Blocking Engineering Experiments - Part 03

~ Friday, April 2, 2010

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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