【正文】 h10,000 data points, there is still somedifferences in the histogram. If a betterestimate is required, a different data setcould be constructed with exactly equalcounts of each possible oute. Try itand see if the numbers are any different. Sampling a Nonnormal Distribution – Exercise
Each person in the class is to toss a single die sixteentimes and record the data. Calculate the mean and standard deviation of eachsample of sixteen Record the means and standard deviations from eachperson in the class in a Minitab worksheet
Use Minitab’s Graphical Summary routine for analysis Stat Basic Statistics Display Descriptive Statistics…Alternately, a sample of sixteen throwsof the dice can be simulated in Minitab asfollows:Select: Calc Random Data Integer… fromthe main menuGenerate 16 rows of data in C1: Min = 1, Max= 6Analyze the Sample Data
What is the mean of the sample averages? Mean ≈
What is the standard deviation of the sample averages? Sigma ≈
Is the distribution normal? What is the pvalue?
What is the relationship between the average of thesample means and the population average?
What is the relationship between the sigma of theaverages and the sigma of the individuals?The Central Limit Theorem
Formal Definition:
If random samples of n measurements are repeatedlydrawn from a population with a finite mean μμμμand a standarddeviation σ σσ σ , then, when n is large, the relative frequencyhistogram for the sample means (calculated from therepeated samples) will be approximately normal with amean μμμμand a standard deviation equal to the populationstandard deviation, σ σσ σ , divided by the square root of n.(Note: The approximation bees more precise as nincreases.)Central Limit Theorem – Exercise
From a Minitab analysis of the uniformly distributeddata:
For an exercise, verify that the Central Limit Theorem isvalid for this uniform dataVariable N Mean StDevn=1 (Individuals) 10000 n=2 (Means) 10000 n=5 (Means) 10000 n=30 (Means) 10000 相關(guān)性及簡(jiǎn)單線性回歸:Regression amp。 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(xiàng)目運(yùn)作實(shí)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(duì)測(cè)量系統(tǒng)能力研究結(jié)果進(jìn)行分析10，確定適當(dāng)?shù)暮罄m(xù)措施定量型量具 Ramp。R結(jié)果量具偏差（σmeasurement system ）真實(shí)值 精確度（量具偏差）觀察值測(cè)量系統(tǒng)的精確度（P）：精確度包括重復(fù)性和復(fù)制性測(cè)量系統(tǒng)的指標(biāo)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?jǐn)?shù)來(lái)表示最好的情形P/T10%可接受的P/T30%工藝能力計(jì)算實(shí)例一位技師負(fù)責(zé)醫(yī)院設(shè)備的蒸汽殺菌過(guò)程。