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Split-plot designs Martin Arvidsson

Split-plot designs Martin Arvidsson. 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

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Split-plot designs Martin Arvidsson

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  1. Split-plot designsMartin Arvidsson

  2. 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

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

  4. Individual value plot

  5. Individual value plot – two outliers removed

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

  7. Histogram of the”populations”

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

  9. 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.

  10. Resetting of factor levels

  11. Responses arenot independent! If factors are not reset between each experiment, contrasts will have unequal variance!

  12. 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 control factors (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

  13. Experimental design Product Process variables (control factors) 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

  14. Confounding pattern

  15. Contrasts!

  16. Analysis of the experiment B BG G contrasts

  17. Confounding pattern

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

  19. Variances of the contrasts

  20. 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

  21. Model B ≈ 1.4

  22. 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.

  23. 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

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