Robust Designs Against Data Loss: A General Approach

We describe an algorithm that, given an initial design Fn of size n and a linear model with p parameters, provides a sequence Fn⊃⋯⊃Fn-k⊃⋯⊃Fp of nested robust designs. The sequence is obtained by removing each individual run of Fn until a p-run saturated design Fp is obtained. The potential impact of the algorithm on real applications is high, because it can be used in a wide spectrum of designs. The initial fraction Fn can be of any type and the output sequence can be used to organize the experimental activity. The experiments can start with the runs corresponding to Fp and then continue by adding one run after the other (from Fn-k to Fn-k+1) until the initial design Fn is obtained. In this way, if for some unexpected reasons the experimental activity has to be interrupted before the end when only n-k runs have been completed, the corresponding Fn-k will have a high value of robustness for k∈{1,…,n-p}. The algorithm uses the circuit basis, a special representation of the kernel of a matrix with integer entries.