a “skewed” pattern rather than the “normal distribution” is “normal”, representing the behavior of a stable process, one affected by only common causes. Both variable and attribute-generated distributions possess the properties of central tendency and dispersion. * The mean is the most widely used measure of central tendency. The mean is the sum of all observations in a sample, divided by the number of observations. The mean can be affected by extreme values. The median is the “middlemost” value in a sample. To find medians when faced with an “even” number of samples, the two “middlemost” numbers are averaged. Note that the presence of “outliers” will have less impact on the median than on the mean. The median is sometimes a better measure of where more of the values lie than is the average. The median is also usually easier to find, as it does not involve a lot of calculations. The mode is the most often occurring value in a sample. The mode is the easiest measure of central tendency to find, because visual inspection can be used. Sometimes a distribution will have more than one “mode” or “high point”. This can happen when the distribution actually represents the data from two processes. * Range is the difference between largest and least numbers in a sample. Find the range by simple subtraction. The range does not consider the pattern of variation within the spread of the numbers. The range is the same whether the numbers between the largest and least arrange themselves in a bell-shape or any other pattern. Standard deviation is a measure that focuses on variations within the spread of the numbers. More specific definitions of the standard deviation are rather technical, and sometimes prone to challenge. Usually, we have to estimate the standard deviation, or sigma, from sample data, and for formulas that vary. Six standard deviations -- three in either direction from the average -- account for 99-100% of the variation in most stable processes. If the mean and standard deviation of a normally-distributed process are known, a very accurate view of what that process looks like may be developed. * 1) Capability as the dispersion of a process In its “purest” sense, “Capability” refers to the dispersion of a process, without regard to any specification. It is the expression of the Voice of the Process. The dispersion of a process is estimated by using the standard deviation. Walter Shewhart found that a six standard deviation-wide zone encompassed 99-100% of the individual measurements or results in most stable distributions. This discovery came not as a result of abstract theory, but experience. It became the basis for Shewhart’s development of the control chart, which is fundamental to statistical thinking. In most cases we have to estimate the standard deviation. For processes whose stability is unknown, a formula is used which employs all of the data in whatever sample is available. The formula also includes a “fudge factor” which causes the result to be somewhat greater than the dispersion within the sample itself. Where the process shows stability as shown by control charts for variables, the estimate of the process standard deviation formula can be more simply figured. An average dispersion value from a range or standard deviation chart is divided by a factor from a table. This procedure gives satisfactory results from less computations “Pure” capability is not used as much as the other measures which compare the process to some kind of specification. * 2) Comparison of dispersion to the width of a specification Most capability ratios compare what the process is and does to some requirement; they compare the Voice of the Process with the Voice of the Customer. These measures form a ratio, either by dividing the 6 standard deviation dispersion by the width of a specification, or the inverse. Capability Ratio (CR) is the inverse of Capability Index (CP). They are used for stable processes, and represent the “best” that the process can do. As such, they can be used for predicting future behavior. A “good” Capability Ratio would be less than 1; a “good” Capability Index would be greater than 1. However, statisticians usually demand CRs of less than .75 and CPs greater than . Performance Ratio (PR) and Performance Index (Pp) are inverses, and are used when the process is unstable. They represent what the process has actually done, its total variation, including times when it was affected by outside factors. These measures may be useful in evaluating a supplier’s past performance, for example, as evidence for their dedication to process control. Performance measurements can also be compared to the two Capability measurements for a process while it was stable. If there is a considerable difference, this would strongly argue for process improvement. * However, “good” capability or performance ratios or indices do not mean that the process is actually performing well. These measures just relate the process’ variation to the tolerance width. There is no question here of where the process is actually centered. A “good” process seen only from this perspective could have some of the processes’ output out-of-specification, such as shown by “Process B” in this example. There could even