【正文】 CorrelationIntroduction
Used for quantitative variables (X’s and Y’s)
For review: What is the focus of Six Sigma?Q. What does this equation represent?A. A mathematical model of a process
Purpose of Regression: to predict Y from a setting of x Examples:
Distance = f(acceleration, initial velocity, time)
Product yield = f(concentrations of reactants)
Hardness = f(alloy, anneal temperature)) ( x f Y =Remember, the focus of Six Sigma is todetermine the defining equation of theprocess. It is to identify the important inputvariables, determine the relationship to theoutputs, determine the optimum values of thecritical inputs and then control the inputs atthe optimum settings.To do this, the Black Belt must know therelationship between the inputs and theoutputs. This module discusses linearmodeling techniques for identifying therelationship between continuous variableinputs and continuous variable outputs.A Simple Linear ModelLinear equations require continuous inputand output variables. One other assumption isthat the independent variable (input) is knownand fixed and that all of the variation is in thedependent variable (output). This is notusually the case, but often the inputs aresettings on dials or gauges or software thatseems fixed and invariable. Many times thevariation in the output is a function of theinability of the input controller to hold theinput at the same value. Collecting Data (y amp。 storage plan (who, what, when, where,etc.) The supervisor collected the data and entered it in a worksheet6. Describe the procedure and settings used to run the process Standard, constant process settings.7. Assemble and train the team. Define responsibilities. For a small project, the supervisor did all the work8. Collect the data. The data are in Minitab worksheet 9. Analyze the data Analysis is on the following slides regression (an analysis of the effect ofcontinuous X’s on continuous Y’s), analysisof variance (ANOVA) and the General LinearModel (GLM), both numerical analyses ofvariance data.Multivari analyses will help identify thevariation sources with the purpose of reducingor eliminating them.A MultiVari Plan1. Clearly state the objective2. List the X’s and Y’s to be studied3. Ensure measurement system capability4. Describe the sampling plan5. Describe the data collection amp。 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。 knowledge
For the future:
FMEA helps evaluate the risk of process changes
FMEA identifies areas for other studies –multivari, ANOVA, DOE6s Process FMEA Terminology
FMEA: A systematic analysis of a process used to identify potentialfailures and to prevent their occurrence
Potential Failure mode: The manner in which the process couldpotentially fail to meet the process requirements.
Potential Failure Effect: The results of the failure mode on thecustomer. Severity: An assessment of the seriousness of a failure mode.Severity applies to the effects only.
Cause: How the failure could occur, described in terms of somethingthat can be corrected or controlled.
Occurrence: The likelihood that a specific failure mode is projectedto occur. Detection: The effectiveness of current process controls to identifythe failure mode (or the failure effect) prior to occurring, prior torelease to production, or prior to shipment to the customer.
RPN Risk Priority Number: The product of Severity, Occurrenceamp。 the Camp。 ponents early in designstage Process – Focuses on process flow, sequence, equipment, tooling,gauges, inputs, outputs, set points, etcWho? When?
Who constructs the FMEA?
The Black Belt is the team leader.
The process owner inherits the finished FMEA.
Use the process mapping, Camp。R結(jié)果ANOVA表P值是變化源在統(tǒng)計(jì)上對(duì)總偏差影響是否不顯著的概率在這個(gè)例子中，部件和員工均為顯著的偏差源另外，你能用Minitab的計(jì)算器計(jì)算總的平方和嗎？這個(gè)值代表什么意思？R研究選項(xiàng)輸入該工藝公差和偏差，如果你想要Minitab幫你計(jì)算P/T 和 P/TV的話。運(yùn)用Minitab分析數(shù)據(jù)并評(píng)估量具能力StatQuality ToolsGage Ramp。R Minitab 實(shí)例:一個(gè)黑帶想對(duì)冶金工藝使用的溫度表進(jìn)行量具研究，他嚴(yán)格按前面一頁(yè)的方法進(jìn)行實(shí)驗(yàn)，并將數(shù)據(jù)輸進(jìn)了Ramp。也盡量打亂員工次序8，用 Minitab 作下列兩個(gè)分析StatQuality ToolsGage Ramp。量具研究偏差并不一定代表真實(shí)的工藝偏差當(dāng)量具樣本中的偏差代表真實(shí)工藝偏差時(shí)，P/TV等于P/SV定量型量具 Ramp。量具研究偏差并不一定代表真實(shí)的工藝偏差P/TV（%Ramp。測(cè)量系統(tǒng)的測(cè)量方法P/TV:精確度與總偏差之比代表量具偏差占據(jù)總偏差的部分此部分通常用百分率來表示最好情形10% 量具可接受條件30%測(cè)量系統(tǒng)的指標(biāo)分辨指數(shù) :分辨指數(shù)是測(cè)量系統(tǒng)從工藝數(shù)據(jù)中可辨認(rèn)的不同讀數(shù)的數(shù)量分辨指數(shù)是一個(gè)分辨率指標(biāo)分辨指數(shù)是重復(fù)性和復(fù)制性的函數(shù)最好情形：4 ，可接受的：34P/T 和 P/TV 的用處:P/T （% 公差）最常用于測(cè)量系統(tǒng)的精確度評(píng)估將量具的精確度與公差要求進(jìn)行對(duì)比如果量具用來對(duì)生產(chǎn)樣品進(jìn)行分類 P/T 還可以P/SV（%Ramp。測(cè)量系統(tǒng)的指標(biāo):量具Ramp。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多總是連續(xù)變量長(zhǎng)期數(shù)據(jù)在很多的周期，間隔，機(jī)器和員工中采集可以是離散或連續(xù)數(shù)據(jù)離散數(shù)據(jù)幾乎都是長(zhǎng)期性的第四步： 計(jì)算ZU和ZL:Z分?jǐn)?shù)提供統(tǒng)計(jì)數(shù)據(jù)以便用共同語(yǔ)言交流