IntroductiontoDOE诺基亚公司DOE设计实验培训教材.ppt

*,Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,1999 Six Sigma QualtecSSQ 352 01_seg3.DOEintro,Design of ExperimentsIntroduction and Overview,Version 1.1.0,We Will Now Begin To Finalize Our Identification Of Critical X Variables,And To Begin Our Investigations Of The Nature Of“F,”,The Transfer Function In The Equation Above.,The Focus of the Improve PhaseY=f(X),At this point in the Six Sigma process,we should have:,An understanding of the magnitude and scope of the problem,including defects per unit(DPU)and Cost of Poor Quality(COPQ),Concrete goals and objectives,including projected DPU reductions and cost savings.,A Y variable with a reliable measurement system,A capability analysis of Y with an understanding of the nature of process deficienciesis there a problem with mean,variance,distribution shape,or some combination of the three?,A short list of potential X variables obtained through analysis of process demographics,multi-vari analysis,and other graphical and statistical techniques,2,Experiments,An“experiment”is.,Any testing in which the inputs are either controlled or directly manipulated according to a plan,A“designed experiment”.,Adds structure to the plan and a specific methodology to the analysis of the results,3,Experimentation Strategy,Define the problem.,Establish the experimental objective.,Select the output(response)variables.,Select the input(independent)variables.,Choose the levels for the input variables.,Select the experimental design.,Execute the experiment and collect data.,Analyze the data.,Draw statistical conclusions.,Replicate or validate the experimental results.,Draw practical solutions.,Implement the solutions.,4,As we move down this list,the experiments generate more and more powerful data.Usually,this comes at the price of larger experimental designs,more samples,or increased complexity.We must determine,as a part of our planning activities,the quality of information we need to improve our process or product.,Hierarchy of Experimentation,One factor at a time,Screening designs(Fractional-Factorials),Characterization designs(Full-Factorials),Optimization designs(response surface methods),5,Device:The Catapult,Ball Type,“Wiffle”,“Solid”,Pin Position,Number of,Rubber Bands,(1 or 2),Cup Position,Hook Position,Stop Position,3,4,5,1,2,3,4,1,2,3,4,5,6,Start Angle,6,1,2,Process Design ProblemHow to Launch a Ball a Specific Distance,6,Define the problemSet up an accurate catapult,Establish the experimental objectiveLaunch the ball 5 meters with minimal variability,Select the output(response)variablesDistance(in meters),Select the input(independent)variables,Start angle,Ball type,Number of bands,Others,Stop angle,Band tension,Band type,Choose the levels for the input variables,Only two levels allowed,Must be wide enough apart to see the differences,Select the experimental design,Experimental designs are matrices of-1 and+1 values arranged such that certain mathematical characteristics are maintained,Execute the experiment and collect data,Analyze data,Main effects plots,Interaction plots,Cube plots,Draw statistical conclusions,Does the experiment provide useful results?,Are there important main effects or interactions?,Replicate or validate the experimental results,Draw practical solutions,Implement solutions,Executing the Experiment Strategy,Questions:,What Does“Predictable”Mean?How Do We Measure The Distance?How Good Is Our Distance Measurement?,7,Evaluate the ResponseMeasurement System,There are a number of potential measurement systems for distance.,Break into groups and do a quick measurement system evaluation.,Establish a standard measurement methodology to be used in future experimentation.,A suggested measurement method is to have multiple“spotters”who agree on the distance the ball has traveled.,Develop a standard process procedure.,For the purposes of experimentation,you should try to eliminate as many outside sources of error as possible.That means that only one person should launch balls in the experiment.,Make sure you track each treatment.For the class exercises,you may use Minitab,but when you run real experiments,you should generate paper-based data-collection sheets.,8,Gage name:,Date of study:,Reported by:,Tolerance:,Misc:,Catapult Distance,Session 3,Black Belt Candidates,1,2,3,4,5,6,7,8,9,10,30,31,32,33,34,35,36,37,38,39,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,Part,Xbar Chart,Sample Mean,X=35.37,3.0SL=36.49,-3.0SL=34.24,1,2,3,4,5,6,7,8,9,10,0,1,2,3,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,10,Part,R Chart,Sample Range,R=1.100,3.0SL=2.832,-3.0SL=0.000,1,2,3,4,5,6,7,8,9,10,30,31,32,33,34,35,36,37,38,39,Part,By Part,%Total Var,%Study Var,Gage R&R,Part-to-Part,0,50,100,Components of Variation,Percent,Gage Capability for Catapult Distance,Source,%Contribution,%Study Var,Total Gage R&R4.5321.29,Repeatability4.5321.29,Part-to-Part95.4797.71,Total Variation100.00100.00,Acceptable Gage R&R