be a “Process C”, whose distribution was totally outside the specification limits, but which would be “good” from the standpoint of these measures. * 3) Comparison of both the dispersion and central tendency of a process to specification limits. Cpk is used for stable processes, while Ppk is used for processes that have been affected by instability. The value for the estimate of the standard deviation for Cpk uses the control chart formula, while the value for the standard deviation for Ppk uses the more involved calculation. In both of these cases, the standard deviation measurement is multiplied by 3 instead of 6, hence the “3s” used in the equations on the slide. A “good” measurement value for these measures will be over 1, which means that even where the average is nearer to a specification limit, at least three standard deviations of the distribution are within specification. However, we demand values in the realm of or better or even or higher for some processes, especially from our suppliers and where we are specifying the best that the process can do, rather than total process variation. A value of less than one means that in at least one “tail” of the distribution, less than three standard deviations of the distribution are in-specification. When a negative measurement value is reported, this means that the distribution average itself is out-of-specification. * The leader must help ensure the accurate and unbiased use and interpretation of these tools. * It is important to distinguish between special and common cause problems in terms of what can be expected from either source of variation. Remember that a “point out” is only one example of a signal of “Special Cause” variation! * * * 23 * SAY: On the last overhead we saw that at the starting point for your project there are questions that need to be answered. One of the tools we use to answer these questions and define the project is a “Team Charter”. Here are the basic components of a charter. * The first concept is the Concept of Variation REVIEW THE 3 RULES: Rule 1: READ & ASK THE CLASS IF THEY AGREE Rule 2: READ AND SAY: this rule will not be address in this module. We will address this very important rule in Voice of the Process Module Rule 3: READ AND SAY: this module will provide context to help you understand the components of variation, provide the methods to quantify the variation, and then introduce terms to interpret what the variation “means” from two perspectives of 1) Opportunities for improvement and 2) Impact to the customer * Now that we have defined the concept of Variation, How do we understand, quantify and interpret Variation? We use the science of Statistics. Before we go any further, this module is not intended to make YOU FOLKS statisticians. The intent is to make you aware of the power found within the use of statistics. You are expected to able to collect, analyze and quantify variation with simple calculations. If you have problems with the concepts, let your mentoring BB know and they will help you. Statistics has the methods and tools to determine the Y= f (x) It has the ability to Quantify Y’s Quantify x’s on Y’s Establish a confidence of the influences of X’s on the Y overtime * The final concept we’ll define is the concept of DATA. But, What is data? Data are observations made upon our environment. Examples are listed: Data are also raw material used to interpret reality AND MUST BE IN CONTEXT We define context as: contains at least 2 values , also known as VARIABLES Data must be INTERPRETED EQUALLY BY ALL OBSERVERS It is ACTIONABLE And last key point: Data is classified either as QUALITATIVE or QUANTITATIVE, which we will discuss in the next two slides THE KEY POINTS about data is recognizing that it is a key source of information our ability to extract knowledge from it lies within the context of data and applying SIMPLE statistical methods. * We’re now going to briefly define the terms Qualitative and Quantitative and show a comparison on a knowledge continuum scale. Characteristics of Qualitative Data are: a minimum of 2 variable values or representation of (note examples) can assume a finite number of values, usually in integer form representation can be ranked or non ranked (note examples) AND NO meaningful information exists BETWEEN variables NOTE: DRAW A SCALE AS BELOW FINAL POINT: Qualitative data is commonly referred to as ATTRIBUTE data. Meaningful information No meaningful information between values Additional notes Not ranked Representation of values (colors and temperature) Ranked Numeric Red Frozen 1 Orange Cold 2 Blue Mild 3 Green Hot 4 Purple Fried 5 * Now that we’ve defined qualitative, let’s defined quantitative data Characteristics of Quantitative data are: .data can potentially data on any value SEE EXAMPLES .values are numeric and have equal units of measure SEE EXAMPLES .meaningful information exists BETWEEN variables RETURNING TO THE DRAWN SCALE: FINAL POINT: QUANTITATIVE data is commonly referred to as CONTINUOUS data. 1 2 3 4 5 Meaningful information Meaningful information between values ADDITIONAL NOTES Ranked is implicit ALWAYS NUMERIC * In summary, Data is classified into two type or categories The distinction of the types lie within the context of