实验设计(英文).doc

Module #: Module TitleDesign of Experiments (DOE)Program TitleMod #-1Participant Guide 2001 Ford Motor CompanyRev Date: 2005-3-30 下午 04:322005-3-30 15:32 实验设计.docDOE.doc file pathCourse TitleInstructor GuideThe subject matter contained herein is covered by a copyright owned by:FORD MOTOR COMPANYCORPORATE QUALITY DEVELOPMENT CENTERDEARBORN, MICopyright 2001 Ford Motor CompanyThis document contains information that may be proprietary. The contents of this document may not be duplicated by any means without the written permission of Ford Motor Company.All rights reservedNotes:iVersion April 2001 2001 Ford Motor Company Design of Experiments (DOE) 大量的管理资料下载Participant GuideTable of ContentsIntroduction3Agenda3Purpose of the Course5Goal5Objectives5Design of Experiments (DOE) History7DOE and the STA Engineer7Definition of DOE7Uses of DOE9Planning10Steps for Experimental Design10DOE Plan Analysis13Common Failures13Influences on Control Factors13Evaluation Procedures15Steps of the DOE17Checklist for DOE19Questions to Ask the Supplier about the Plan21Adding up (Pool) Standard Deviations22Steps for Simple Analysis24Factorial Experiments25Basic Concept25Interaction Effects29Fractional Factorials30Use of the Results32A Practical Aid for Experimenters33Significance of Factor Effects35Activity: Typical Three-factor two-level experiment36Fractional Factorial Design37DOE Methods39Classical Versus Taguchi Methods39Taguchis Loss Function41Optimal cost of quality42Taguchi Method44Taguchi Cake-Baking Example45Tips from Taguchi47Signal-to-Noise Ratio49Controlling Noise51Inner and Outer Arrays52Signal to Noise for Maximum or Minimum54Confirming the Experiment56Evolutionary Operation (EvOp)58ANOVA Methods60Assumptions for Applying ANOVA60Analysis of Variance62Calculations for ANOVA Table64Case Studies69Case Study 1 The Mismatched Muffler70Case Study 271Summary74Additional Resources76Subject Matter Expert (SME)76Additional Training76References76Review of Answers to Pre-Test and Post-Test77 2001 Ford Motor Company Pilot AprilVersion: June 2001iiiIntroductionWelcome to the Design of Experiments (DOE) course, part of the Corporate Quality Development Center curriculum. This is one of the courses in the Quality Tools module, which is designed to provide STA Engineers with practical knowledge of the tools required to successfully accomplish their jobs. AgendaIntroductionDesign of Experiment (DOE) HistoryPlanningDOE Plan AnalysisFactorial ExperimentsDOE MethodsCase StudiesSummaryAdditional ResourcesPurpose of the CourseThis course presents statistical concepts needed to design, conduct, analyze, and interpret multi-factor experiments, which are used in factor screening, characterizing and optimizing of processes. GoalThe goal of this course is to provide STA Engineers with the knowledge to review a Suppliers DOE to determine if it has been set up, performed, implemented and analyzed correctly.ObjectivesUpon completion of this course, the participant will be able to: Define the role of the STA Engineer in relation to DOE and process improvement Define the purpose of DOE and application types (Classical and Taguchi) Identify criteria for conducting a DOE Explain the basic steps of conducting a DOE Recognize appropriate and inappropriate outcomes and processes of a Supplier DOE (case studies) Identify common failures that an STA Engineer may encounter while reviewing a DOE Identify strategic questions that should be asked when reviewing a DOE Explain the relationship between DOE and the rest of the quality tools Identify additional resources available to assist with the conduct or analysis of a DOEDesign of Experiments (DOE) HistoryThe history of DOE goes back to the 1920s, when it was used in agriculture. Today it is a widely expected engineering tool used at Ford and by its Suppliers.DOE and the STA EngineerThe role of an STA Engineer is to understand DOE in order to make sound judgments when dealing with Suppliers. The STA Engineer will need to recognize if a Supplier has the ability to set up, perform, implement, and analyze the improvement process correctly.Definition of DOEDOE is a total plan of action aimed at obtaining knowledge about a given process to improve it or to solve a problem. The objective of a designed experiment is to obtain more information with less expenditure of resources than can be obtained by traditional (one factor at a time) techniques.DOE was pioneered by R.A. Fisher, an agricultural scientist, in England in the 1920s. He used the technique to study the effect on the outcome of multiple variables simultaneously. Fisher wanted to find out how much rain, water, fertilizer, sunshine, etc. were needed to produce the best crop.PESTICIDEB2B12468A1FERTILIZERA2Uses of DOEDesign of Experiments can play a key role in understanding and improving the reliability of Fords vehicles.Experimentation can be used to: Model degradation of function in vehicle systems Identify factors that significantly improve system life or degradation rate Model multivariate functional relationships that can be used for optimization studiesDOE at Ford will: Reduce imperfections in parts Reduce costs Reduce guess work Reduce lost time Improve customer relations Improve relations with Suppliers Improve productivityClassical DOE provides a predictive equation.Taguchi DOE quickly solves problems. PlanningSteps for Experimental Design1. State the problem(s): Use quality measures to clearly indicate the level of quality or loss. This may come from the Global 8D analysis. The problem