定性型量具 Ramp。 定性測(cè)量系統(tǒng)研究:定性型量具 Ramp。更改及更新：更改記?。? Sigma 的目標(biāo)之一是找出：Y=F（X）隨著對(duì)工藝的深入了解，更新工藝圖以反映新的信息更新項(xiàng)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(cè)量系統(tǒng)分析及工藝能力分析結(jié)果精簡(jiǎn)制造與5S:精簡(jiǎn)制造例似于日本的5S精簡(jiǎn)制造與5S:魚骨圖:魚骨圖一種系統(tǒng)確認(rèn)所有可能導(dǎo)致問(wèn)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(diǎn)所有設(shè)備/工具各步驟表明增值性（VA）和非增值性（NVA）控制標(biāo)準(zhǔn)文件用標(biāo)準(zhǔn)符號(hào)繪制工藝流程：在Microsoft OfficeTM 等軟件中可找到 8，完成財(cái)務(wù)評(píng)估。？3，完成問(wèn)題陳述：a4因果矩陣圖a2 Pareto圖分析a選擇項(xiàng)目的工具c可交付使用的2對(duì)與生產(chǎn)來(lái)說(shuō)：如何定義一個(gè)項(xiàng)目？項(xiàng)目定義是由冠軍來(lái)完成的。5，描述項(xiàng)目的主線。2在哪里和什么時(shí)間發(fā)現(xiàn)的？6你是如何得知這些的？ 《6 Sigma項(xiàng)目運(yùn)作實(shí)例》《定義階段》如何繪制宏觀圖如何繪制宏觀圖? 繪制宏觀圖的順序：供應(yīng)商輸入工序輸出客戶《6 Sigma項(xiàng)目運(yùn)作實(shí)例》《定義階段》項(xiàng)目的目標(biāo)陳述要點(diǎn) 項(xiàng)目的目標(biāo)陳述要點(diǎn): 1,目標(biāo)陳述2，計(jì)算方法3，全年節(jié)省額確定Team Members成員:1，小組成員要包括技術(shù)人員2，包括維修人員（如果需要）3，包括操作者4，小組人員不超過(guò)5人(特殊情況除外)。應(yīng)使用最新的控制文件標(biāo)明所有隱形工廠步驟的輸入輸出指標(biāo)：對(duì)各種詳細(xì)列出的因子再列出其輸入變量。標(biāo)準(zhǔn)值由一個(gè)高準(zhǔn)確度量具所測(cè)的平均值生產(chǎn)者偏差員工傾向于把不合格（有缺陷的）產(chǎn)品判為合格篩選用檢驗(yàn)方法對(duì)產(chǎn)品進(jìn)行100%的評(píng)估篩選有效性定性量具系統(tǒng)區(qū)別合格與不合格的能力檢查員分?jǐn)?shù)如果大多數(shù)員工都是100%，則培訓(xùn)作用極為有限篩選有效分?jǐn)?shù)如果員工本身前后一致但是相互間不一致，則重新培訓(xùn)可幫助減少錯(cuò)誤。第二步：采集數(shù)據(jù)合理編組應(yīng)采集數(shù)據(jù)獲得“短期”性能，如可能，“長(zhǎng)期”性能通過(guò)固定時(shí)間區(qū)間采集一系列快照型數(shù)據(jù)應(yīng)按合理編組采集快照數(shù)據(jù)什么是合理編組？從流程連續(xù)不斷產(chǎn)生的零件或產(chǎn)品中合理取樣以期捕獲最小工藝偏差的方法組內(nèi)偏差反映一般偏差平均標(biāo)準(zhǔn)差（用一種均方差方法平均）是對(duì)工藝應(yīng)有能力的良好估計(jì)第二步：采樣例子例子：技師在暴露周期從控溫探針讀數(shù)中選取五個(gè)數(shù)據(jù)，并從連續(xù)七個(gè)殺菌運(yùn)轉(zhuǎn)周期采集數(shù)據(jù)，第三步：確定短期偏差多數(shù)現(xiàn)有數(shù)據(jù)居于長(zhǎng)期和短期之間為了估計(jì)真實(shí)短期數(shù)據(jù)：小心設(shè)計(jì)工藝能力研究方法確保編組策略合理某些工藝無(wú)法研究短期數(shù)據(jù)如低產(chǎn)量和長(zhǎng)循環(huán)周期工藝采樣昂貴或難以取樣的工藝第三步：短期還是長(zhǎng)期？一個(gè)指導(dǎo)思想：如果允許80%的輸入指標(biāo)在其自然范圍內(nèi)浮動(dòng)，數(shù)據(jù)就是長(zhǎng)期的 短期及長(zhǎng)期：組內(nèi)及組間平均標(biāo)準(zhǔn)差與總標(biāo)準(zhǔn)差對(duì)各組方差取平均值可得到組內(nèi)標(biāo)準(zhǔn)差的平均值總標(biāo)準(zhǔn)差由所有數(shù)據(jù)算出，不計(jì)編組平均標(biāo)準(zhǔn)差不計(jì)組間偏差，而總標(biāo)準(zhǔn)差計(jì)入組間偏差平均標(biāo)準(zhǔn)差是對(duì)組內(nèi)標(biāo)準(zhǔn)差的最佳估計(jì)長(zhǎng)期和短期指導(dǎo)思想短期數(shù)據(jù)在有限的周期或間隔采集數(shù)據(jù)在有限的機(jī)器和員工中采集差不