Split-plot designs Martin Arvidsson

1. Split-plot designsMartin Arvidsson

2. 2 Bone Anchored Hearing Aids

3. Details of the improvement work The objective of the project is to improve the production yield of transducers • Transducers are made up by a rather large number of components • The assembly process of transducers include a rather large number of operations • The assembly process requires that measurement equipment work satisfactory

4. A simple test performed at Cochlear BAS to evaluate a new supplier of components • The objective of the test was to evaluate whether washers from a new supplier could be used • Altogether 120 transducers where produced, 60 with washersordinary used and 60 with washers from a new potential supplier • The order in which the 120 transducers was produced was randomised

5. Individual value plot

6. Individual value plot – two outliers removed

7. Time series plot to investigate whether the process was stable during the test

8. Histogram of the”populations”

9. Complete randomisation • Randomisation of run order • Resetting of all factor levels between each experiment

10. order Exp. A B C Y nr 8 1 - - - 53.8 5 2 + - - 51.8 1 3 - + - 47.4 2 4 + + - 47.8 4 5 - - + 50.6 7 6 + - + 51.8 6 7 - + + 48.2 3 8 + + + 48.6 Randomizing • Problem: Systematic dependence between the experiments. • Solution: Make the experiments in random order.

11. Resetting of factor levels

12. Responses arenot independent! If factors are not reset between each experiment, estimated effects will have unequal variance!

13. Split-plot designs: A Composite Material Example Manufacturing process of composite material y – bending strength response variable • Four different process conditions • Eight batches of raw material ? A – curing temperature B – pressure C – holding time Design parameters (process variables) y = f (A,B,C,D,E,F,G,H) D – proportion of hardener E – thermo-plastic content F – proportion of epoxy G – material ageing H – process type noise factors

14. Experimental design Product Process variables (design parameters) A Curing temperature B Pressure C Holding time Incoming material (noise factors) D Proportion of hardener E Thermo-plastic content F Proportion of epoxy G Material aging H Type of process Process

15. Confounding pattern

16. Estimated Effects!

17. Analysis of the experiment B BG G effects

18. Confounding pattern

19. εs εw ε εs1 ε1 εw1 εs2 εw2 εw3 εw4 ε32 Error structure of a Strip-Block Experiment

21. Variances of the effects

22. Identification of location effects Process factors Factors and interactionsassociated with incoming material Interactions between ”process factors”and ”incoming material factors” • B, G and BG was determined to be active based on engineering knowledge and the normal plots

23. Model B ≈ 1.4

24. Conclusions • The storage time of the incoming material (G) is causing variation in the bending strength of the composite material. • If the pressure (B) is set at high level the bending strength is made insensitive to the storage time.

25. 25 Noise factors: Ambient temperature, moisture, customer misuse, quality of components etc. Response:The signal transferred to the Cochlea Signal Factor: Sounds of different frequencies and complete failure… Control Factors:Choice of design solution, choice of nominal value of components, choice of materials, choice of assembly etc. P-diagram sound processor … a Robust product performs as intended despite the existence of noise factors

26. Randomisation and split-plot • View randomisation as an insurance against unknown factors - buy as much as you can afford • It is not always advisable to reset all factor levels between each experiment! • Can be very time consuming and expensive • Split-plot designs allow some contrasts of interest to be estimated with great precision. This characteristic can, for example, be useful in robust design experiments