statement should address the following:a. What data exists that characterizes the problem as it occursb. How the problem is observedc. When the problem occursd. How severe the problem ise. Where the problem occurs2. State the objective of the experiment: This statement should address the scope of the experiment and should be based on:a. The problem statementb. Competitive benchmark information concerning the problemc. Customer information concerning the problemStart Date _End Date _3. Select the quality characteristics and measurement systems: The characteristics (responses, dependent variables, or output variables) should be related to customer needs and expectations. The chart below captures the response, the type, and the anticipated range that helps to determine the method of measurementResponseTypeAnticipated RangeMeasurement Method/AccuracySteps for Experimental Design, continued4. Select the factors that may influence the selected quality characteristics: Process flow diagrams, cause/effect diagrams, specifications, statistical process control chart results are some sources for this information and may be captured in a chart similar to the one below.FactorTypeControllable or NoiseRange of InterestLevelsAnticipated Interactions withHow Measured.5. Determine the number of resources to be used in the experiment: Consider the desired number, the cost per resource, time per experimental trial and the maximum allowable number of resources.6. Determine which design types and analysis strategies are appropriate: Discuss advantages and disadvantages of each.7. Select the best design type and analysis strategy to suit the needs.8. Determine if all the runs can be randomized and which factors are most difficult to randomize.9. Conduct the experiment and record the data: Monitor both the events for accuracy.10. Analyze the data, draw conclusions, make predictions, and do confirmatory tests.11. Assess results, make decisions, and document results: Evaluate new state of quality and compare with level prior to improvement effort.DOE Plan AnalysisWhen analyzing the plan, it is important to understand the common failures and influences of control factors in order to verify that the plan has accounted for these factors.Common FailuresThe common failures that occur when conducting a DOE are: Data is collected when there is only one variable. Supplier often leaves out the interaction. Supplier has not identified recent changes in the process.Influences on Control Factors Temperature Different operators Humidity Location of plant Environmental factors Lack of consistency Different sample sizeEvaluation Procedures Define precisely the procedures for running the experiment, indicating which factors can be easily changed from one run to the next. Get information regarding past data and repeatability. Determine desirability and opportunities for running the experiment in stages. List relationship between the independent variable and response variable.Steps of the DOETasksTask AidsWhoState problem(s)Quality Function Deployment, test failures, warranty items, scrap items, Pareto AnalysisProduct and/or process expertsState objective(s)Customer requirements, competitive benchmarksSelect quality characteristic(s) & measurement system(s)Gage repeatability & reproducibility analysisSelect factors and interactions; determine control and noise factorsFishbone diagram, flowcharts, SPC chartsSelect levelsSpecification limits, operational limitsSelect orthogonal array(s)OA selection tables D-1, D-2; blank OAsAssign factors & interactions to orthogonal array(s)Assignment tables D-3, D-4; interaction tables; OA modification rulesDOE expertConduct testsComputer software, trial data sheets, randomization plan, part serialization plan, material logistics planProduct, process, and DOE expertsAnalyze and interpret dataObservation method, column effects method, ANOVA, computer software, plotting, ranking (magnitude & time order)DOE expertConduct Confirmation TestEstimates of the mean confirmation experiment flowchartProduct, process, and DOE expertsChecklist for DOE Identify the proper people to be involved in the process/product team and the leader of the investigation team. Describe in measurable terms the problemhow the present situation differs from what is desired. Obtain agreement from those involved on: Scope of the investigation Other constraints such as time or resources Obtain agreement on the goal of the investigation. Determine if staging for DOE is appropriate or if other research, such as SPC, should be accomplished first. Use brainstorming and problem-solving tools to determine what factors may be important and which of them could interact. Total agreement is required to eliminate any. Choose a response that relates to the underlying cause and not the symptom and is measurable, if possible. Determine the test procedure to be used and assess repeatability and reproducibility if applicable. Determine which of the factors are controllable and which are not. Determine the levels to be tested for each factor (experiment boldly). Choose or develop the appropriate experimental design. Obtain final agreement from all involved parties on the: Goal Approach Allocation of roles Experimental design Test procedure Timing of the work plan Arrange to stage appropriate product, machinery, and testing facilities. Monitor the experiment to ensure proper procedures are followed. Use the appropriate techniques to analyze the data. Prepare a summary of the experiment with graphical portrayal