Quality Management - Taguchi Techniques

Robust Design: Experiments for Better Products Taguchi Techniques Robust Design and Quality in the Product Development Process Planning Planning Concept System-Level Concept System-Level Development Design Development Design Robust Concept and System Design Detail Detail Design Design Testing Testingand and Refinement Refinement Production Production Ramp-Up Ramp-Up Robust Quality efforts are Parameter & typically made here, Tolerance when it is too late. Design COST $ COST $ Goalpost vs Taguchi View Nominal Value Nominal Value General Loss Function Product & Process Engineer (a priori) [ Manufacturing (daily) k ⋅ σ + (µ − m ) 2 2 ] Nominal Value Average Value Variance Cost Factor Who is the better target shooter? Pat Drew Exploiting Non-Linearities YB YA XA XB Goals for Designed Experiments Understanding relationships between design parameters and product performance „ Understanding effects of noise factors „ Reducing product or process variations „ Robust Designs A Robust Product or Process performs correctly, even in the presence of noise factors. „ Outer Noise Environmental changes, Operating conditions, People „ Inner Noise „ „ Function & Time related (Wear, Deterioration) Product Noise „ Part-to-Part Variations Parameter Design Procedure Step 1: P-Diagram Step 1: Select appropriate controls, response, and noise factors to explore experimentally. „ controllable input parameters „ measurable performance response „ uncontrollable noise factors The “P” Diagram Uncontrollable Noise Factors Product Productor or Process Process Controllable Input Parameters Measurable Performance Response Example: Brownie Mix „ Controllable Input Parameters „ „ „ „ Uncontrollable Noise Factors „ „ „ „ Recipe Ingredients (quantity of eggs, flour, chocolate) Recipe Directions (mixing, baking, cooling) Equipment (bowls, pans, oven) Quality of Ingredients (size of eggs, type of oil) Following Directions (stirring time, measuring) Equipment Variations (pan shape, oven temp) Measurable Performance Response „ „ Taste Testing by Customers Sweetness, Moisture, Density Step 2: Objective Function Step 2: Define an objective function (of the response) to optimize. „ maximize desired performance „ minimize variations „ quadratic loss „ signal-to-noise ratio Types of Objective Functions Larger-the-Better e.g. performance ƒ(y) = y2 Smaller-the-Better e.g. variance ƒ(y) = 1/y2 Nominal-the-Best e.g. target ƒ(y) = 1/(y–t)2 Signal-to-Noise e.g. trade-off ƒ(y) = 10log[µ2/σ2] Step 3: Plan the Experiment Elicit desired effects: „ „ „ Use full or fractional factorial designs to identify interactions. Use an orthogonal array to identify main effects with minimum of trials. Use inner and outer arrays to see the effects of noise factors. Experiment Design: Full Factorial „ „ „ „ Consider k factors, n levels each. Test all combinations of the factors. The number of experiments is nk . Generally this is too many experiments, but we are able to reveal all of the interactions. Experiment Design: Full Factorial Expt # Param A Param B 1 A1 B1 2 A1 B2 3 A1 B3 4 A2 B1 5 A2 B2 6 A2 B3 7 A3 B1 8 A3 B2 9 A3 B3 2 factors, 3 levels each: nk = 32 = 9 trials 4 factors, 3 levels each: nk = 34 = 81 trials Experiment Design: One Factor at a Time „ „ „ „ Consider k factors, n levels each. Test all levels of each factor while freezing the others at nominal level. The number of experiments is 1+k(n-1). BUT this is an unbalanced experiment design. Experiment Design: One Factor at a Time Expt # Param A Param B Param C Param D 1 A2 B2 C2 D2 2 A1 B2 C2 D2 3 A3 B2 C2 D2 4 A2 B1 C2 D2 5 A2 B3 C2 D2 6 A2 B2 C1 D2 7 A2 B2 C3 D2 8 A2 B2 C2 D1 9 A2 B2 C2 D3 4 factors, 3 levels each: 1+k(n-1) = 1+4(3-1) = 9 trials Experiment Design: Orthogonal Array „ „ „ „ „ Consider k factors, n levels each. Test all levels of each factor in a balanced way. The number of experiments is n(k-1). This is the smallest balanced experiment design. BUT main effects and interactions are confounded. Experiment Design: Orthogonal Array Expt # Param A Param B Param C Param D 1 A1 B1 C1 D1 2 A1 B2 C2 D2 3 A1 B3 C3 D3 4 A2 B1 C2 D3 5 A2 B2 C3 D1 6 A2 B3 C1 D2 7 A3 B1 C3 D2 8 A3 B2 C1 D3 9 A3 B3 C2 D1 4 factors, 3 levels each: n(k-1) = 3(4-1) = 9 trials Using Inner and Outer Arrays „ Induce the same noise factor levels for each combination of controls in a balanced manner 4 factors, 3 levels each: L9 inner array for controls A1 A1 A1 A2 A2 A2 A3 A3 A3 B1 B2 B3 B1 B2 B3 B1 B2 B3 C1 C2 C3 C2 C3 C1 C3 C1 C2 D1 D2 D3 D3 D1 D2 D2 D3 D1 3 factors, 2 levels each: L4 outer array for noise E1 F1 G2 E1 F2 G1 E2 F1 G2 E2 F2 G1 inner x outer = L9 x L4 = 36 trials Step 4: Run the Experiment Step 4: Conduct the experiment. „ Vary the input and noise parameters „ Record the output response „ Compute the objective function Paper Airplane Experiment Expt # Weight Winglet Nose 1 A1 B1 C1 2 A1 B2 C2 3 A1 B3 C3 4 A2 B1 C2 5 A2 B2 C3 6 A2 B3 C1 7 A3 B1 C3 8 A3 B2 C1 9 A3 B3 C2 Wing D1 D2 D3 D3 D1 D2 D2 D3 D1 Trials Mean Std Dev S/N Step 5: Conduct Analysis Step 5: Perform analysis of means. „ Compute the mean value of the objective function for each parameter setting. „ Identify which parameters reduce the effects of noise and which ones can be used to scale the response. (2-Step Optimization) Parameter Design Procedure Step 6: Select Setpoints „ Parameters can effect Average and Variation (tune S/N) „ Variation only (tune noise) „ Average only (tune performance) „ Neither (reduce costs) „ Parameter Design Procedure Step 6: Advanced Use Conduct confirming experiments. „ Set scaling parameters to tune response. „ Iterate to find optimal point. „ Use higher fractions to find interaction effects. „ Test additional control and noise factors. „ Confounding Interactions „ „ Generally the main effects dominate the response. BUT sometimes interactions are important. This is generally the case when the confirming trial fails. To explore interactions, use a fractional factorial experiment design. S/N Confounding Interactions A1 A2 A3 B1 B2 B3 Key Concepts of Robust Design „ „ „ „ „ „ „ Variation causes quality loss Parameter Design to reduce Variation Matrix experiments (orthogonal arrays) Two-step optimization Inducing noise (outer array or repetition) Data analysis and prediction Interactions and confirmation