(From Xiaohong Zhang, personal communication) A polymer scientist is developing a fabric intended for use in clothing for strenuous exercise. The objective is to develop a fiber that would have a high water transmission rate. The first step in producing such a fiber is to heat a polymer chip in an extruder. In the extruder the polymer takes on the consistency of a gel. It is then extruded through a 3-inch die with about 90 0.4-mm holes. Air is blown through an air hole in the top of the die; the air pressure affects how fast the gel is cooled. The very fine fiber emerging from the die is in semiliquid form. The fiber is collected on a drum, which is at room temperature, and it solidifies into a web on the drum. Several factors can be adjusted during this process: the air pressure, the extruder speed or throughput, the drum speed or takeup speed, and the distance from the die to the drum. One response variable of interest is the pore size distribution of the finished web of fiber.
Propose a suitable experimental design for modeling the effects of these factors, using the following levels of the four factors in 40 experimental runs: (a) throughput (75%, 100%, 150%, 175%, 200%); (b) takeup speed (18, 22, 26, 30 in./min); (c) air pressure (10, 20, 30, 40 psi); and (d) die-to-collecting distance (4, 6, 8, 10 in.).