information and knowledge. Data of a qualitative type yields a low rating on an information continuum scale. An opportunity exists to transform qualitative data into a quantitative type. If your data is qualitative type see your mentoring BB on ways to transform into a quantitative type * Your effort on these projects to make improvements. If you don’t have any data then you are in a failure mode to complete your project either in a timely manner or to reach your goals. Data is the foundation of taking the right actions. Without data the chance of your success is limited. You have to ask yourself then your chartering manger if you cannot collect data, and investment of resources are not appropriate, then the value of your project comes into question. * Now that we understand data concepts and the nature of our project data, How do we begin to extract knowledge from a data set? We begin by asking three leading questions: READ FROM SLIDE To answer the questions we’re going to introduce FREQUENCY DISTRIBUTIONS, which is simply a count of how frequently the variable shows up in the data set. * NOTE: Frequency tables presented over the next 3 slides are provided as an overview to acquaint the student to it’s terms, method, and it’s linkage with histograms. Since current software packages automatically establish tables, we are presenting this material to establish the foundation for histograms which greenbelts should have knowledge of and can explain. In order to look at the frequency distribution we have to build the foundation. This foundation is a frequency table. Since Honeywell has the power to generate frequency distributions through the PC software. This discussion on Frequency Tables is a cursory review highlighting the basic elements. The table is a method that summarizes the data set in terms of class interval, midpoint, frequency, and relative frequency Class Interval established the range of the variable values and depends on the number of classes, usually between 5 and 20 READ THE RULES Next element for the intervals are, the Boundary Values of the intervals. The boundaries must be set where no over lap occurs. It means that the data set variable can only exist in one of the intervals Each interval must have equal value and is calculated by taking the range of the data set and dividing by a chosen number of class intervals REVIEW THE EXAMPLE Here is the data set from the Exercise conducted by the brigade. It is the same exercise where the King has threatened to turn Captain Green into a projectile. Review the class interval result * Moving on to the next element, which is Midpoint. Midpoint is the middle value in the interval. Review midpoint in the example Frequency is the count of the number of times a variable falls within the class Review the example - point out the 102 value and show in data set. The relative frequency is a count of the interval as compared to the entire data set. Review example. * Here is a method to use if you want to manually build a table. Since software (. excel, minitab, etc.) can build histogram we are not going to spend any time here. But let’s note here is a complete frequency table for the Statapult exercise data set. * Now that a data table exists, we can build a visual graph of the frequency distribution. By graphing the data points we can see Symmetry (SHOW ON GRAPH) Clusters (Show on Graph Focus on high frequency values) Spreads (show on Graph) Gaps ( There aren’t any here) Outliers (there aren’t any here) These are the Key points of information you can extract from the Histogram. With today’s software you can adjust the class intervals to see what happens to the 5 information elements * Let’s review the shapes of Frequency Distributions. Distributions can take on all different looks. However they will have a tendency to comply with a theoretical model. There are a series of theoretical models which 5 are presented here. Here again it is not the scope of this for Gb’s to derive these shapes. Gb are expected to know that different shapes exist and you can compare your data to the above sets. In the majority of cases with Quantitative type data the Normal distribution appears most often For the Statapult exercise data histogram, what common theoretical shape does it represent? (ANS: NORMAL) * Before continuing with Normal distributions: We are going to spend the next few minutes defining common characteristics of a Frequency distribution. There are two: First there is Measure of central tendency Second there is Measures of dispersion Measures of Central tendencies are 3 sets of measures that describe the “clustering of the Variable values” 3 measures are mode, median, mean The 3 answer the leading question of : READ QUESTION (Time 2 minutes) * The first measure is Mode. The Mode is the variable or variables which occurs most frequently. It’s the easiest measure to look for, find, and interpret. REVIEW EXAMPLE Since Qualitative data has no meaning Between Variables its very useful for qualitative data. It also identifies cluster or clusters that exist. DRAW THREE DISTRIBUTION S ILLUSTRATING UNIMODAL(one hump), BIMODAL(two humps), MULTIMODAL (3 or more humps) If more than one mode exists, there is an opportunity to question the composition