Direct way of computing the variability of modal assurance criteria

•The variability of modal assurance criteria (MAC) is studied.•A direct method for computing the sensitivity of MAC value is presented.•The method is an exact method.•The method is efficient for the number of design variables is larger than one.•The method is efficient in the storage capacity involved.

The study considers the variability of modal assurance criteria (MAC) for undamped systems with distinct eigenvalues, which is often approximated by the first-order Taylor series. So far all the methods for computing the sensitivity of MAC value belong to the indirect method. This study presents a direct method carried out by constructing a Lagrange function. When the number of design variables is larger than one, the proposed method will be efficient in computational time and storage capacity. The validity is illustrated using a numerical example.