中文摘要：

在Rao给出的理想纱条定义的基础上,进一步提出了理想纱条纤维排列的新定义.新定义考虑了纤维的长度分布,从纤维头端排列的概率分布角度指出了理想纱条的形态,新的理想纱条定义完全满足Rao理想纱条的4个条件.使用随机过程对这个新定义的理想纱条进行了分析,证明了这个随机过程是一个弱平稳过程,进一步求出了这个平稳过程的期望、方差和相关函数表达式,为理解理想纱条的意义和拟合非理想纱条建立了理论基础,也给出了理想纱条仿真的数学方法和途径.

英文摘要：

Based on the definition of ideal slivers given by Rao, a new definition of ideal slivers concerning the fiber alignment in slivers is proposed. The new definition takes account of the length distribution of the constituent fibers and gives the probability distribution of fiber tips along the length direction of the ideal sliver. The new definition of ideal slivers is proved to be consistent to the four conditions of the former definition given by Rao. A stochastic process analysis is carried out and the result is proved that the stochastic process of the number of fibers in the cross section of the ideal sliver is weakly stationary. And further work is done to have found out the mathematical expectation, the variance and the co - variance of the process. All these works are helpful to the understanding of the ideal sliver and the fitting of the non - ideal slivers. The stochastic process analysis is also a platform of generating ideal silver by simulations.