of the data set. It does have limited properties, therefore no further knowledge can be extracted from it independent of the other measures. It is used by statisticians in combination with the mean and median to look at skewness of a normal distribution. (Time 2 minutes) * The Next measure of central tendency is the MEDIAN. Simply stated it is the midpoint variable in the data set. It is truly the center value and is insensitive to extreme values. If data set contains an odd number of Variable the Median is the midpoint If the data set contains an even number of variables the median is the average of the two middle variables SEE EXAMPLE: Statapult data set contain an even number of variables, therefore we take the sum of the two middle values and divide by 2. Which is 107 Good to use median for small data set with extreme variable value EXAMPLE WRITE: 6,7,5,9,6,7,8,5,32 It also has limited properties, therefore no further knowledge can be extracted from it independent of the other measures. It is used by statisticians in combination with the mean and mode to look at skewness of a normal distribution. (Time 3 minutes) * The final measure of central tendency is the MEAN. The mean is the SUM of the values divided by the QUANTITY of VARIABLES in the DATA set. It takes into account every numerical value in the data equation and simplify with x1+x2+X3/N N=# IN DATA SET. Review example. DRAW NORMAL DISTRIBTION and with mean line :LABEL mean. Show the sum of variables left of mean = sum of variables right of mean line. To get mean in excel Write Formula: = average(___:___) FOR the issue of being Susceptible draw : normal curve label,mean mode, median at midpoint. Then draw a skewed right distribution. Label mode at hump, median to the right, and then mean further right and explain That what makes the mean a powerful measure of centrality is also it’s weakness , therefore knowing the shape of a distribution is important, you must have a graphical insight to distribution to correctly take the next steps. By the way if you have a distribution that is appears not to be normal CALL A BB OR MBB (Time 3 minutes) * The second Characteristic of a Frequency Distribution is : MEASURES OF DISPERSION which is the degree to which the data tend to spread about the mean. Dispersion answers the leading question of “What is the spread of the data set?” ASK: Why do we want to ask this question? Write answers on posters? Then draw the figure below: The figure illustrates test acceptance test data of three Statapults A, B, and C. Each Statapult has five shots. It shows that just looking at the measures of central tendency does not tell you enough about the data set. The three Statapults have different spreads. Additional bits of information need to be analyzed and interpreted. COME BACK AT END OF CLASS DURING SUMMARY. There are three common measures are range, variance and standard deviation. 10 20 30 40 50 A Average or mean values are all the same (value of 30). But the spreads are different! 10 20 30 40 50 B 10 20 30 40 50 C * The first measure is RANGE. It is the difference between the largest and smallest variable values within a data set. This measure is the simplest to find and provides the lowest amount of knowledge about dispersion Review example and go over 4 steps. Range is an appropriate measure when a data set contains a small number of variables. The strongest application of range will be expanded upon in the Voice of the process module. * The second measure of dispersion is VARIANCE. Variance is the SUM of the difference between each data set value and the data set mean divided by the number in the sample minus 1. Draw a normal distribution and label X and a few points on the curve as x1, x2, and x3. Show how the equation works. For the example, the equation sums for 50 data points. As previously noted GB are not expected to derive equations. You’ll just have to know that the variance uses all the data set points. ALSO note: For data sets containing a number of values greater than 30, dividing by n-1 changes to dividing by n.. * A key to interpreting Variance is the by looking at it graphically. On the slide Statapult A’s variance is smaller than Statapult B. This also holds true numerically: a low variable value represent a small variance and vice versa. * The standard deviation is the most common form of dispersion. It accounts for all the values of the data set. It is the square root of the variance. The square root function keeps the unit of measure consistent with the other measures of the data set Review the equation and example . * These are the questions the standard deviation answers. Standard deviation contains the most knowledge and is in the right units of measure Go back to the example drawn for the dispersion discussion. The Standard deviation for Statapult a, b, and c are different. Which one intuitively will be the smallest? Largest? Of course A has no spread and standard deviation of zero, C is larger because more points are dispersed from the center. * ACTIVTY BREAKOUT: This activity can be done by individuals or teams. Have student calculate the measures of centrality and dispersion. Should have calculators. Review the table and assign the activity (1 min to set