A simple step-down non-parametric method for saturated orthogonal designs under unreplication

Abstract

Quality screening experiments are efficiently organised by the employment of fractional factorial designs. Saturated orthogonal arrays require specialised statistical treatment if trial-runs lack replication. The work presented here offers an alternative version of applying non-parametric techniques in solving single-response multifactorial problems. The technique is based on testing family compatibility of formed median differences between factor settings for a nominated control factor group. A step-down distribution-free check is performed to obtain an indication of the association among effect magnitudes. Overall, the method is simple and practical while it reduces convincingly the amount of work needed to reach to a decision in search for active factors. These claims are illustrated via two case studies. It is shown that the method may be competing with leading screening tests for saturated orthogonal arrays.