关于当量工序能力指数c′_p的近似展开

在文1]中已引进当量工序能力指数,并已推得其计算公式为c'_p=(1/3)φ~(-1){(1/2)φ(((T/2)+E)/σ))+φ(((T/2)-E)/σ))]} (1) 其中,φ(·)为标准正态分布的分布函数,φ~(-1)(·)为其反函数,T为公差,E为偏离距,σ为当分布中心与公差中心一致时的标准差。本文讨论它的线性与2次及5次多项式的近似问题。

Approximate Representations for the Index of Equivalent Process Capability

The index of equivalent process capability c_p~' has already defined in refenence 1]. c_p~'=1/3φ~(-1){1/2φ(T/2+E/σ)+φ(T/2-E/σ)]} (1) where φ(·) stands for the distribution function of the stardard normal distribution, φ~(-1)(·) is its inverse function, T stands for tolerance, E denotes the deviate distance of the center of tolerance from the center of distribution, σ is the standard deviation when the center of tolerance and the center of distribution are the same. Approximate representations of c_p~' are discussed in this article.