  The detection of insufficiently resolved or ill-conditioned integrand
structures is critical for the reliability assessment of the quadrature rule
outputs. We discuss a method of analysis of the profile of the integrand at the
quadrature knots which allows inferences approaching the theoretical 100% rate
of success, under error estimate sharpening. The proposed procedure is of the
highest interest for the solution of parametric integrals arising in complex
physical models.
