Design of economical experiments for estimation of a response function's moments in a partially controlled laboratory environment is studied. The noise factors affecting the response are assumed to be statistically independent and normally distributed. It is also assumed that if a factor is set to a specific level in the experimentation, its actual value is also a normally distributed random variable with a smaller variance. Experimental design levels of the factors are found by matching first few moments of the response function calculated from the distributions of the factors, with the moments of that calculated from the distributions of the experimental values of the factors. These levels are evaluated with regard to the performance of appropriate moment estimators of the response. Suggestions are made as to which levels and experimental design should be used for different degrees of control in the experimentation environment. (C) 1998 Elsevier Science Ltd. All rights reserved.