基于Lambert W函数的装备经济寿命分析

摘要

To improve the solving method of the current economic life model,which is difficult to calculate and analyze,a new method is proposed.Firstly,the accurate analytic equation is obtained by introducing the Lambert W function.Then,polynomial fitting and rational fitting are used to estimate for Lambert W Function, and the results are compared with the approximate solutions and the exact solutions,based on which a high-accuracy estimation formation is proposed.Tests show that the estimation formation is a piecewise function, and the accuracy of the proposed model for the economic life estimation is within 1 year.Compared with the classical trial and try method,the proposed method has advantages on its intuitive features and is easy to use, furthermore,it is better for analyzing influence factors and the changing rule of the economic life.%为改进现有装备经济寿命模型求解时计算量大、不便于分析等缺点，提出了一种新的装备经济寿命确定方法。首先通过 Lambert W 函数求解出装备经济寿命的精确计算解析式，其次采用多项式拟合、有理拟合对Lambert W 函数进行精确估算，并将结果与 Lambert W 函数近似解和精确解进行比较，在此基础上得出了装备经济寿命的精确估算公式。实验表明，估算公式是一个分段函数形式，对经济寿命的估算精度可控制在±1年。该方法与传统的列表法相比，不仅具有直观性，利于掌握和计算，同时便于进一步分析经济寿命的影响因素和变化规律。