DQWR KWWS HNR VWDII XQV DF LGMicrosoft PowerPoint - Workshop 2 Author: Asti Created Date: 5/5/2018 11:49:54 AM

DOE Basics in 90’

Eko Pujiyanto08122783991http://eko.staff.uns.ac.id

Out lines

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

http://eko.staff.uns.ac.id

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


Randomization

Simple Random Sampling

Permuted block randomization

Stratified Random Sampling.


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.


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.


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


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.


Choice of factors, levels, and ranges






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.




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.



The Analysis of Variance






The Plasma Etching Experiment





Randomized Block


Blocking is a technique for dealing with nuisancefactors

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

Randomized Block


Many industrial experiments involve blocking (or should)

Failure to block is a common flaw in designing an experiment (consequences?)

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



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



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



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 randomizationAll runs within a block are randomized



Anova to the RCBD


Suppose that there are a treatments (factor levels) and bblocks

A statistical model (effects model) for the RCBD is

The relevant (fixed effects) hypotheses are

1,2,...,

1,2,...,ij i j ij

i ay

j b

Anova to the RCBD


Anova to the RCBDExample : 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.






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DQWR KWWS HNR VWDII XQV DF LGMicrosoft PowerPoint - Workshop 2 Author: Asti Created Date: 5/5/2018 11:49:54 AM