IE 673Session 7 - Process Improvement (Continued) 1 Process Improvement (Continued)

IE 673Session 7 - Process Improvement (Continued) 2 Introduction to Design of Experiments (DOE) Quickly optimize processes Reduce development time Reduce manufacturing costs Reduce scrap and rework Increase throughput Improve product quality Make products/processes more robust Reduce need for control charting

IE 673Session 7 - Process Improvement (Continued) 3 Experimental designs are specific collections of trials run so the information content about a multi- variable process is maximized. With response- surface experimental designs, the goal is to put this information into a picture of the process. – J. Stuart Hunter - Definition of DOE

IE 673Session 7 - Process Improvement (Continued) 4 Important Contributions From Different Approaches

IE 673Session 7 - Process Improvement (Continued) 5 Process Knowledge If what we know about our processes can’t be expresses in numbers, we don’t know much about them. If we don’t know much about them, we can’t control them. If we can’t control them, we can’t compete. –Motorola University -

IE 673Session 7 - Process Improvement (Continued) 6 Old Philosophy of Quality Quality is based on conformance to specifications Loss due to scrap & rework Loss due to scrap & rework LSLUSL

IE 673Session 7 - Process Improvement (Continued) 7 New Philosophy of Quality LSL USL Target L1 L2 L3 L3 > L2 > L1

IE 673Session 7 - Process Improvement (Continued) 8 Taguchi’s Concept DESIGN quality into the product and process. Design the PRODUCT to be least sensitive to variations rather than trying to control the factors. Design the product so that its performance parameters are CLOSEST TO THE TARGET. Minimize costs within quality constraints rather than maximize quality within cost constraints.

IE 673Session 7 - Process Improvement (Continued) 9 Quality Effort by Activity Development DesignManufacturingSolve Problems

IE 673Session 7 - Process Improvement (Continued) 10 Taguchi’s Quadratic Loss Function LSL USLTarget L0L0 L 1 = k(y 1 - T) 2

IE 673Session 7 - Process Improvement (Continued) 11 Example Let V(out) = 115 Vdc y = V(out) m = 115Vdc LD(50) = 115 +/- 20 Vdc (Consumer’s Tolerance) Repair Cost = $100 L(y) = k(y - 115) 2 k = L(y)/(y - m) 2 = $100/20 2 k = 0.25 If V(out) = 110 Vdc L(110) = 0.25( )^2 = $6.25

IE 673Session 7 - Process Improvement (Continued) 12 Example Suppose adjustment costs $2.00, i.e., the cost to rework. When should a unit be reworked? L(y) = 0.25 (y - 115)^2 $2.00 = 0.25 (y - 115)^2 8 = (y - 115)^2 y = 115 +/- 8 ^ 0.5 y = 115 +/- 2.83

IE 673Session 7 - Process Improvement (Continued) 13 System Design Parameter Design Tolerance Design Basis of The Taguchi Method

IE 673Session 7 - Process Improvement (Continued) 14 Purposeful changes of the inputs (factors) to a process in order to observe corresponding changes in the output (responses). What is Designed Experiments?

IE 673Session 7 - Process Improvement (Continued) 15 Strategies for Experimentation Screening Modeling (Characterization) Sensitivity Optimization Robust (parameter) Design Tolerance Design

IE 673Session 7 - Process Improvement (Continued) 16 Objectives of an Experimental Design Obtain maximum information using minimum resources. Determine which factors shift average response, which shift variability, which have no effect. Find factor settings that optimize the response and minimize the cost. Build empirical models relating the response of interest to input factors

IE 673Session 7 - Process Improvement (Continued) 17 Methods of Experimentation Full Factorials Fractional Factorials Plackett-Burman Latin Square Hadamard Matrices Foldover Designs Box-Behnken Designs D-Optimal Designs Taguchi Designs

IE 673Session 7 - Process Improvement (Continued) 18 Full Factorial Experiments Advantages –Tests all factors at all levels –Evaluates all main effects –Evaluates all interactions

IE 673Session 7 - Process Improvement (Continued) 19 Full Factorial Experiments Disadvantages –Large number of runs –Large number of samples –Takes long time to run –Expensive

IE 673Session 7 - Process Improvement (Continued) 20 Fractional Factorial Experiments Advantages –Fewer runs –Faster to complete –Fewer Samples –Less costly

IE 673Session 7 - Process Improvement (Continued) 21 Fractional Factorial Experiments Disadvantages –Cannot test all factors at all levels –Cannot evaluate all main effects –Cannot evaluates all interactions

IE 673Session 7 - Process Improvement (Continued) 22 Factorial Versus Taguchi

IE 673Session 7 - Process Improvement (Continued) 23 Taguchi Designs Orthogonal Arrays Screening Designs Robust Designs Minimal Runs

IE 673Session 7 - Process Improvement (Continued) 24 Layout for Taguchi L-8

IE 673Session 7 - Process Improvement (Continued) 25 Example