The plane Poiseuille flow is one of the elementary flow configurations. Although its laminar-turbulent transition mechanism has been investigated intensively in the last century, the significant difference in the critical Reynolds number between the experiments and the theory lacks a clear explanation. In this paper, an attempt is made to reduce this gap by analyzing the solution of the Reynolds-Orr equation. Recent published results have shown that the usage of enstrophy (the volume integral of the squared vorticity) instead of the kinetic energy as the norm of perturbations predicts higher Reynolds numbers in the two-dimensional case. In addition, other research show has shown an improvement of the original Reynolds-Orr energy equation using the weighted norm in a tilted coordinate system. In this paper the enstrophy is used in three dimensions combined with the tilted coordinate system approach. The zero-enstrophy-growth constraint is applied to the classical Reynolds-Orr equation, and then the solution is further refined in the tilted coordinate system. The results are compared to direct numerical simulations published previously.