Output,9,Executing the Experiment Strategy,Define the problemSet up an accurate catapult,Establish the experimental objectiveLaunch the ball 5 meters with minimal variability,Select the output(response)variablesDistance(in meters),Select the input(independent)variables,Start angle,Ball type,Number of bands,Others,Stop angle,Band tension,Band type,Choose the levels for the input variables,Only two levels allowed,Must be wide enough apart to see the differences,Select the experimental design,Experimental designs are matrices of-1 and+1 values arranged such that certain mathematical characteristics are maintained,Execute the experiment and collect data,Analyze data,Main effects plots,Interaction plots,Cube plots,Draw statistical conclusions,Does the experiment provide useful results?,Are there important main effects or interactions?,Replicate or validate the experimental results,Draw practical solutions,Implement solutions,10,Selecting the Input VariablesUsually Called“Factors”in DOE Terminology,Use multi-vari and other basic techniques to reduce the“trivial many”let the process talk to you.,Results from previous experiments.,Use your process knowledge.,Consult with the process expertsthe team.,Rules of thumb:,Experience says it is likely that there are only two to six“vital few”Xs.,The challenge is to find the influential variables and the test range that will allow you to verify their importance.,Test the most likely factors first.keep the design simple.,It is a judgment callsometimes you will have to pick more.,11,ExerciseBrainstorm“X”Variables,Break into groups and brainstorm potential X variables.Shoot some balls to get a feel for how the system works.There are more than 10 potential X variables.Try to get the selection down to fewer than six.,12,Executing the Experiment Strategy,Define the problemSet up an accurate catapult,Establish the experimental objectiveLaunch the ball 5 meters with minimal variability,Select the output(response)variablesDistance(in meters),Select the input(independent)variables,Start angle,Ball type,Number of bands,Others,Stop angle,Band tension,Band type,Choose the levels for the input variables,Only two levels allowed,Must be wide enough apart to see the differences,Select the experimental design,Experimental designs are matrices of-1 and+1 values arranged such that certain mathematical characteristics are maintained,Execute the experiment and collect data,Analyze data,Main effects plots,Interaction plots,Cube plots,Draw statistical conclusions,Does the experiment provide useful results?,Are there important main effects or interactions?,Replicate or validate the experimental results,Draw practical solutions,Implement solutions,13,Choosing Variable Levels,The two levels(low and high)are coded as-1 and+1.,For the catapult problem,we might choose two start angles:,Low level(-1)-140 degrees,High level(+1)-180 degrees,The range must be wide enough to show a difference if it is there.,Not beyond the range of feasibility(may be beyond the current process range).,Realize that some combinations in the test will produce unacceptable units and that these results are expected and accepted.,A starting place for continuous Xs is the limits of the current operating conditions.,14,Executing the Experiment Strategy,Define the problemSet up an accurate catapult,Establish the experimental objectiveLaunch the ball 5 meters with minimal variability,Select the output(response)variablesDistance(in meters),Select the input(independent)variables,Start angle,Ball type,Number of bands,Others,Stop angle,Band tension,Band type,Choose the levels for the input variables,Only two levels allowed,Must be wide enough apart to see the differences,Select the experimental design,Experimental designs are matrices of-1 and+1 values arranged such that certain mathematical characteristics are maintained,Execute the experiment and collect data,Analyze data,Main effects plots,Interaction plots,Cube plots,Draw statistical conclusions,Does the experiment provide useful results?,Are there important main effects or interactions?,Replicate or validate the experimental results,Draw practical solutions,Implement solutions,15,Two-Variable Full-Factorial,A,B,A LOW,B LOW,-1(A),-1(B),A HIGH,B LOW,1(A),-1(B),A LOW,B HIGH,-1(A),1(B),A HIGH,B HIGH,1(A),1(B),0(A),0(B),Simple design,Four tests to control,One interaction,Only information on two factors and their interaction,Pros,Cons,16,A,B,A*B,-1,+1,-1,+1,-1,-1,+1,+1,+1,-1,-1,+1,A,Low,High,B,Low,High,Design,Low,High,Low,High,A,B,Other Views of the Two-VariableFull-Factorial,17,Two-Variable Full-Factorial Design,Run,Order,A,B,AB,1,-1,-1,+1,2,+1,-1,-1,3,-1,+1,-1,4,+1,+1,+1,Features of Factorial DesignsBalance,Balance:Each of the variables in the experiment has the same number of runs at the high and low levels.In the design below,variable“A”has two runs in which it is at its high level and two runs in which it is at its low level.If we sum the A column,we get(-1)+(+1)+(-1)+(+1)=0.This