Operating Window Experiments.ppt

Operating Window Experiments Outline Paper Feeder Example Operating Window Paper feeder example continued Examples Effect of Noise Factors Optimization SN Ratio Probability of failure modeling Performance Measure Modeling and Optimization Generalized Performance Measure Sequential Design/Estimation A Real Example Summary A rigorous statistical foundation Operating window SN ratio is justified using PerMIA theory under some restrictive modeling assumptions New and more effective modeling and optimization strategy Generalized performance measure (GPM) under more general modeling assumptions Logit-MLE method for sequential design Superiority of the proposed strategy is illustrated with an example * C. F. Jeff Wu and V. Roshan Joseph Department of Statistics University of Michigan Ann Arbor, MI, USA To appear in Journal of Quality Technology, 2002 Available in /~jeffwu/ Paper Feeder Example SN Ratio Probability of Failure Modeling Performance Measure Modeling and Optimization Generalized Performance Measure Sequential Design/Estimation Application to Real Data Summary Two failure modes Misfeed : fails to feed a sheet Multifeed: Feeds more than one sheet Objective: Minimize both misfeed and multifeed through parameter design optimization. Approach 1 Feed, say, 1000 sheets at different design settings Observe # of misfeeds and # of multifeeds Choose a design setting to minimize both Problems: Large sample size required to get reasonable power for statistical tests Conflicting levels: design settings that minimizes misfeeds tend to increase multifeeds Difficult to distinguish between two design settings Approach 2 Failures are extremities of certain functional characteristics Identify functional characteristics (continuous variables) that relates to misfeed and multifeed Do nominal-the-best optimization on these characteristics Example Misfeed : Roller-to-paper friction force Multifeed : Paper-to-paper friction force