Multi-response multi-factorial master ranking in non-linear replicated-saturated DOE for qualimetrics

Multi-response screening in chemometrics is greatly facilitated by fractional factorial analysis. A method is presented in this work that is an amalgamation of non-linear orthogonal arrays for planning data collection supported by multi-response order statistics to attain robust inference for replicated trials. The rank-sum estimator is the instrumental data compressor which is easily adapted to accommodate importance weights for concurrent optimization. Rank ordering allows the uniform scaling for all examined characteristics. As a result, a master response is created that carries all relevant information to a single manageable response. The concept of selective leveling is introduced to provide preference of a categorical factor setting over other choices. The technique has many advantages because simplifies the overall data planning and analysis while maintaining a distribution-free character with no sparsity assumptions to be imposed on the solution for effect contrasting to be successful. The technique is tested on screening three controlling factors and one interaction for profiling four quality characteristics of an epoxy product in a chemical laboratory of a resin manufacturer. Robustified resin qualimetrics are data mined from repeated trials properly weighted for synchronous screening. The data collector scheme was adapted to conform to an L9(34) orthogonal array. The selective leveling property is applied on the three-setting substrate factor to demonstrate the influence of this property on terminal decision making. Results are discussed in the non-linear distribution-free domain. The rank ordering approach proposed in this work may supplement testing procedures for laboratory data analysis as required by ISO 17025:2005 standard.

► Non-linear order statistics treats saturated screening for replicated trials.
► Multi-response rank ordering transforms several quality traits concurrently.
► Three-factor screening with one interaction is applied for a four-response problem.
► Resin qualimetrics are data mined for weighted synchronous screening.