【正文】 face Analysis, all X’s must be continuous variables. 40 15 20 Plating (mm) Soak Time (min.) 50 60 25 Concentration (%) x2 x1 y x2 x1 y = Plating (mm) Wire Diagram 35 Central Composite Designs Since we have previously covered the design of a full factorial with more than two levels, we will now focus on the Central Composite Design. ? is used to represent the distance the axial point is from the center point in scaled units. ? is chosen to assure rotatability and orthogonal blocking Factorial points Axial points Center points ? This design has desirable properties, including: ? It can be run in sequential orthogonal blocks, first cube points, then axial points ? ? can be chosen for rotatability 36 Optimizing for Multiple Responses The results of this mand are shown below: An overall desirability score less than 1 shows a trade off was necessary between the responses The Cur values are the factor level settings that achieve the optimum desirability. The y values listed give the response at the Cur settings The vertical lines slide. As you move them, you can see the effect on the desirability score 37 Recap of DOE Module A. Awareness B. Full Factorial Designs Topic Purpose Subtopics Get people thinking about what’s involved with running an experiment Demonstrate benefits of structured multifactor experiments Learn ways to reduce the number of trials needed for a designed experiment and still get all the information you need Understand the practical aspects of experimental design How we currently run an experiment ? Change one thing at a time ? Change everything we think matters all at once Do by hand Using Minitab to design and analyze experiments Random ization Replica tion , Residuals Main effects Inter actions Effects amp。 Ppk Estimated PPM Actual Observed PPM 19 ANALYZE IMPROVE 20 The Focus of Analyze Y = f (X1, X2, X3, ..., Xn) X1, X3, X5 Identification Verification Quantification What vital few process and input variables (Xs) affect critical to quality process performance or output measures (Ys)? 21 Process or Data Door? Process Door Data Door ?To understand the drivers of variation in the process ?To tackle quality problems and waste ?To understand the root cause of differences between outputs ?To improve the understanding of process flow ?To tackle cycle time problems ?To identify opportunities to reduce process costs Stratification Scatter Diagrams MultiVari Analysis Detailed Process Map Value Added Analysis Cycle Time Analysis It is remended to go through both doors to make sure that potential causes are not overlooked. 22 Two Types of Errors in Hypothesis Testing A ctual (Truth )Groups areSameGroups areD if f eren tAc c ept H 0 :Gro u p s a r e S a m eN o Error T y pe I I Err orC o n cl u si o norD eci si o n R ejec t H0 :Gro u p s a r e Diffe r e n tT y pe I Error N o ErrorThere are four possible outes to any decision we make based on a hypothesis test: We can decide the groups are the same or different, and we can be right or wrong. ? Both types of error are important. ? Guarding too heavily against one error increases the risk of the other error. ? Increasing the sample size: ? Reduces the risk of Type II errors. ?Allows you to detect smaller differences. Actual (Truth) Innocent Guilty Innocent Innocent Guilty amp。 factorial plots C. Half Fractions D. Other Fractions E. Screening Designs F. Planning an experiment Which runs we’d pick intuitively Nice properties (balance, collapsing) Cost of fraction ation is confound ing For large half fractions, get same results as full fraction Using Minitab to design Resolution, standard notation Practice interpreting Regular vs . Plackett Burman Practice interpreting Using the Experimenter’s Checklist Learn how to quantify an optimal solution G. Response Surface Methodology 38 Three Rules ? Plot the Data ? Plot the Data ? Plot the Data 39 IMPROVE IMPROVE 40 Creativity Techniques More Involved Techniques: Idea Box ? A way to automatically bine parameters or characteristics of a challenge into new ideas ? Example – Improved design for a laundry hamper Material Shape Finish Position Wicker Square Natural Sits on Floor Plastic Cylindrical Painted On Ceiling Paper Rectangle Clear On wall Metal Hexagonal Luminous Chute to Basement Net material Cube Neon On door INSTRUCTOR NOTES: Run through this example and show how one then circles one or more items from each column (so long as they are not mutually exclusive) to form a specific solution. This is a good team activity which results in a useful munication tool for 3rd parties. Different solutions which arise from this or other tools can be rated and analyzed using the Solution Prioritization Matrix ing up in a few slides. 41 Evaluating Alternative Ideas In order to get better solutions, we will follow these steps: ? Generate Criteria ? Weight Criteria ? Evaluate Ideas The tool we will use for this is the Solution Prioritization Matrix. Solution A B C D 2 5 2 10 6 Easy Quick Tech Hi Impact Customers SUM 2 2 1 1 10 4 4 2 5 7 155 1 1 10 2 4 136 102 2 10 2 10 168 1 Criteria and Weights INSTRUCTOR NOTES: Briefly introduce this tool as a concept. Details are in subsequent slides. 42 Benefits Analys