In this article remanence deviations of a permanent magnet synchronous machine are studied with the proper orthogonal decomposition (POD). The design of experiments enables to create designs with a reduced sample size compared to full factorial designs without decreasing the stochastic significance of the remanence distributions. Next, a POD basis is created with the belonging design, that is distinctly smaller than the reference. From the POD basis the projection matrix is built to compute the flux density solutions. The machine's output is then analyzed regarding accuracy originating from numerical errors. Different parameters are evaluated and compared to the reference to appraise the accuracy of the flux density solutions, which includes the POD basis size, rotor angle step size and dimension of the reduced system. Results show, that the most influence has the dimension of the reduced system. Depending on the dimension and other parameters about one quarter of computational effort can be conserved without a significant loss in accuracy.