Lab session 3: Questions
Question 1: Balance Incomplete Block Design (BIBD)
As an example, suppose that a chemical engineer thinks that the time of reaction for a chemical process is a function of the type of catalyst employed. Four catalysts are currently being investigated. The experimental procedure consists of selecting a batch of raw material, loading the pilot plant, applying each catalyst in a separate run of the pilot plant, and observing the reaction time. Because variations in the batches of raw material may affect the performance of the catalysts, the engineer decides to use batches of raw material as blocks. However, each batch is only large enough to permit three catalysts to be run. Therefore, a randomized incomplete block design must be used. The balanced incomplete block design for this experiment, along with the observations recorded, is shown in next Table. The order in which the catalysts are run in each block is randomized.
a) Input the data into the software.
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Treatment (Catalyst)
Block (Batch of Raw Material)
7374 71 75 67 72
b) How many times each pair of treatments appears in the same block?
c) Test if there is a difference between the four treatments (Catalysts)? Draw your conclusions using α = 5%.
d) Obtain the estimates of treatment means (i.e., the adjusted means or the least square means) and the standard error of the difference between two treatment mean estimates (i.e. the standard error of 𝜏𝑖 – 𝜏𝑗 ).
e) Compare all pairs of treatment means by using the Tukey test.
f) Generate a block design with five treatments in four blocks of three. Generate the
design in a Table and test if this design is a Balanced Incomplete Block Design (BIBD)?
g) Generate a block design with five treatments in seven blocks of three elements.
Generate the design in a Table and test if this design is a Balanced Incomplete Block Design (BIBD)?
Question 2: Full Factorial Designs
a) Generate a full factorial design with two variables each with three levels.
b) Generate a full factorial design with three variables, two of them with three levels and one
with two levels. Name the variables as A, B and C, respectively.
c) Generate a full factorial design with three variables, one with two levels, one with three
levels and one with six levels. Name the variables as A, B and C respectively.
d) Generate a full factorial design with two variables each with three levels, but this time
include 4 replications of the design. Name the variables as Matype and Temp, respectively.
e) As an example of a factorial design involving two factors, an engineer is designing a battery for use in a device that will be subject to some extreme variations in temperature. The only
design parameter that he can select at this point is the plate material for the battery, and he has three possible choices. When the device is manufactured and is shipped to the field, the engineer has no control over the temperature extremes that the device will encounter, and he knows from experience that temperature will probably affect the effective battery life. However, temperature can be controlled in the product development laboratory for the purposes of a test.
• What effect do the type of the material and the temperature have on the life of the battery?
• Is there a choice of material that would give uniformly long life regardless of the temperature?
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