DOE - Introduction

1、Introduction to DOEIntro to Design of ExperimentsIs the process stable? You cannot accurately predict product quality (location or dispersion) without a stable process. Stability(assessed with control charts) ensures that the experimental results will provide an accurate process predictionWhat are t

2、he goals for the experiment?What factors are important? How do the factors work together to drive the process? How can you achieve optimal results from the process?These questions are actually sequential; you cannot answer the last question without having the answers tp the first two.What is the wor

3、king environment? Do you have unlimited access to the process to be able to change settings (production line Vs pilot plant access to experimentation)? How many runs can you afford in terms of time and money? Is cost a limiting issue? Will experimental results apply directly to the process or will t

4、hey need verification?These are key concepts because you want to minimize the cost of obtaining information.What is your knowledge of the process? What do you know about important factors and how they work together (interactions)? How close to optimum are you currently running? What is the operating

5、 range of each factor?Once you define your goal, your environment and your knowledge, you can choose an adequate experimental design.Four questions to determine the type of designDOE - ObjectivesTo determine those variables / predictors (time, temperature etc) that are most influential on the respon

6、seTo assess the best settings / levels of those significant variables that result in a response near a desired value - maximum / minimum / nominal.To assess the best settings / levels of those significant variables that miminise variability in the response.To assess the best settings / levels of tho

7、se significant variables that reduce the effect / impact of noise nuisance variables DOE - The basicsA Basic ModelA body of explanatory dataMeasurement of Response(Potential Causes)(Effect)x1 x2 x3y_ _ _ _ _ _ _xyIndependent VariableY = a + bx parameters coefficientsabDependent VariableA Straight Li

8、neA Statistical Modely = 0 + 1X1 + 2X2 + 3X1X2 + ErrorLinear 2 factor modelNeed to determine coefficientsTo find our estimate of real worldAll other variables of influenceX3X1X1HLHLHLX2Basic Design Doubles No. runsOne Factor At A TimeMost commonly used traditional methodAllows controlled comparison

9、of the two levels of each factorAdvantages Easy to conduct and analyseLogicalDisadvantagesNot representative of “Real” conditionsDo not know if result is significantDo not know the result (effect) if other factor levels were changedPresence of variation means misleading conclusionsRun Factors Number

10、 A B C D E F G Response 123456781112222211112222111112221111112211111112123456781222222211222222Full Factorial ExperimentAll possible combinations of factor levels are investigatedAdvantages Excellent understanding of effect of factors on responseDisadvantagesGenerally impractical to conduct Very ex

11、pensiveAlternative “fractional” factorial designs available that give good results at far less cost Run Factors A B C D E F G Response 12345678910111213141516.1261271281111111111111111.2221111111111111111.2221111111111111111.2221111111122222222.2221111222211112222.2221122112211221122.122121212121212

12、1212.212DOE - The Benefits Far fewer trials than conventional approach Identifies those process parameters that affect output quality Reduce process / product variability Enables output quality average to be closer to target Minimise the effects of noise Enable products to be developed that seldom f

13、ail Reduce product development lead time Reducing time and cost to commission new plant and equipmentProduct / process environmentMany objectives Complex evaluation and optimisationDesign elementFocused objectives & quality criteria Manageable evaluation and optimisationintegrating team experience a

14、nd knowledge with benefits of applied statistical techniques Planning for Success - the design environmentPlanning for Success - the route mapManagement / Team BriefingDesign Trial Prepare & ConductTrialsAnalyse & InterpretDataConduct & AnalyseConfirmation TrialImplement NewOperating ConditionsConti

15、nue toImproveTraining ProgramFeedback ANOVA Factorial / ResidualPlots Significance testing Robust design Establish best conditionsScreening & Optimisation Trial Loop Define the problem - a clear statement of the problem to be solved- involving all appropriate people who can contribute Determine the

16、objective - identify the output quality characteristics(dependent response variables) - define the measurement system Identify key parameters for design - brainstorm all independent variables - categorise (control / constant / nuisance) and prioritise - assess for interaction effects Select paramete

17、rs - agree number variables and their values Design the experimental array - select the best (least trials) orthogonal array(s) for independent variables - assign variables (and interactions) to array columns Plan the experiment - establish plans for process stability and taking measurement - answer

18、 questions; what, when, who, where, and how - prepare randomisation and repetition plans - determine controls for constant factors Planning for success - key steps Design of Experiments - Common MistakesSetting levelsToo close means no difference in response will be detectedToo wide means non-linear

19、ities might pass undetectedConsidering NoiseFailing to recognise and deal with nuisance variablesEmphasis On CurvatureBelief in complexity rather than simplicityDesire To OptimiseNeed to isolate “vital few” and identify key leverage variables before optimisingRandomise TrialsUsing standard run order

20、 leading to noise impact trends and biasIgnoring InteractionsLeading to compounding/aliasing and sub optimal resultsConfirmation RunChecking results of experiment before implementationPlanning / PreparationInsufficient time given to deciding on design plan, logistics and quality characteristics (may

21、 be several)DOE - Why Industrial Experiments Fail Attacking one variable / response at - a - time. Ignoring the possibility of interactions Failing to recognise and deal with nuisance variables Putting too much emphasis on curvature (belief in complexity rather than simplicity) Designing to optimise

22、 the process before establishing important variables Not sequencing trials to randomise time effects Believing you are the seat of all wisdom and excluding others Too much fiddling with the levels of key variables Throwing out observations on the excuse they are outliers Failing to carry out a confi

23、rmation runA Two Level Factorial DesignEffect of pressure is difference in mean response between runs where it is at plus (high) level and minus (low) levelEffect is 4.65 units but do not know if this is significantAnalysing the design - calculating the “effect” of changing the factors : level minus

