Blocking Engineering Experiments - Part 03
Design of Engineering Experiments
Part 3 – The Blocking Principle
- Text Reference, Chapter 4
- Blocking and nuisance factors
- The randomized complete block design or the RCBD
- Extension of the ANOVA to the RCBD
- Other blocking scenarios…Latin square designs
2
The Blocking Principle
- 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, time (shifts, days, etc.), different experimental units
- Many industrial experiments involve blocking (or should)
- Failure to block is a common flaw in designing an experiment (consequences?)
3
The Blocking Principle
- If the nuisance variable is known and controllable, we use blocking
- If the nuisance factor is known and uncontrollable, sometimes we can use the analysis of covariance (see Chapter 15) to remove the effect of the nuisance factor from the analysis
- If the nuisance factor is unknown and uncontrollable (a “lurking” variable), we hope that randomization balances out its impact across the experiment
- Sometimes several sources of variability are combined in a block, so the block becomes an aggregate variable
4
The Hardness Testing Example
- Text reference, pg 120
- We wish to determine whether 4 different tips produce different (mean) hardness reading on a Rockwell hardness tester
- Gauge & measurement systems capability studies are frequent areas for applying DOX
- 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
- Alternatively, the experimenter may want to test the tips across coupons of various hardness levels
- The need for blocking.....................
~
Friday, April 2, 2010
0
comments
