1. DEMA2008 Post-Fractionated Strip-Block Designs with Applications to Robust Design and Multistage Processes Carla A. Vivacqua Universidade Federal do Rio Grande do Norte (UFRN) - Brazil vivacqua@ccet.ufrn.br Søren Bisgaard University of Massachusetts Amherst (UMASS) – USA University of Amsterdam – The Netherlands bisgaard@som.umass.edu

2. DEMA2008 2 Outline Introduction: –Strip-block designs –Battery cells case study New Arrangement: Post-Fractionated Strip-Block Design Analysis Conclusions

3. DEMA2008 3 Introduction Competitive environment requires: –Design of high-quality products and processes at low cost Six Sigma initiatives: –Design of experiments (DOE) plays a critical role

4. DEMA2008 4 Research Question How to reduce costs of experimentation? –Robust Design Products insensitive to different sources of variation –Multistage Processes

5. DEMA2008 5 Project Home

6. DEMA2008 6 The Problem High percentage of rejected batteries Annual losses of over $154,000 2 millions batteries scraped annually

7. DEMA2008 7 Customer Requirements High performance batteries Specification limits for the critical to quality issues: –Open Circuit Voltage (OCV) [1.00V, 1.38V] –Impedance [2Ω, 8Ω]

8. DEMA2008 8 Various Types of Batteries

9. DEMA2008 9 Battery Cells Case Study Task 2 Task 1 Task n Curing Process End Begin Assembly Process Defective rate: 5% Cause of cells rejection: high OCV Consequences of high OCV: self-discharging, leading to low performance or dead cells.

10. DEMA2008 10 Objective Identify settings of process variables leading to high quality battery cells –Close to target –Least amount of variation

11. DEMA2008 11 Process Characteristics Two shifts for production One curing room Storage cycle: at least five days Six factors for investigation – Assembly process: A, B, C, D – Curing process: E, F

12. DEMA2008 12 Approach 1 Completely randomized design 2 6 = 64 independent trials 64 changes in assembly configuration –Could not be run in one shift 64 changes in curing conditions –Data collection: 64 * 5 = 320 days

13. DEMA2008 13 (16)‏ (2)‏ (1)‏ (4)‏(3)‏(2)‏(1)‏ Curing Variables (2 2 )‏ Curing Conditions Assembly Variables (2 4 )‏ Fully Randomized Arrangement

14. DEMA2008 14 Approach 2 EFEF A B C D Storage Variables Sub-plots Assembly Variables Whole-plots } 2 2 full factorial design with 16 replicates 2 4 full factorial design Requires 16 changes in assembly configuration Still requires 64 changes in the storage configuration

15. DEMA2008 15 (16)‏ (2)‏ (1)‏ (4)‏(3)‏(2)‏(1)‏ Storage Variables (2 2 with 16 replicates)‏ Storage Conditions Assembly Variables (2 4 )‏ Run Split-Plot Design Whole Plot Sub-Plot

16. DEMA2008 16 Approach 3 EFEF A B C D Curing VariablesAssembly Variables } 2 2 full factorial design 2 4 full factorial design 16 trials Advantages: – only 16 changes in the assembly configuration – only 4 changes in the curing configuration

17. DEMA2008 17 (16)‏ (2)‏ (1)‏ (4)‏(3)‏(2)‏(1)‏ Curing Variables (2 2 )‏ Curing Conditions Assembly Variables (2 4 )‏ Run Strip-Block Design

18. DEMA2008 18 Strip-Block Experiment

19. DEMA2008 19 Scenario Space restrictions in storage room Only 8 sub-lots can be placed in the storage room simultaneously

20. DEMA2008 20 State-of-the-Art Approach – Use of Fractional Factorials Generator: D = ABC Resolution IV design

21. DEMA2008 21 New Approach: Post-Fractionated Strip-Block Design Generator: EF = ABCD Resolution VI design

22. DEMA2008 22 Post-Fractionated Strip-Block Design (2)‏ Generators: E = ABC, F = BCD Reduces to a split-plot design

23. DEMA2008 23 Maximum Post-Fractionation Order Base strip-block design: 2 k-p x 2 q-r Maximum value for post-fractionation order to preserve the strip-block structure: f = min(k-p, q-r) - 1. Ex.: 2 4 x 2 2 base design f = min(4, 2) – 1 = 2 – 1 = 1

24. DEMA2008 24 Analysis of Post-Fractionated Strip-Block Designs Compute main effects and interactions Not all effects with same precision Group effects with same variance Separate analyses for each stratum Four different strata

25. DEMA2008 25 Contrast Estimates f = 1 generator of post-fraction k-p = 4 basic factors of row design Remaining effects q-r = 2 basic factors of column design

26. DEMA2008 26 Variances

27. DEMA2008 27 Results Based on the analysis of the OCV mean only and taking into account that the problem is cells with high OCV the recommended levels would be: A  high level (+)B  high level (+)‏ C  low level (-)D  low level (-)‏ F  high level (+)‏

28. DEMA2008 28 Results – cont. Considering the OCV sub-lot variability and other variables of interest, the recommended settings are: A  low level (-)B  low level (-)‏ C  low level (-)D  low level (-)‏ E  low level (-)F  high level (+)‏

29. DEMA2008 29 Conclusions Post-fractionated strip-block designs –Cost-effective method to gather knowledge about products and processes –Attention to conduct appropriate analysis Catalogs of maximum resolution post- fractionated strip-block designs –16-run and 32-run designs –Up to 11 factors

30. DEMA2008 30 Summary Strip-block experiments: –Reduction of experimentation costs –Easy to execute –Logically suitable to available resources and restrictions

31. DEMA2008 31 Before vs. After Implementation 80% reduction on defective rate and 75% reduction on process variability!!!!

32. DEMA2008 32 Questions?

33. DEMA2008 33