24、 (low) to level plus (high)Std Order12345678Run Order47315862Pressure55-70+55-70+55-70+55-70+HeatMed -Med -High +High +Med -Med -High +High +Time6-6-6-6-8+8+8+8+Response23.526.726.930.619.925.720.626.5Effect of pressure = 26.7 + 30.6 + 25.7 + 26.5 - 23.5 + 26.9 + 19.9 + 20.6 = 4.65 4 4To compare the

25、 mean values where pressure is high and lowA Two Level Factorial Design Analysing the design - use the contrast methodAdd the responses, taking account of minus/plus signs (modulus) and then divide by number of runs divided by 2Pressure-+-+-+-+Heat-+-+Time-+Pr*He+-+-+Pr*Ti+-+-+-+He*Ti+-+Pr*He*Ti-+-+

26、-+Pressure-23.5+26.7-26.9+30.6-19.9+25.7-20.6+26.5+18.6Heat-23.5-26.7+26.9+30.6-19.9-25.7+20.6+26.5+8.8Time-23.5-26.7-26.9-30.6+19.9+25.7+20.6+26.5-15.0Pr*He+23.5-26.7-26.9+30.6+19.9-25.7-20.6+26.5+0.6Pr*Ti+23.5-26.7+26.9-30.6-19.9+25.7-20.6+26.5+4.8He*Ti+23.5+26.7-26.9-30.6-19.9-25.7+20.6+26.5-5.8P

27、r*He*Ti-23.5+26.7+26.9-30.6+19.9-25.7-20.6+26.5-0.4 +4.65 +2.20 -3.75 +0.15 +1.20 -1.45 -0.10 Effect = contrast / (N/2)Response23.526.726.930.619.925.720.626.5A Two Level Factorial DesignCoefficients determined by dividing effect by 2Constant found by the mean of all responses Pressure Heat Time Pr*

28、He Pr*Ti He*Ti Pr*He*Ti +4.65 +2.20 -3.75 +0.15 +1.20 -1.45 -0.10 +2.32 +1.10 -1.88 +0.08 +0.60 -0.72 -0.05 Coefficient = Effect / 2Mean Value Of All Responses(23.5+26.7+26.9+30.6+19.9+25.7+20.6+26.5) / 8+25.05Modelling the response variableResponse = 25.05+2.32 * Pressure +1.01 * Heat - 1.88 * Time

29、 + 0.08 * Pressure * Heat + 0.60 * Pressure * Time - 0.72 * Heat * Time -0.05 * Pressure * Heat * Time Linear model with two levels. Curvilinear effect cannot be determinedA Two Level Factorial DesignRun order is a randomised standard orderPlus signs and minus signs show high and low levels of facto

30、r settings (coded units)Can use actual settings rather than plus and minus signs (uncoded units)Experiment run order 4 means factor A, B and C set at plus, plus, minusOutcome of experiment noted in response columnCREATING A DESIGN STRUCTURE12 345678Factor CFactor AFactor BStd Order12345678Run Order3

31、1746582Factor A-+-+-+-+Factor B-+-+Factor C-+ResponseCreating & Analyzing Factorial DesignsProblem : In the final stages of production, a steel auger is cleaned just prior to packaging. Temperature, time and concentration of the cleaning solution have been identified as the key input variables that

32、affect the cleanliness. The task is to find the factor settings that produce the cleanest parts. Procedure: After cleaning each part, the cleanliness of the auger is evaluated by measuring the remaining residue on the part. To do this, the auger is soaked in a solvent. The solvent is then evaporated

33、 and the remaining residue is measured. You are looking for the treatment that produces the lowest residue. You replicate the experiment so you will have two runs for each treatment. Only eight runs can be made in a single day. Because you need a total of 16 runs, you will use Day as a blocking fact

34、or. Experimental Unit : Steel augers.Factor levels : Temperature (120,180 F); Time (10, 30 sec);Concentration (2,6)Measurement : Remaining residue after cleaning. Replicates : 2 Blocks : 2 (Day)Data Set : 08 RESIDUE.MPJExample 8 : Minimizing residue in an industrial cleaning processReplicated Factor

35、ial Designs with Text VariablesProblem : You want to study the effect of oil viscosity, temperature, and a special additive on engine wear. Procedure: You are looking for the treatment that produces the least wear. You replicate the experiments so you will have two runs for each treatment and will b

36、e able to test all possible interactions. All experiments can be run in a single day. Factor levels : Viscosity (30,40);Temperature (75, 100 F); Additive ( A, B);Measurement : Engine wearReplicates : 2 Data Set : 09 ENGWEAR.MPJGroup Work : Engine wear2k Factorial Design - DescriptionSpecialised desi

37、gn consisting of K factors, each observed at only two levels Two-level full factorial designs can have up to 7 factorsTwo-level fractional designs can have up to 15 factors (Resolution IV) or 47 factors (Resolution III, Plackett Burman)Can be quantitative, such as two levels of temperature or pressu

38、reor qualitative , such as two machines or two locationsa full factorial 2K is efficient - efficient design requires the least number of runs of any full factorial designBecause of its simplicity and efficiency, it is the experimental design most commonly used in industry.Both full and fractional fa

39、ctorial designs can be used to screen important factorsin early stages of experimentation2K Factorial DesignFactor A, B, C = 2 Levels12 345678BAC6General Full Factorial Design - DescriptionA design in which there are K factors, each having a limited number of levelsMenu command allows up to 9 factors, each having up to 10 levelsSession command allows 9 factors, more than 10 levelsCan have qualitative or quantitative factorsLimiting each factor to two levels simplifies the