up) Five to eight minutes for exercise Five minute debrief to go over the answers and debrief the activity Last statement is : We have defined the simple calculations to quantify a data set. Now what don’t we know? * ASK: How can we use the distribution? Earlier in the module we defined frequency distributions. We are now going to continue the discussion by using the Normal Distribution. We’re focusing the discussion around the normal distribution since so many of the observations and data sets created exhibit a normal or near normal shape. The key characteristic of the normal distribution is symmetry. The mean is therefore at the center of the distribution. The area under the curve represents 100% of the population. The value 1 Sigma represent % of the population. Therefore we +/- 1 Sigma we are capturing % of the population. By the way 1 sigma is the point of inflection of the curve. In other words it’s where the curve stops facing downward And begins facing upwards. (For you practitioners of Calculus, the points of inflection occur where the 2nd derivative is zero.) Those of us who are less adept in the science of calculus ask: .. the 2nd what? For +/- 2 Sigma values we capture approximately 95% and at +/- 3 Sigma % So how can we apply the characteristics we just defined? * Since the normal distribution captures 100% of the population we can ask two questions about the data set. First, What percentage of observations will occur for any value? As in the Captain Green and the King Statapult case study the exercise data set, what is the percentage of the shots landed at 108? then say 104? ASK THE CLASS. What is the reason for this question? ANSWER: This data is a sample of a total population, and yield indicators of the future. If no changes are made, the same results will occur with some degree of accuracy. The second question asks, What is the relative location of an observed valve? Another way to ask this question in terms of context of a project is, where does the specification values align with the data set distribution? ASK THE CLASS: What is the reason to ask this question? Write down some of the answers, and HOLD the ANSWER until slide 7-34 HOWEVER in order to answer these questions we must reorganize that all data are different. They have different variable values (Set A 1,2,3…; Set B .01, .02, .03…; Set C $100,$5, $1100….) the data sets difference therefore yield different means and standard deviations. In order to keep it SIMPLE a method exists that standardizes all the data sets into a single numeric value. It is called Z SCORE * This single numeric value represents a data set variable as a number of standard deviations that variable lies from the mean within it’s distribution. The Z score takes the data set variable subtracts the mean of the data set and divides the result by the data set standard deviation. The Z score distribution establishes a value of 0 for the mean and a standard deviation of 1. REVIEW the graphics in the EXAMPLE starting the Z distribution. Point out the mean and standard deviation and values then relate the brigade data distribution pointing out the relationship of the means and standard deviations. Go back to the attributes and review. Show them the area is symmetric, therefore 50% of the distribution lies to the right and 50% lies to the left. Z scores then assign a plus to the right and a minus the left. The Z scores has a table of probabilities which we can look up after calculating which will we discuss on the next slide. The key attributes of Z scores are: )it provides a basis in comparing a wide range of distributions for a vast array of data sets )It can determine and predict impact to customers in the form of DEFECTS REVIEW the problem statement mathematics in the EXAMPLE. Show them how we get the minimum value and target. If you want calculate the z for the maximum spec value. * Remember a few ago we asked : Where does the specification values align with the data set distribution? And the we Asked: What is the reason to ask this question? REVIEW answers. Then note that the practical application of knowing the distribution z score is the relationship to CUSTOMERS. If we know the Z Score we can calculate the probability of DEFECTS that will be produced As stated previously the Z score has a look up table that calculates the area under the curve beyond the Z score (Right of the plus side, Left on the minus side). This area represents the probability of defects occurring. The table is an abbreviated representation of a Z score table. Let’s review the example. READ the EXAMPLE and point the values on the TABLE. ASK THE CLASS: If you were a customer, which Z score would you want? It is expected that GBs must have an awareness of Z Score and that you can recognize that 1) a higher Z score is better and 2) and the higher the Z score the lower the defects. NOTE: Some Gbs may catch the fact that the table shows the defects occur at a z score of . Tell them to hold that question and tell them that it is correct. The table does not exhibit a shift. The shift will be covered in a few minutes. * Now we are going to drop the heavy mathematics for a few minutes. Let’s step back and review few more concepts. Let’s talk about data set shape and the 