of conclusions and recommendations.Questions to Ask the Supplier about the Plan Has the problem been adequately defined based on reported effects? Was the 8D process followed to determine interim actions and identify process elements contributing to the problem? Is sufficient statistical data/evidence available to narrow down variables to the significant few? What statistical tools were used? Is there an established procedure for applying DOE techniques and evaluating test results? Has adequate screening been performed to determine process alternatives against “must” criteria and/or eliminate unacceptable alternatives? Is there sufficient statistical evidence for verifying levels of process stability and capability over the recent past? Have any process changes, as defined in the PPAP manual, been made in the recent past including subcontractor processes? Has a criteria matrix been completed with weighting of “desirable criteria” (all potential improvements) in selection of response variables?Note: Response variables must be customer Critical to Quality (CTQ) characteristics in addressing given problems. In defining the experimental program, what criteria was used in selecting the independent factors affecting the response variable? Was appropriate screening done to eliminate factors not judged as having a major impact on response variable? To further refine the list of factors, were traditional testing methods, such as Trial and Error, Special Batch Runs, Pilot Runs, and Planned Comparisons, used to identify the 2-3 factors having the biggest impact on the response variable? Was/is the experiment designed to test the impact of the factors together rather than testing one factor at a time? Was an objective measurement system using qualified test or gaging methods selected to measure responses?Adding up (Pool) Standard Deviations First square the standard deviations (= the variance)Multiply each variance (S2 ) by n-1 (to weight them properly).Then add them and divide by the sum of the two (n-1)sHere is the formula:Steps for Simple Analysis1. Check data for accuracy.2. Conduct visual analysis of the data.3. Calculate the average at each level for each column.4. Calculate the effects and half-effects for each column.5. Plot the averages from Step #3.6. Generate a Pareto diagram of the absolute value of each half-effect from Step #4.7. Determine the “importance” of each half-effect.* When appropriate, construct interaction plots for “important” interactions.8. Generate a prediction equation using “important” half-effects.9. Based upon your objective, select the best settings for important factors/interactions.10. Using the prediction equation generated in Step #8, predict the response. Use this value as a target for verification runs.*If using software such as DOE KISS, use statistical significance to determine important half-effects (coefficients).Adapted from the Air Academy Association Factorial ExperimentsBasic ConceptThe first factorial experiments were done in England, before WWII, by R.A. Fisher. These were agricultural experiments. The purpose was to see how various factors affected crop growth by applying “treatments” to “blocks” of land.Example 1:A block of land is divided into four parts. Two types of fertilizer (A1 and A2) are applied from east to west, and two types of pesticide (B1 and B2) are applied from north to south.PESTICIDEB2B12468A2A1FERTILIZER The numbers inside the squares represent the average growth for each square of land. Even without further analysis, it seems obvious that fertilizer A2 and pesticide B2 would be good choices.Example1: (continued)To determine the effect of each factor, calculate the average for levels 1 and 2 of each factor, and then find the difference.FERTILIZERA1A2B1B2PESTICIDEAVE.EFFECTAVE.EFFECT3746422468Interaction EffectsAlthough the effect is 4 inches and the pesticide effect is 2 inches, a check is needed to see whether these effects are additive. It is possible that when the best fertilizer and the best pesticide are combined, the result will be 0 inches or 12 inches instead of 6 inches. Averaging diagonally does the check for additive effects. If the factor effects are additive, then diagonal averages are just estimates of the grand average and the interaction effects should be relatively small. If there is a lack of additivity, it is called an “interaction.”FERTILIZERA1A2B1B2PESTICIDEEFFECTAB5502468Fractional FactorialsSo far there are six averages from only four sets of measurements. This tremendous efficiency can be increased further if we happen to know from experience that the factors are additive.Example 2:Assume that the watering schedule will be additive with fertilizer and pesticide. A third factor can be added by putting different watering schedules on the diagonal squares.C1C2PESTICIDEB2B1A2A1FERTILIZER The additional factor might change the averages, but if the hypothesis about additivity is correct, the difference in the averages (effect) will stay the same for factors A and B. This is called a fractional factorial because there is not enough data to separate all the interactions that are theoretically possible.Use of the ResultsThe factor effects as computed represent the difference between the response at the high and low levels of the factors. If the factor effect is divided by the difference between the high and low levels of the factors, the results will be the change in the response for a coded unit change in the factor.The model underlying the two-level factorial is written in terms