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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Fuel Cell Highlights from the Los Angeles Show

Hot Wheels 10 Car Pack (Styles May Vary)

Honda unveiled a fuel cell concept sports car, the FC Sport, at its press event, and had the FCX Clarity in the “Green Car” ride-and-drive held in conjunction with the Green Car of the Year program.

Volkswagen held a media event prior to the show at which it offered drives in three different fuel cell vehicles: the Touran minivan, Tiguan SUV and Passat Lingyu, a sedan developed in China. VW also detailed its advances in high-temperature fuel cells, a breakthrough it claims will allow simpler and cheaper fuel cell stack configuration because it will require less complicated cooling than other versions.

Kia unveiled its second-generation fuel cell vehicle, the Borrego FCEV at its press conference. This vehicle has a power stack that is almost 50 percent more powerful than the previous generation and uses a supercapacitor for energy storage, but also delivers an impressive 54 miles to the gallon.

Nissan had its fuel cell vehicle, the X-Trail FCV, in the ride-and-drive. The new fuel cell stack in the Nissan doubles the power density of the previous generation stack and also achieves a 35 percent cost reduction mainly due to using half the platinum of earlier versions.

General Motors also had its Chevy Equinox FCV in the ride-and-drive program, one of 100 being used in its Project Driveway program that has thousands of regular citizens as well as key influencers evaluating daily life with a fuel cell vehicle.

Fuel cell vehicles certainly face challenges before becoming a mainstream product, but many in the industry and government still see them as the “holy grail,” capable of delivering all of the convenience and performance of an internal combustion engine without the pollution and greenhouse gases, or dependence on fossil fuel.