3 problems that can reside with respect to customer specifications. The first problem is large spread. Assuming the data set is aligned on the specification target. The result is portion of the data set population lies beyond the specification values. We say the data set is accurate with respect to the specification target. (Measures of central tendency “cluster” about the target). However the data is “not Precise” because the data spread is large. (The Measures of dispersion are large when compare to the range of the specification.) The second problem is Not centered. Assuming that the measure of dispersion is much less than the range of the specification. We say the data set is precise. However, the population mean is not aligned with the specification of the target and therefore not accurate. The last problem is the combination of large spread and not centered. This problem is neither precise nor accurate. Review the EXAMPLE in class. Set up the figure and values ASK THE CLASS: Why are these concepts important? ANSWER: The key point here is: knowing the problem helps define the scope of improvement actions. A lot of time is spent needlessly in taking inappropriate actions. Some solutions become readily apparent and easy to fix. * Another concept about data sets is the impact of time. Studies conducted over the past fifty years show that over time variation increases +/- sigma. The shifts are due the shift of the data set mean. The shifts of the mean result from the changes of inputs (x’s) over time. GO TO FIGURE SHOW TIME 1 AND THE SHIFT IN MEANS FOR TIME 2 , 3 AND 4. ASK: What are the implications of time to understanding data sets? Answer: We must account for the impact when we are attempting to gain knowledge from our data set. We do this by simply determining whether the data set is SHORT term or LONG term. Based on the answer will adjust our analysis when required. GBs are expected to recognize the impact of time and interpret a data set exhibiting characteristics of Long or short term. To assess whether our data set is short or long term we consider the following: READ THE LIST in a form of a question. GIVE A QUICK Example: for a data set noted choose if the 3 products would be short or long term. Answers: Spark Plugs: Short Invoice: Long term Reports: Could be either, need to ask about changes in material, measurement, Mother Nature * Okay, now we are going back into the language of numbers and mathematics. We are going to now introduce the concept and define Process capability Ratios. Process capability ratios have been around a long time and are predominately used in the manufacturing portion of our business. There are two statistics The first is Cp which compares the width of the data set variation to the width of the spec The second is Cpk is the MINIMUM calculated value of comparing the mean and standard deviation to the upper and lower specification values * Getting a little more detailed, the Cp is looking at the process and spec width. It assumes the process mean is aligned with the spec target. ASK THE CLASS: We discussed a while ago the attributes of Precision and Accuracy, Cp is quantifying what attribute? ANSWER: Precision The industry standard for Cp is 1 the Six Sigma goal is 2 * Cpk is the calculated value that will provide the lowest value. Case in point the figure provides a example . The distribution is shifted to the left of the target value. We can see the area to the left of the LSL is much greater than the area to the right of the USL. Therefore the lower Cpk value will be used for the LSL value. Cpk is the more robust ratio because it uses the mean, standard deviation, and the specification width. It provides a better indicator for process capability. A Cpk of less than 1 is considered poor A process exhibiting a Cpk of for short term data is our target. A value of sustained over the long term should initiate an action to remove the measurement. * Now let’s look at A process capability ratio table. The table compare Z score, Cp, and Cpk. Note that Z= 3*Cp. The capability ratios are then align with the Defects in PPM. The two PPM are different in that the left column has a sigma shift. LOOK at and 6 and point to the Defect values. The column with the shift is normally used. It is used due to the fact that all process data is reported as short term. The associated defects for the values in accounting for the long term effects are then automatically accounted for. * ACTIVTY BREAKOUT: Break into teams and for the figure and Calculate the capability ratios. Use the table on the previous page to approximate the defects. Give the teams five minutes. Debrief exercise. Have the formulas on mathematics done on a poster sheet Then close exercise by indicating that there are rations to look at a data set ability to comply with customer specs. With the ratios we can then predict what the defect levels will be without any adjustments to the process that produced the data sets. * Distribute the post assessments to the students. Allow approximately 10 minutes for students to complete the assessment. Review assessment answers with the students and ask them to grade their own assessments. Distribute module evaluation forms to all students. Instructs students