MGFM: Modified Gray Genetic Forecast Method for Achieving Sample Expansion and Improving the Weibull Parameter Estimation Performance With Small Samples

ABSTRACT As the theoretical basis of reliability analysis, the Weibull distribution is widely used to process life data. However, due to the increasing cost and reliability of mechanical products, only few life failure data can be collected, while the accuracy and stability of Weibull parameter estimation become inferior. Therefore, to improve the performance of parameter estimation with small samples, a new sample expansion method called modified gray genetic forecast method (MGFM) is proposed. The hybrid gray genetic algorithm with modified maximum likelihood method is employed for explicit parameter estimation. Moreover, for enhancing the credibility of the study, the proposed MGFM is compared with three existing sample expansion methods (midpoint interpolation method, golden section interpolation method, mean‐variance interpolation method) as well as three machine learning algorithms (particle swarm optimization (PSO) algorithm, adaptive moment estimation (ADAM) algorithm, fish school search (FSS) algorithm). Then, seven evaluation parameters are selected, including mean absolute deviation, mean root square error, and so on. Subsequently, Monte‐Carlo sampling simulations are performed to obtain the post‐expansion samples and parameter estimation results. The results show that the accuracy, stability, fitting degree, and reliability evaluation performance of the post‐expansion samples using MGFM are the best, which indicates the MGFM can improve the parameter estimation performance in simulation experiments. Then the extended applications and challenges are discussed. Finally, the advantages of MGFM in engineering are illustrated by two examples.