DOE Basics in 90. Eko Pujiyanto

Transcription

1 DOE Basics in 90 Eko Pujiyanto

2 Out lines Basic Principles Guidelines for Designing Experiments Experiment with a single Factor Randomized Block

3 Basic Principles Randomization Running the trials in an experiment in random order Notion of balancing out effects of lurking variables Replication Sample size (improving precision of effect estimation, estimation of error or background noise) Replication versus repeat measurements? Blocking Dealing with nuisance factors

4 Randomization Simple Random Sampling Permuted block randomization Stratified Random Sampling.

5 Replication Replication is the repetition of an experimental condition so that the variability associated with the phenomenon can be estimated. Replication is not the same as repeated measurements Replication reflects sources of variability both between runs and (potentially) within runs.

6 Blocking Blocking is a design technique used to improve the precision with which comparisons among the factors of interest are made. Blocking is used to reduce or eliminate the variability transmitted from nuisance factors that is, factors that may influence the experimental response but in which we are not directly interested.

7 Guidelines for Designing Experiments 1. Recognition of the statement of problem 2. Selection of the response variable(s) 3. Choice of factors, levels, and ranges 4. Choice of design 5. Conducting the experiment 6. Statistical analysis 7. Drawing conclusions, recommendations

8 Selection of the response variable(s) In selecting the response variable, the experimenter should be certain that this variable really provides useful information about the process under study. Most often, the average or standard deviation (or both) of the measured characteristic will be the response variable.

9 Choice of factors, levels, and ranges

10 Choice of factors, levels, and ranges

11 Choice of factors, levels, and ranges

12 Experiment with a single Factor An engineer is interested in investigating the relationship between the RF power setting and the etch rate for this tool. The objective of an experiment like this is to specify the power setting that will give a desired target etch rate. She wants to test four levels of RF power: 160, 180, 200, and 220 W. She decided to test five wafers at each level of RF power.

13 Experiment with a single Factor This is an example of a single-factor experiment with a 4 levels of the factor and n 5 replicates. The 20 runs should be made in random order.

14 Experiment with a single Factor

15 The Analysis of Variance

16 The Analysis of Variance

17 The Analysis of Variance The Plasma Etching Experiment

18 The Analysis of Variance

19 The Analysis of Variance

20 Randomized Block Blocking is a technique for dealing with nuisance factors A nuisance factor is a factor that probably has some effect on the response, but it s of no interest to the experimenter, however, the variability it transmits to the response needs to be minimized Typical nuisance factors include batches of raw material, operators, pieces of test equipment and time

21 Randomized Block Many industrial experiments involve blocking (or should) Failure to block is a common flaw in designing an experiment (consequences?)

22 Hardness testing experiment We wish to determine whether 4 different tips produce different (mean) hardness reading on a Rockwell hardness tester Assignment of the tips to an experimental unit; that is, a test coupon

23 Hardness testing experiment Structure of a completely randomized experiment The test coupons are a source of nuisance variability To conduct this experiment as a RCBD, assign all 4 tips to each coupon

24 Hardness testing experiment Each coupon is called a block ; that is, it s a more homogenous experimental unit on which to test the tips Variability between blocks can be large, variability within a block should be relatively small

25 Hardness testing experiment In general, a block is a specific level of the nuisance factor A complete replicate of the basic experiment is conducted in each block A block represents a restriction on randomization All runs within a block are randomized

26 Hardness testing experiment

27 Anova to the RCBD Suppose that there are a treatments (factor levels) and b blocks A statistical model (effects model) for the RCBD is y i 1, 2,..., a j 1,2,..., b ij i j ij The relevant (fixed effects) hypotheses are

28 Anova to the RCBD

29 Anova to the RCBD Example : Vascular Graft Experiment A medical device manufacturer produces vascular grafts (artificial veins). These grafts are produced by extruding billets of polytetrafluoroethylene (PTFE) resin combined with a lubricant into tubes. Frequently, some of the tubes in a production run contain small, hard protrusions on the external surface.

30 Anova to the RCBD Example : Vascular Graft Experiment

31 Anova to the RCBD Example : Vascular Graft Experiment

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