Performance evaluation of problematic samples: a robust nonparametric approach for wastewater treatment plants

This paper explores robust unconditional and conditional nonparametric approaches to support performance evaluation in problematic samples. Real-world assessments often face critical problems regarding available data, as samples may be relatively small, with high variability in the magnitude of the observed indicators and contextual conditions. This paper explores the possibility of mitigating the impact of potential outlier observations and variability in small samples using a robust nonparametric approach. This approach has the advantage of avoiding unnecessary loss of relevant information, retaining all the decision-making units of the original sample. We devote particular attention to identifying peers and targets in the robust nonparametric approach to guide improvements for underperforming units. The results are compared with a traditional deterministic approach to highlight the proposed method's benefits for problematic samples. This framework's applicability in internal benchmarking studies is illustrated with a case study within the wastewater treatment industry in Portugal.