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CSUN Engineering Management Six Sigma Quality Engineering Week 11 Improve Phase

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Objectives Overview of Design of Experiments A structured method to learn about a process by changing many factors at the same time. It occurs in Improvement Phase. Fractional factorial experiments are used for initial screening Full factorial experiments are smaller and more precise Graphical Analysis Main effects plots Interaction plots Cube plots Statistical Analysis P value for main effects and interactions

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Six Sigma - DMAIC Roadmap

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Establish Optimum Process Select Solutions Prepare improvement Plans FMEA for Solution Cost Benefit Analysis Verify Metrics Prioritization Matrix Document ‘To Be’ Process Pilot Solution Implementation & Deployment Plans Process Documentation Improvement Strategies Screen Critical Inputs (DOE Plan) Refine Model Define & Confirm Y = f (x) Improve Phase Improve Develop, try out & implement solutions that address root causes Key Deliverables Solutions Risk Assessment on Solution Pilot Results Implementation Plans Goal: Develop, try out, and implement solutions that address root causes Output: Planned, tested actions that eliminate or reduce the impact of the identified root causes

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Improve Phase Cost-Benefit Analysis Generating Solutions Generate solutions including Benchmarking and select best approach based on screening criteria A B C D 4 1 3 2 Perform cost-benefit analysis for the preferred solution Assessing Risks Use FMEA to identify risks associated with the solution and take preventive actions Piloting Test Full scale Original Pilot the solution on a small scale and evaluate the results 2 4 8 6 10 G 13 5 7 9 A B C D F E J IH G Implementation Develop & Execute a full plan for implementation and change management Selecting the Solution Recommend a solution involving key stakeholders. Design of Experiments Use DOE and response surface optimization to quantify relationships.

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CSUN Engineering Management Design of Experiments

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What is a Designed Experiment? A method to change all the factors at once in a structured pattern to determine their effects on the output(s) The structured pattern is known as an orthogonal array ABA X B 1-1-1 1 2 1-1 -1 3-1 1 -1 4 1 1 1 0 0 0

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Full Factorial Designs Full Factorial: Examines factor effects and interaction effects. These become large rather quickly. 2 2 Full Factorial = 2 factors, 2 levels = 4 runs2 2 Full Factorial = 2 factors, 2 levels = 4 runs 3 Full Factorial = 3 factors, 2 levels = 8 runs2 3 Full Factorial = 3 factors, 2 levels = 8 runs 2 4 Full Factorial = 4 factors, 2 levels = 16 runs2 4 Full Factorial = 4 factors, 2 levels = 16 runs 2 5 Full Factorial = 5 factors, 2 levels = 32 runs2 5 Full Factorial = 5 factors, 2 levels = 32 runs Used after initial screening experiments or where the process is simple or well known. The experiment is run to optimize the process using a vital few factors.

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2 3 Example of a 2 3 Full Factorial Design Run

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Fractional Factorial Designs Fractional Factorial: Examines factor effects and a carefully selected portion of interaction effects. Shrinks the number of runs for each fraction by one half. 2 7 Full Factorial = 7 factors, 2 levels = 128 runs2 7 Full Factorial = 7 factors, 2 levels = 128 runs 2 (7-1) 1/2 Fractional Factorial = 7 factors, 2 levels = 64 runs2 (7-1) 1/2 Fractional Factorial = 7 factors, 2 levels = 64 runs 2 (7-2) 1/4 Fractional Factorial = 7 factors, 2 levels = 32 runs2 (7-2) 1/4 Fractional Factorial = 7 factors, 2 levels = 32 runs 2 (7-3) 1/8 Fractional Factorial = 7 factors, 2 levels = 16 runs2 (7-3) 1/8 Fractional Factorial = 7 factors, 2 levels = 16 runs 2 (7-4) 1/16 Fractional Factorial = 7 factors, 2 levels = 8 runs2 (7-4) 1/16 Fractional Factorial = 7 factors, 2 levels = 8 runs

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Fractional Factorial Designs Uses interaction column settings to estimate the effects of main factors. Used for initial screening designs to isolate the important (vital few) factors. One DoE leads to another. Fractional Factorial DoE’s lead to smaller Full Factorial DoE’s.

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Basic Experimental Terms

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The Idea of Confounding A B AB 2 (a) 3 (b) 5 (c) 8 (abc) 1 - 1 1 1 1 1 C - 1 1 AC 1 BC 1 1 11111111 ABC Same Signs Was “Y” affected by A or by the interaction of B and C?

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Basic Experimental Terms

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General Comments In general, industry considers 3rd and 4th order interactions to be negligible. Fractional Factorial experiments “pool” the effects of interactions to estimate residual error. No replicates are run - USE WITH CAUTION! Use Fractional Factorial Experiments for screening, then follow up with Full Factorial Designs. Keep your experiments simple

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Be Proactive! DOE is a proactive tool. If DoE output is inconclusive: You may be working with the wrong variables Your measurement system may not be capable The range between high and low levels may be insufficient There is no such thing as a failed experiment Something is always learned New data prompts asking new questions and generates follow-on studies

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CSUN Engineering Management Design of Experiments Minitab practice

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The resolution number tells you what factor and interactions will be confounded with one another. Design Resolution

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Questions? Comments?

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Design-plots for factorial and fractional-factorial designs Russell R Barton Journal of Quality Technology; 30, 1 ; Jan 1998 報告者：李秦漢.

Design-plots for factorial and fractional-factorial designs Russell R Barton Journal of Quality Technology; 30, 1 ; Jan 1998 報告者：李秦漢.

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