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.....................

5

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

The Hardness Testing Example

• 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 randomization
• All runs within a block are randomized

6

The Hardness Testing Example

• Suppose that we use b = 4 blocks:

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