ABSTRACT
Since the beginnings of optimal design by Box and Lucas, (1959) industrial statisticians have developed many matrix-based criteria which they label alphabetically. Dealing with nonsimplex constraints is our focus for applying optimal designs. However, these designs, typically computer-generated, can be customized to any shape for any order of polynomial desired by the experiment. With the aid of software, it is quite easy to generate an optimal experiment design. Cosmetic chemists needed help for an experiment to optimize foam height in a shampoo. The ultimate test on foam is the “half-head test” because it provides a real-live one-to-one comparison of a newly developed shampoo versus a reference product. This case study on the shampoo experiment provides a good start on how to contend with constraints that do not form a simplex. This experiment design looks a bit cramped in the rectangular “penthouse” of the triangular structure.
