Robust uniform design with errors in the design variables

Uniform design has become a standard tool in experimental design over the last two decades. Its properties are analyzed for a situation when the actual values of the control variables are subject to some error in factor level values. A closed form for the expected discrepancy is established, under some mild assumptions. A thorough Monte Carlo study is conducted under various potential scenarios. Some general properties have been revealed. Both theoretical and simulation results are consistent. The robustness of uniform design under error in control variables is also investigated. It is shown that uniform designs are highly robust with regard to uniformly distributed errors in design variables.