Design of experiments when experimental resources are scarce
by
Nam-Ky Nguyen
Agriculture Victoria Biometrics, Department of Natural Resources and Environment, Institute for Horticultural Development, Australia

Designing an experiment when there is a constraint in the experimental resource is always a challenge to statisticians. This talk introduces new classes of design recently available in the literature by discussing three design problems:1. Supersaturated designs (Nguyen, 1996a): A car manufacturer wishes to conduct a passenger-impact crash test on a planned new 4WD range. The objective of this experiment is to find a subset of 54 safety features to be included in the new car's total safety system such as driver's airbag, bull bar, bonded windscreen, (twin front) crush cans, etc.... A suitable design for this test is a Hadamard matrix of order 56, which requires 56 runs (car prototypes). What type of design is to be used when the R&D Department of the car manufacturer can only afford at most half of the number of required cars for this test.

2. Near-orthogonal arrays (Nguyen, 1996b): Phadke and his coworkers at AT & T Bell Laboratories conducted an integrated circuit fabrication experiment (Phadke, 1983). The experiment had nine factors: (1) mask dimension, (2) photoresist viscosity, (3) spin speed, (4) bake temperature, (5), bake time, (6) aperture, (7) exposure time, (8) developing time and (9) plasma etch time. Factors 1, 2 and 4 are at two levels and the rest are at three levels. The design for this experiment was a near-OA L'18(36,23) obtained by collapsing the first 3-level column of an OA L'18(37,2) of Taguchi (1987, p. 36) to two level columns using the scheme 0 to 00, 1 to 10 and 2 to 01 and retaining the remaining factors. We will compare this near-OA with another one obtained by Nguyen (1996b).

3. Near-orthogonally blocked designs (Nguyen, 2001): Consider a factorial experiment with cotton which involves five factors: (1) variety (2) N, (3) P, (4) dates of sowing (5) spacing, each at two levels. Because of the fragmentation of the experimental site, the 32 treatment combinations have been divided into 8 blocks. A suitable plan for this experiment is the one in the Appendix 3A of Wu & Hamada (2000). This plan which uses 135, 235 and 1234 as block generators, unfortunately confounds two 2-factor interactions 12 and 34 with blocks. We will show how the divide this 32 combinations such that all interactions can be studied and thus, avoid having an additional replicate of 32 combinations to study the confounded interactions.

References Nam-Ky Nguyen (1996a) An algorithmic approach to constructing supersaturated designs. Technometrics 38, 69-73.

Nam-Ky Nguyen (1996b) A note on constructing near-orthogonal arrays with economic run size. Technometrics 38, 279-283.

Nam-Ky Nguyen (2001) Cutting experimental designs into blocks. Austral. & New Zealand J. of Statistics 43, 367-374.

Wu, C.F.J & M. Hamada (2000). Experiments: Planning, Analysis and Parameter Design Optimization. New York: John Wiley & Sons, Inc.

Date received: April 5, 2002