【正文】 m2. State the null hypothesis3. State the alternatehypothesis4. Test the assumptions ofthe data*5. Calculate theappropriate test statistic(or calculate pvalue)6. Lookup the critical valuefrom the appropriatedistribution (or set alpha)7. If the calculated statisticmeets the decision rulecriteria (or if pvalue α )then reject H08. Formulate the statisticalconclusion into apractical solutionThis is the general recipe for hypothesistesting. The tests differ in the appropriatestatistics and appropriate distributions.The means tests recipe is the same as waswhat learned for variance testing.Example – One Mean Vs. Target
Background – A pany audits its stock of tennis balls by testing the bounceheight of 10 randomly selected balls. The average bounce height of thesample is in. The historical data is μ= and σ = . Has storagedegraded the bounce of the tennis balls? Use α = .1. State the practical problem: Is the bounce height of the stored population less than the historicalvalue?2. State the null hypothesis H o : μstored = 3. State the alternate hypothesis H A : μstored 4. Test assumptions: normality of the data pvalue = – Data is normalA very mon test is sampling stockfrom the warehouse for conformity to astandard.This example has a tennis ball panychecking whether the balls in storage stillmeet the bounce specification.Exercise – Mean Vs. Target
Some local farmers believe that this year’ssoybean crop has an exceptionally high yield. Thestatewide average yield for the past five years has been520 bushels/acre with a standard deviation of 117.Thirtysix farms were sampled and。 6
What is the shortterm process capability? What is the longterm process capability?
Are these good or bad values?Remember, one goal of Six Sigma is toreduce variation, which will increasecapability. It is always important tounderstand the process capability. Preparing Data for Marginal Plot by “Slot”
Marginal plots require both variables to be defined numerically
We need to convert “Slot” to a numeric column first
Step 1: Convert “Slot”
ManipCodeText to NumericManip Code Text to NumericMultiVari Analysis – Defined
A graphical analysis tool Uses logical subgrouping
Analyzes the effects of discrete X’s on continuous Y’s
A capability and process analysis tool
Data collected for a relatively short time
Data can estimate capability, stability, and y = f(x)’s
Major focus: study uncontrolled noise variation first Variation in noise variables produces chronic and acutemean shifts, changes in variability, and instability
Noise variation must be reduced or eliminated in order toleverage the important controllable variables systematicallyMultivari analysis is a very useful toolfor graphically identifying sources ofvariation, especially noise variation. Laterthis week, we will be studying correlation amp。 《6 Sigma項目運作實例》《分析階段》失效模式及后果分析失效模式及后果分析: Failure Modes and Effects Analysis (FMEA)Background:
