An article in the Journal of Applied Electrochemistry (May 2008, Vol. 38(5), pp. 583€“590) presented a 27€“3 fractional factorial design to perform optimization of polybenzimidazole-based membrane electrode assemblies for H₂/O₂fuel cells. The design and data are shown in the following table.

The factors and levels are shown in the following table.

(a) Write down the alias relationships.

(b) Estimate the main effects.

(c) Prepare a normal probability plot for the effects and interpret the results.

(d) Calculate the sum of squares for the alias set that contains the ABG interaction from the corresponding effect estimate.

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в с Current Density (CD mA cm²) 160 20 Runs D E F 1 -1 -1 -1 -1 -1 -1 +1 +1 +1 +1 -1 +1 +1 -1 +1 80 317 4 -1 +1 +1 +1 +1 +1 -1 -1 19 +1 -1 4 -1 +1 +1 +1 -1 +1 -1 -1 +1 -1 +1 +1 +1 -1 -1 +1 +1 -1 88 +1 2.