to complete the form and to return it before leaving class. This is a written summary of what we just discovered ASK: Any questions? * Calculate DPU for each failure mode and calculate a Total Defects per Unit (TDU). You can do this two ways: TDU = Sum of all DPU’s or TDU = Total # Defects / # Units (it works out the same) ASK: What is DPU? (most get it without having you show them). either write out the equation on a flip chart or throw up this slide. ASK: Why do we calculate DPU? It normalizes the data, lets those who haven’t seen the raw data interpret the results. ASK: Based on what we’ve done so far, where’s the biggest problem? what should we attack first? ASK: Does the TDU mean that X% of the M&M’s are defective? The answer is no -- some M&M’s might have more than one defect. This highlights the difference in perspective between defects and defective parts. We did this double-bookkeeping in order to be able to look for the right place to improve our processes. For the class, we’ve taken all the data we need to prioritize our actions. The rest of the scorecard massages the data so that others can understand what it means. * ASK: What does Yield mean? Write it down or show the slide. Yield is just a different way of looking at DPU. Calculate yield for each failure mode. ASK: Why didn’t I calculate a total yield? This hearkens back to the discussion from the last slide about double-bookkeeping defects. Such a total yield number is not meaningful. Restate the definition of yield, and introduce the idea that these yields can be attributed to steps in a process for making m&m’s. Draw the fabrication process from the next slide on a flip chart, and tell them that we are going to take this data and assign it to the steps in the process. Make it clear that this is not a good practice in real-life situations; refer to the Value Chain discussion from slide 10. Attribute the yields of each failure mode to the appropriate process step: Deformed M&M’s ==> Form Chocolates Cracked M&M’s ==> Coat Pieces M not properly marked ==> Stamp m’s ASK: What is the yield of the M&M fabrication process? How would I figure it out? (Next Slide) * If the students have trouble with the concept, ASK: What is the probability that a single m&m could go through the manufacturing process without incurring a single defect? That’s the definition of Rolled Throughput Yield. RTY is good high-level metric for overall process quality. (one could argue it belongs under the next objective, but the class flows better if it is introduced here) Calculate the RTY. Compare it to any other definition of yield that the class might have come up with before, and discuss the differences. RTY will be important to the student in understanding why Six Sigma is the Goal, later on in the module. Now move on to Opportunities... * ASK: What is an opportunity? ASK: How many opportunities did we give a single M&M to be cracked? ANSWER: One: either it’s cracked or it’s not. This is a characteristic of attribute data. Talk about situations where a failure mode, or a process step, might have more than one opportunity per unit. An example is an impeller, which may have an opportunity for each blade, or a form that may have an opportunity for each data field. ASK: How many opportunities did we give a single M&M to be defective? ANSWER: Three, based on our definition of the Failure Modes. This is the sum of all the opportunities per unit for each failure mode. ASK: Why do we bother to count opportunities? ANSWER: We count opportunities to account for varying complexity between products and processes. Cite examples across the business, . a spark plug vs. an aircraft engine. Also, ask the class to think about opportunities in their own processes. Talk about opportunities in administrative, design and manufacturing processes. ASK: Does anyone see any pitfalls in this opportunity counting business? This question leads into the next slide. * Make certain to stress all of the points on this slide. Highlight the differences between a customer Sigma, where the customer sees one opportunity for one unit to be defective, and an internal Sigma, in which we might see many opportunities to create defects. (Cite your local method of calculating Sigma, if you know it). ASK: Which Sigma is the correct one? They are both correct. The trick is to use each Sigma for its appropriate purpose, as stated in the first guideline. If the Greenbelt teams are going to use the tools presented in this module, have them discuss opportunity counting with their Mentors, or have them contact someone with experience in this area, such as the module owner Honeywell has a corporate document that outlines the method used to calculate Sigma. Contact your local focal point or Master Black Belt for more information. * DPMO is used rather than DPO because it is more intuitive to grasp. Calculate DPMO for each failure mode, and then calculate the total DPMO using the following equation: DPMO = (TDU / (Total Opps per unit) ) * 1,000,000 Accounting for opportunities eliminates the double-bookkeeping problem encountered when we tried to calculate the yield --- DPMO tells a more realistic story about the quality of the m&m’s, in a way general enough to be flowed up to higher levels