Failure Modes and Effects Analysis (FMEA) First developed in the 1950’s Appropriated by NASA in the 1960’s for the space program Ford Motor Company was the first North American pany to widelyimplement the use of FMEAs
Types of FMEA System – Toplevel, early stage analysis of plex systems Design – Systems, subsystems, parts amp。R Study(Crossed)StatQuality ToolsGage Run Chart9，對測量系統(tǒng)能力研究結果進行分析10，確定適當?shù)暮罄m(xù)措施定量型量具 Ramp。R結果量具偏差（σmeasurement system ）真實值 精確度（量具偏差）觀察值測量系統(tǒng)的精確度（P）：精確度包括重復性和復制性測量系統(tǒng)的指標PT:精確度與公差之比P/T代表量具偏差占公差的部分此部分通常用百分數(shù)來表示最好的情形P/T10%可接受的P/T30%工藝能力計算實例一位技師負責醫(yī)院設備的蒸汽殺菌過程。定性型量具 Ramp。 定性測量系統(tǒng)研究:定性型量具 Ramp。更改及更新：更改記住：6 Sigma 的目標之一是找出：Y=F（X）隨著對工藝的深入了解，更新工藝圖以反映新的信息更新項目最終成果之一是現(xiàn)有的工藝的流程圖更新工藝圖以反映任何工藝改變加入測量系統(tǒng)分析及工藝能力分析結果精簡制造與5S:精簡制造例似于日本的5S精簡制造與5S:魚骨圖:魚骨圖一種系統(tǒng)確認所有可能導致問題(后果)產(chǎn)生的原因方法。工藝流程圖（PFD）:6 Sigma 工藝流程圖的要素：所有工藝步驟包括隱形工廠數(shù)據(jù)采集點所有設備/工具各步驟表明增值性（VA）和非增值性（NVA）控制標準文件用標準符號繪制工藝流程：在Microsoft OfficeTM 等軟件中可找到 8，完成財務評估。？3，完成問題陳述：a4因果矩陣圖a2 Pareto圖分析a選擇項目的工具c可交付使用的2對與生產(chǎn)來說：《6 Sigma項目運作實例》如何定義一個項目？項目定義是由冠軍來完成的。2，完成項目預測節(jié)省金額。7，組成項目小組，列出小組成員。3問題將涉及哪些工序？確定工藝范圍:范圍至觀重要越窄越好！大量工藝步驟可能表明項目定義不佳或問題源于幾個項目問題藏于問題中若問題可以由粗略分析解決，管理層會去做繪制可執(zhí)行的工藝圖你能確認缺陷來源嗎？我們能有意識地改變輸入指標變量嗎？有意識的改變輸入指標變量能直接影響輸出結果嗎？標準限和工藝能力：工藝及產(chǎn)品標準加入X的工藝設置加入Y 的標準限 標明未記錄的Y和可控的X測量系統(tǒng)加入量具重復性及復驗性數(shù)據(jù)標明須做測量系統(tǒng)分析的量具工藝能力展示RTY，DPU，CPK等的估計值標明哪些工藝步驟數(shù)據(jù)陳舊或不完整而需做工藝能力分析R 的目的:工藝評估評估你的檢查標準或工作質(zhì)量標準與客戶要求的一致性確定所有班次，機器等的檢查人員是否使用相同標準來決定合格與不合格量化檢查人員準確重復其檢驗結果的能力確定檢查人員與“已知標準”的一致性及傾向于消費者偏差還是生產(chǎn)者偏差工藝改進發(fā)現(xiàn)是否需要培訓，缺少工序或缺乏標準工藝能力研究連續(xù)數(shù)據(jù) 離散數(shù)據(jù) ：短期還是長期？： （通常是長期）： ：Ⅰ ZU,ZL ：Ⅱ CP Ⅰ PPMⅢ CPK Ⅱ Sigma水平ZLTⅣ Sigma水平ZST Ⅲ PPK： ：Ⅰ Sigma水平ZLT Ⅰ Sigma水平ZSTⅡ PPK Ⅱ CPK測量系統(tǒng)的指標:量具Ramp。也盡量打亂員工次序8，用 Minitab 作下列兩個分析StatQuality ToolsGage Ramp。R結果ANOVA表P值是變化源在統(tǒng)計上對總偏差影響是否不顯著的概率在這個例子中，部件和員工均為顯著的偏差源另外，你能用Minitab的計算器計算總的平方和嗎？這個值代表什么意思？ 6.
Four times a day the supervisor would go to the press and gather up theparts produced by five consecutive cycles of the press. Since each cycleproduced four parts, he would have 20 parts to measure every two hours.The supervisor kept track of the cycle and the cavity from which each partcame and wrote his twentymeasurements in an array likethis: The supervisor collected samples four times a day for five days (20 samplestotal, 20 parts per sample). Calculate the process capability and use a MultiVarichart to help determine sources of variation.A BCDES1 18 19 20 19 21S2 13 16 14 13 13S3 10 11 13 10 13S4 11 12 13 13 13Exercise: Determine Capability Using Minitab, analyze the Thick datain for process capability
Remember, the specifications are: 11 177