关键词: 最小二乘估计, 导数最小二乘估计, 可靠性增长, Duane模型, 预测

Abstract:

The least square estimation (LSE) has been widely used in both natural science and social science, which is a standard approach to parameter estimation and inference in statistics. Furthermore, many of the inference methods in statistics are developed based on LSE. But the traditional LSE can only make use of the information of model itself, and is helpless with the dynamic change of the curve. The formulas estimated by the least square method can only be used within the test section, and predicting outside the test section will usually cause a great error. In this article, based on the principle of minimizing the distance between random sample and curve’s derivative function in scale of probability, the conception of derivative least square estimation (DLSE) is established, which can extend the condition and scope of the traditional one. Besides this, the ordinary and the optimal DLSE are given in detail combined with the reliability growth Duane model for complex repairable system. The statistical properties indicate that the parameter’s DLSE has uniformly smaller variance than the traditional estimators. Finally, an example of contrastive analysis is given, which can illustrate the performance of the presented method in both estimation and prediction.

Key words: least , square , estimation,  , derivative , least , square , estimation,  , reliability , growth,  , Duane , model,  , prediction