An engineer has been asked to identify and apply an absolutely objective metric to evaluate...

An absolutely objective way to measure risk does not exist. Risk assessment inherently involves some level of subjectivity due to the uncertainty and variability in processes and outcomes. While various tools and metrics (e.g., lean metrics, six sigma metrics, quality function deployment) can aid in evaluating and managing risk, none provide an entirely objective measure. Reference: "Risk Management: Concepts and Guidance" by Carl L. Pritchard, which discusses the challenges of achieving absolute objectivity in risk assessment.