A reliability assessment method for harmonic reducer based on grey theory using small sample data

A small-sample reliability evaluation method for harmonic reducers is developed based on grey system theory. Initially, a power-law model is employed to construct two original data sequences under equidistant stress and equal proportional stress conditions. The GM(1,1) model is subsequently applied to predict each sequence independently, resulting in two sets of life prediction data. Hypothesis testing and fitting error analysis are then conducted to determine the most appropriate approach for constructing the original sequence that aligns with the power-law model. Following this, hypothesis testing is performed on the parameters within the weight sequence to derive the interval for the weight parameter, thereby establishing the upper and lower bounds of the GM-based prediction data. Case study results involving harmonic reducers confirm that the equal proportional stress condition is better suited for constructing the original sequence of the power-law model. The proposed method effectively facilitates reliability assessment of harmonic reducers under small-sample conditions and exhibits strong applicability and robustness in practical engineering contexts.