Slide 1Definition of Robust DesignSlide 3Purpose of this ModuleObjectives of this ModuleStrategies to Detect Variation EffectsThe Passive ApproachHow to ensure that noise is noisy?A Passive ExampleExample output from a Passive DesignThe ModelsExample: A Passive Noise ExperimentDesign Capability Analysis24 Full Factorial ExperimentPassive Analysis Roadmap - Part 1 (for Mean Only)Interaction PlotMain Effects PlotFactorial AnalysisReduce Model to Significant TermsThe Role of Residual Plots in RDWhat Next?Passive Analysis Roadmap - Part 2 (if Variation effect present)Create a Variability ResponseUses Natural Log (Standard Dev of Y)Create a Variability ResponseCreate a Variability ResponseAnalyze the VariabilityAnalyze the VariabilityPareto Chart of the EffectsFinal Model for ln StDevY1Interaction Plot for StDevY1Main Effects Plot for StDevY1Determine Mean & Variation EffectsQuality Check: Status of Your ModelsMultiple Response OptimizerMultiple Response OptimizerUse the Equations to Confirm Y1Use the Equations to Confirm StDevY1Final Design Capability AnalysisRemember the Two Strategies?The Active ApproachExample: An Active Noise ExperimentActive Analysis Roadmap – Plots OnlyExample: An Active Noise ExperimentDesign Capability AnalysisExample: An Active Noise ExperimentThe Experimental DesignFactorial AnalysisFit the Reduced ModelInteraction PlotInteraction Plot – A Closer LookMain Effects PlotNew Settings : Capability AnalysisHow much should we shift factor A?New Setting for A : Capability AnalysisSummaryObjectives RevisitedDesign forDFSS-1Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.Executing Robust DesignDesign forDFSS-2Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.Definition of Robust DesignRobustness is defined as a condition in which the product or process will be minimally affected by sources of variation.A product can be robust:Against variation in raw materialsAgainst variation in manufacturing conditionsAgainst variation in manufacturing personnelAgainst variation in the end use environment` Against variation in end-usersAgainst wear-out or deteriorationDesign forDFSS-3Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.Why We Need to Reduce VariationCostLow Variation;Minimum CostLSLLSLUSLUSLNomNomCostHigh Variation;High CostLSLLSLUSLUSLNomNomDesign forDFSS-4Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.Purpose of this ModuleTo introduce a variation improvement investigation strategy–Can noise factors be manipulated?To provide the MINITAB steps to design, execute, and analyze a variability response experimentTo provide the MINITAB steps to optimize a design for both mean and variation effectsDesign forDFSS-5Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.Objectives of this ModuleAt the end of this module, participants will be able to :Identify possible variation effects from residual plotsCreate a variability response from replicatesIdentify possible mean and variance adjustment factors from noise-factor interaction plotsUse the MINITAB Response Optimizer to achieve a process on target with minimum variationDesign forDFSS-6Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.Strategies to Detect Variation EffectsPassive Approach–Noise factors are NOT included, manipulated or controlled in the experimental design–Possible variation effects are identified through analysis of the variability of replicates from an experimental designActive Approach–Noise factors ARE included in the experimental design in order to force variability to occur–Analysis is similar to the passive approachDesign forDFSS-7Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.The Passive ApproachA factorial experiment is performed using Control factors. Noise factors are not explicitly manipulated nor is an attempt made to control them during the course of the experiment.Pros–Simple extension of standard experimental techniques–Does not require explicit identification of noise factorsCons–Requires larger number of replicates than would typically be required to determine mean effects–Requires “true” randomization and replication–Requires that noise factors be “noisy” during the execution of the experimentDesign forDFSS-8Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.How to ensure that noise is noisy?Let excluded factors varyCompare noise factor variations prior to and within DOE–Monitor noise factor levels during normal process conditions–Monitor noise factor variation during course of experiment–Compare before/during levelsRun DOE over a longer period of time with :–More replicates–Full randomizationDesign forDFSS-9Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.A Passive ExampleA and B are control factors. Within each treatment combination, noise factors are allowed to naturally fluctuate. Within treatment variation is largely driven by this background noise.ABDesign forDFSS-10Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.Example output from a Passive DesignThe graphs at right illustrate the type of output which might be obtained from a Robust Parameter Design Experiment. Both are Main Effects plots with the top row showing the main effects of factors A and B on the mean and the bottom row showing the main effects of factors A and B on the variation.Note that in this example the mean and variation can be adjusted independently of each other!BA6.45.44.43.42.4MeanMean YBA0.60.40.20.0-0.2LogVarianceVariation YDesign forDFSS-11Copyright 2003 Cummins, Inc. All Rights Reserved.Copyright 2000-2002 Sigma Breakthrough Technologies, Inc. Used with permission.The ModelsOur objective in performing a designed