A Reliability Prediction Method of Novel Grey Model and its Error Analysis

摘要

This study proposed a reliability prediction method of novel fractional-order discrete grey prediction model FODGM (1,1), which is developed on the discrete grey prediction model DGM (1,1). The modeling error distribution of FODGM (1,1) is systematically studied. The sequences of exponential data are generated for numerical simulation. Later, the mean absolute percentage errors (MAPE) of FODGM (1,1), with different values of order and development coefficient, are compared to the modeling errors of GM (1,1) and DGM (1,1) using numerical simulation. The modeling error distribution graph of FODGM (1,1) with the sequences of exponential data is presented. The findings reveal that DGM (1,1) and the direct modeling DGM (1,1) are both special cases of FODGM (1,1). The outcome provides a foundation to further optimize the grey model by using fractional-order operators and to expand the applicable bound of the grey model.