Six Sigma Quality Engineering

1. Six Sigma Quality Engineering Week 11 Improve Phase

2. 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

3. Six Sigma - DMAIC Roadmap

4. Improve Phase 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 • Key Deliverables • Solutions • Risk Assessment on Solution • Pilot Results • Implementation Plans Improve Establish Optimum Process Select Solutions Prepare improvement Plans Develop, try out & implement solutions that address root causes • Improvement Strategies • Screen Critical Inputs (DOE Plan) • Refine Model • Define & Confirm Y = f (x) • FMEA for Solution • Cost Benefit Analysis • Verify Metrics • Prioritization Matrix • Document ‘To Be’ Process • Pilot Solution • Implementation & Deployment Plans • Process Documentation

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

6. Design of Experiments

7. 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 A B A X B 1 -1 -1 1 2 1 -1 -1 3 -1 1 -1 4 1 1 1 0 0 0

8. Full Factorial Designs • Full Factorial: Examines factor effects and interaction effects. These become large rather quickly. • 22 Full Factorial = 2 factors, 2 levels = 4 runs • 23 Full Factorial = 3 factors, 2 levels = 8 runs • 24 Full Factorial = 4 factors, 2 levels = 16 runs • 25 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.

9. Example of a 23 Full Factorial Design Run

10. 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. • 27 Full Factorial = 7 factors, 2 levels = 128 runs • 2(7-1) 1/2 Fractional Factorial = 7 factors, 2 levels = 64 runs • 2(7-2) 1/4 Fractional Factorial = 7 factors, 2 levels = 32 runs • 2(7-3) 1/8 Fractional Factorial = 7 factors, 2 levels = 16 runs • 2(7-4) 1/16 Fractional Factorial = 7 factors, 2 levels = 8 runs

11. 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.

12. Basic Experimental Terms

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

14. Basic Experimental Terms

15. Basic Experimental Terms

16. Basic Experimental Terms

17. 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

18. 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

19. Design of Experiments Minitab practice

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

21. Questions? Comments?