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Split-plot designs Martin Arvidsson

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addison-oneil
24 diapositives · 434 Views · Nov 21, 2014

This study examines the feasibility of using washers from a new supplier for transducer production at Cochlear BAS. A simple test was conducted with a total of 120 transducers, comparing 60 produced with ordinary washers to 60 with those from the new supplier. The experiments employed a split-plot design to analyze the impact on production yield and stability during assembly, with controlled factors like curing temperature and pressure. Randomization ensured the reliability of results, highlighting important interactions affecting transducer performance.

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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