14-3. In the book Design and Analysis of Experiments, 7th edition (2009, John Wiley & Sons),
the results of an experiment involving a storage battery used in the launching mechanism of
a shoulder-fired ground-to-air missile were presented. Three material types can be used to
make the battery plates. The objective is to design a battery that is relatively unaffected by
the ambient temperature. The output response from the battery is effective life
in hours. Three temperature levels are selected, and a factorial experiment with four
replicates is run. The data are as follows:
(a) Test the appropriate hypotheses and draw conclusions using the analysis of variance with
α = 0.01.
(b) Graphically analyze the interaction.
(c) Analyze the residuals from this experiment.
14-13. An engineer is interested in the effect of cutting speed (A), metal hardness (B), and
cutting angle (C) on the life of a cutting tool. Two levels of each factor are chosen, and two
replicates of a 23 factorial design are run. The tool life data (in hours) are shown in the table
at right.
(a) Analyze the data from this experiment.
(b) Find an appropriate regression model that explains tool life in terms of the variables
used in the experiment.
(c) Analyze the residuals from this experiment.
14-27. An article in Talanta (2005, Vol. 65, pp. 895–899) presented a 23 factorial design to
find lead level by using flame atomic absorption spectrometry (FAAS). The data are shown in
the following table.
(a) Construct a normal probability plot of the effect estimates. Which effects appear to be
large?
(b) Conduct an analysis of variance to confirm your findings for part (a).
(c) Analyze the residuals from this experiment. Are there any problems with model
adequacy?
14-47. Montgomery (2009) described a 24-1 fractional factorial design used to study four
factors in a chemical process. The factors are A = temperature, B = pressure, C =
concentration, and D = stirring rate, and the response is filtration rate. The design and the
data are as follows:
(a) Write down the alias relationships.
(b) Estimate the factor effects. Which factor effects appear large?
(c) Project this design into a full factorial in the three apparently important factors and
provide a practical interpretation of the results.