Weibull distribution research based on Fourier series

With the development of science and technology, the engineering equipment and products are becoming more and more complicated. So, the system reliability has attracted great attention of Scholars and engineers. Because the system reliability is mainly subjected to Weibull distribution, it is important to improve the Weibull model. A new method is proposed in this paper, which can improve calculation efficiency by using Fourier series to transform the probability density function of Weibull distribution into a periodic function. The proposed method is applied to estimate the reliability of fuel system, and the outcome proves that the method is effective.