property helps to simplify the mathematical analysis of the design by giving each level of the variable an equal impact on the final result.,18,Features of Factorial Designs Orthogonality,Orthogonality:If we multiply the signs of each of the variable columns,we get the“AB”column at the right side of the design below.This column represents the interaction between A and B.The property of“orthogonality”ensures that the plus and minus signs are arranged in the main effects columns(A and B)such that their product column will be balanced.This,in turn,ensures that each of the factors will be independent of the others.In the design below,variable“A”has two runs in which it is at its high level and two runs in which it is at its low level.If we sum the AB column,we get(-1)(-1)+(+1)(-1)+(-1)(+1)+(+1)(+1)=0.,Run,Order,A,B,AB,1,(1),-1,-1,+1,2,a,+1,-1,-1,3,b,-1,+1,-1,4,ab,+1,+1,+1,Two-Variable Full-Factorial Design,19,Three-Variable Full-Factorial,A,B,B,C,+,-,+,+,-,-,+,-,A,B,C,-1,-1,-1,+1,-1,-1,-1,+1,-1,+1,+1,-1,-1,-1,+1,+1,-1,+1,-1,+1,+1,+1,+1,+1,Only three factors allowed,Eight tests to control,Simple design,Three two-factor interactions,No confounding(confusion among factors),Pros,Cons,20,A,B,AB,C,AC,BC,ABC,-1,-1,+1,-1,+1,+1,-1,+1,-1,-1,-1,-1,+1,+1,-1,+1,-1,-1,+1,-1,+1,+1,+1,+1,-1,-1,-1,-1,-1,-1,+1,+1,-1,-1,+1,+1,-1,-1,+1,+1,-1,-1,-1,+1,-1,+1,-1,+1,-1,+1,+1,+1,+1,+1,+1,+1,Three-Variable Full-Factorial Matrix,The matrix below shows the variables A,B,and C,referred to as the“main effects,”as well as the interactions that are computed from the main effects.The column AB(typically referred to as a“two-way interaction”)is obtained by multiplying the contents of column A with the contents of column B.The column ABC(the“three-way interaction”)is obtained by multiplying columns A,B,and C together.All full-factorial experiments can be expanded by this method.,21,A,B,C,D,-1,-1,-1,-1,+1,-1,-1,-1,-1,+1,-1,-1,+1,+1,-1,-1,-1,-1,+1,-1,+1,-1,+1,-1,-1,+1,+1,-1,+1,+1,+1,-1,-1,-1,-1,+1,+1,-1,-1,+1,-1,+1,-1,+1,+1,+1,-1,+1,-1,-1,+1,+1,+1,-1,+1,+1,-1,+1,+1,+1,+1,+1,+1,+1,Four factors(main effects),Six two-factor interactions,No confounding(confusion among factors),16 trials required,B,C,A,D,B,C,A,Four-Variable Full-Factorial,Pros,Cons,22,A,B,-1,-1,+1,+1,-1,-1,+1,+1,Two Variables,A,B,C,-1,-1,-1,+1,-1,-1,-1,+1,-1,+1,+1,-1,-1,-1,+1,+1,-1,+1,-1,+1,+1,+1,+1,+1,Three Variables,A,B,C,D,-1,-1,-1,-1,+1,-1,-1,-1,-1,+1,-1,-1,+1,+1,-1,-1,-1,-1,+1,-1,+1,-1,+1,-1,-1,+1,+1,-1,+1,+1,+1,-1,-1,-1,-1,+1,+1,-1,-1,+1,-1,+1,-1,+1,+1,+1,-1,+1,-1,-1,+1,+1,+1,-1,+1,+1,-1,+1,+1,+1,+1,+1,+1,+1,Four Variables,Select Your Variables and Choose Your Design Matrix,23,We want to generate a design for a 2,3,factorial model.There are no blocking factors.We want to run a full-factorial 2 x 2 x 2=eight runs.,Generating Full-Factorial Models(In Minitab),StatDOECreate Factorial Design,24,Well run a three-variable full-factorial experiment with eight runs.You must first specify the number of factors,then press the“Designs”button to get the screen below.Move the highlight bar to the“Full-factorial”row.,Specifying the Three-Variable Model,25,Specifying Design Options,26,Specifying Variable Names and Levels,27,Minitab Design Output,The-1 and+1 can represent a low level and a high level of a factor and can be discrete or continuous.,Examples are temperature,shear stress,cycle time,fixture A and B,etc.,The first column/factor is alternating as:Solid,Holes,Solid,Holes.,The second column/factor is alternating as:140,140,170,170.,The third factor is four negatives and four positives.,This is called“Yates standard order,”developed for ease of computation.,28,Executing the Experiment Strategy,Define the problemSet up an accurate catapult,Establish the experimental objectiveLaunch the ball 5 meters with minimal variability,Select the output(response)variablesDistance(in meters),Select the input(independent)variables,Start angle,Ball type,Number of bands,Others,Stop angle,Band tension,Band type,Choose the levels for the input variables,Only two levels allowed,Must be wide enough apart to see the differences,Select the experimental design,Experimental designs are matrices of-1 and+1 values arranged such that certain mathematical characteristics are maintained,Execute the experiment and collect data,Analyze data,Main effects plots,Interaction plots,Cube plots,Draw statistical conclusions,Does the experiment provide useful results?,Are there important main effects or interactions?,Replicate or validate the experimental results,Draw practical solutions,Implement solutions,29,Run Your Designs!,30,Executing the Experiment Strategy,Define the problemSet up an accurate catapult,Establish the experimental objectiveLaunch the ball 5 meters with minimal variability,Select the output(response)variablesDistance(in meters),Select the input(independent)variables,Start angle,Ball type,Number of bands,Others,Stop angle,Band tension,Band type,Choose the levels for the input variables,Only two levels a