Presentation on theme: "An approach to the SN ratios based on"— Presentation transcript:
1An approach to the SN ratios based on the proportional models and its applicationThe Institute of Statistical Mathematics, Tokyo, JAPANKAWAMURA ToshihikoYokohama College of PharmacyIWASE Kosei
2Robust Parameter Design OutlineTaguchi Design of ExperimentsRobust Parameter DesignSignal-to-Noise (SN) ratiosThe testing problem of the equality for two SN ratios
3Taguchi Design of Experiments Robust Parameter Design, also called the Taguchi Method pioneered by Dr. Genichi TAGUCHI, greatly improves engineering productivity.Comparable in importance to Statistical Process Control, the Deming approach and the Japanese concept of TQCRobust Parameter Design is a method for designing products and manufacturing process that are robust to uncontrollable variations.Based on a Design of Experiments (Fisher’s DOE) methodology for determining parameter levelsDOE is an important tool for designing processes and productsA method for quantitatively identifying the right inputs and parameter levels for making a high quality product or serviceTaguchi approaches design from a robust design perspective
4The Taguchi Approach to DOE Traditional Design of Experiments (Fisher’s DOE) focused on how different design factors affect the average result levelTaguchi’s DOE (robust design)Variation is more interesting to study than the averageRun experiments where controllable design factors and disturbing signal factors take on 2 or 3 levels.
5Robust Design (I)By consciously considering the noise factors and the cost of failure in the Taguchi method helps ensure customer satisfaction.Environmental variation during the product’s usageManufacturing variation, component deteriorationNoise factors (Disturbances) are events that cause the design performance to deviate from its target valuesA three step method for achieving robust designConcept designParameter designTolerance designThe focus of Taguchi is on Parameter design
6Robust Design (II) Robust Parameter Design (e.g. Wu and Hamada 2000) A statistical / engineering methodology that aim at reducing the performance “variation” of a system.The selection of control factors and their optimal levels.The input variables are divided into two board categories.Control factor: the design parameters in product or process design.Noise factor: factors whoes values are hard-to-control during normal process or use conditionsThe “optimal” parameter levels can be determined through experimentation
7Signal to Noise (SN) Ratios (I) Performance measureTaguchi’s SN ratio
9The Taguchi Quality Loss Function The traditional model for quality lossesNo losses within the specification limits!Scrap CostLSLUSLTargetCostThe Taguchi loss functionthe quality loss is zero only if we are on targetloss functionrisk functionSN ratios
10A new performance measure (I) However, if the adopted principles of the signal-response systems are diffent and the physical quantities of the response values are different between the systems, the comparison of the Taguchi’s SN ratios has no sense.A new performance measure for the systems :We propose a dimensionless SN ratios (Kawamura et al. 2006).Proportional model, K loss function, Dynamic SN ratiosThe response and the signal factor values are positive real values.
11A new performance measure (II) The response and the signal factor values are positive real values.Consider two-parameter statistical models for positive continuous observation.Log normal distributionGamma distributionInverse Gaussian distribution etc.Error distribution
12A new performance measure (III) K loss functionK risk function
14A test of the Equality for two SN ratios (I) We consider the testing problem of the equality for two SN ratiosSN ratios for the systems with Dynamic CharacteristicsPerformance comparison of the systems
15A test of the Equality for two SN ratios (II) Data 2Data 1SN ratio A2SN ratio A1Which performance is good ?Testing homogeneity of SN ratios
16A test of the Equality for two SN ratios (III) Null hypothesisA Variance Stabilizing TransformationApproximation Test