Computing more proper covariances of energy dependent nuclear data

• We present conditions for covariances of energy dependent nuclear data to be proper.
• We provide methods to detect non-positive and inconsistent covariances in ENDF-6 format.
• We propose methods to find nearby more proper covariances.
• The methods can be used as a part of a quality assurance program.

We present conditions for covariances of energy dependent nuclear data to be proper in the sense that the covariances are positive, i.e., its eigenvalues are non-negative, and consistent with respect to the sum rules of nuclear data. For the ENDF-6 format covariances we present methods to detect non-positive and inconsistent covariances. These methods would be useful as a part of a quality assurance program.We also propose methods that can be used to find nearby more proper energy dependent covariances. These methods can be used to remove unphysical components, while preserving most of the physical components. We consider several different senses in which the nearness can be measured. These methods could be useful if a re-evaluation of improper covariances is not feasible.Two practical examples are processed and analyzed. These demonstrate some of the properties of the methods.We also demonstrate that the ENDF-6 format covariances of linearly dependent nuclear data should usually be encoded with the derivation rules.