of management. * This concept was introduced in the Intro to Variation Class. Review it here. Since we’re dealing with attribute data rather than variable data, another way to look at the graph is to see that every product (m&m, in this case) that was found to be defective falls outside the customer spec limits on this graph. The area under the curve outside the customer spec limits is then equivalent (after some mathematical maneuvering) to the DPMO. It’s possible then to convert directly to a Z-score from DPMO; a conversion table is shown on the next slide. In reality, the data we’ve collected in this game forms a single-tailed distribution rather than a double-tailed distribution (we do not have variable data, much less upper or lower spec limits). Any questions about the statistics behind this should be handled off-line, since they are beyond the scope of this class. * Show this table when you talk about the Sigma Score for the m&m process. Have the class find the closest sigma value that corresponds with the DPMO. Discuss what it means to get from there to 6-sigma. How many orders of magnitude would we have to reduce the DPMO to get to 6-sigma? ASK: How much would you have to reduce your defects in order to move up just one Sigma on the scale? The answer is in terms of orders of magnitude. Honeywell’s manufacturing processes in 1998 have floated between and sigma. WARNING: Tell the class not to go out and use this chart blindly! Direct their attention to the fine print and review the concept of the -Sigma shift. This chart has that shift embedded in it, so that it turns a DPMO from Long Term Data and turns it into a Short-Term Sigma number. ASK: Was the m&m sample we looked at today long or short term data? Discuss why it’s really short term data, but state for the purposes of the game that we’ll “pretend” that it’s long term data. Refer them to their BB mentors or yourself for help if they plan to use this in their process. Don’t discuss the single-tailed version of the table -- it’s beyond the scope of the class. Tell the class to consult a Black Belt before running off and using this chart to come up with Sigma Scores; they need to be certain they’re using the appropriate chart for the data they have. * Show this table when you talk about the Sigma Score for the m&m process. Have the class find the closest sigma value that corresponds with the DPMO. Discuss what it means to get from there to 6-sigma. How many orders of magnitude would we have to reduce the DPMO to get to 6-sigma? ASK: How much would you have to reduce your defects in order to move up just one Sigma on the scale? The answer is in terms of orders of magnitude. Honeywell’s manufacturing processes in 1998 have floated between and sigma. WARNING: Tell the class not to go out and use this chart blindly! Direct their attention to the fine print and review the concept of the -Sigma shift. This chart has that shift embedded in it, so that it turns a DPMO from Long Term Data and turns it into a Short-Term Sigma number. ASK: Was the m&m sample we looked at today long or short term data? Discuss why it’s really short term data, but state for the purposes of the game that we’ll “pretend” that it’s long term data. Refer them to their BB mentors or yourself for help if they plan to use this in their process. Don’t discuss the single-tailed version of the table -- it’s beyond the scope of the class. Tell the class to consult a Black Belt before running off and using this chart to come up with Sigma Scores; they need to be certain they’re using the appropriate chart for the data they have. * ASK: Why Six Sigma? Why not four or five? What’s so important about the number Six? Describe the chart. Show the massive difference in RTY between 5 and 6-sigma. Relate this to a local site example that people might be familiar with. For example, at Engines and Systems, how often do we go through the entire value chain of building an aircraft engine without creating a single defect? Most people have the intuitive feel that this never happens. This graph explains why their intuition is correct. Relate this back to the game: How many people had a perfect bag of M&M’s? Use the analogy of a single M&M being a part, and the bag being the product. The key take-away from this slide is this: If our parts and processes are coming in at Six Sigma, nine times out of ten we’ll produce a complex product right the first time-- without incurring a defect! Six Sigma processes and products are robust to complexity. * This chart shows that there is some optimum beyond which it does not pay to increase quality. 6 should not always be the goal for an individual process. - Quality for your process may not be as important if a part costs little or nothing to replace…maybe 4 or 5-sigma is adequate. - Some performance requirements or government regulations might require quality to be much higher than 6-sigma. Example: An engine must be able to withstand a 4 lb. birdstrike without resulting in an uncontained failure. The FAA is willing to “allow” a catastrophic engine failure once every 1 billion cycle-hours throughout the life of an engine fleet. This works out to a mandated quality level of sigma. A short break might be appropriate after this slide.