Exercise 5

 

 

 

  1. Suppose that a chemical engineer wants to study the effects of seven variables

on the yield of a chemical reaction and is willing to make 32 runs. He elects to

perform a 27-2 fractional factorial design with the generators I = 1237 and

I = 126. The main effect of variable 1 in this design is confounded with what other:

  1. Main effect(s)?

  2. Two-factor interaction(s)?

  3. Three-factor interaction(s)?

  4. Four-factor interaction(s)?

  5. Five-factor interaction(s)?

    6. (If the main effect of variable 1 is unconfounded with any particular item,write “none”.)

  6. Suggest an alternative plan that produces less confounding of low-order

effects.

 

 

2. A consulting firm engaged in road-building work is asked by one of its clients to carry out an experimental study to determine the effects of six variables on the physical properties of a certain kind of asphalt. Call these variables A,B,C,D,E, and F.

  1. If a full two-level factorial design was used, how many runs would be made?

  2. Write a two-level resolution IV fractional factorial design requiring only 16 runs.

  3. Write a set of generators for this design.

  4. What is the defining relation for this design?

  5. In your design, what effects are confounded with the main effects of variable A? With the two-factor interaction BD?

 

 

3.Suppose that, after you have set up a 214-10 resolution III main effect plan

for an electrical engineer, he says it is essential to split the design into two blocks of equal size because the tests must be done on 2 days and he fears a day-to-day difference in the results. Make recommendations.

 

 

4.An experimenter performs a 25-2 fractional factorial design. The generators for this first design are I = 1234 and I = 135.After analyzing the data from the first design, he decides to perform a second 25-2 fractional factorial exactly the same as the first except that the signs are changed in column 3 of the design matrix.

  1. How many runs does the first design contain?

  2. Give a set of generators for the second design.

  3. What is the resolution of the second design?

  4. What is the defining relation of the combined design? (The combined design is the first and the second designs considered together as a single design.)

  5. What is the resolution of the combined design?

  6. The combined design is a 2k-p fractional factorial design where k and p have what values, that is, k = ? and p = ?

  7. Give one possible reason why the experimenter might have chosen the second design in the way he did.

 

 

5.Design an eight-run fractional factorial design for an experimenter with the following five variables: temperature, concentration, pH, agitation rate, and catalyst type (A or B). He tells you he is particularly concerned about the two-factor interactions between temperature and concentration, and between catalyst type and temperature. He would like a design, if it is possible to construct one, such that these two two-factor interactions are unconfounded with main effects and unconfounded with one another.