摘要
根据非线性最小二乘拟合方法,针对元器件厂家进行工序能力指数Cpk计算时,在不能获得全部数据的情况下无法使用传统方法完成Cpk的正确评估,采用Levenberg-Marquarat算法解决Gauss-Newton算法中的Hessian矩阵病态问题,引入阻尼因子调整取值点的迭代方向,以数学期望公式表征累积分布函数值,建立数据非线性优化拟合模型。以实例检验此数学模型并得出常用数据值。
Process capability index （ Cpk ） is adopted as an indication of the production level in modern industry. When all data for calculating Cpk cannot be acquired and its precision required is very high, using the traditional method to calculate Cpk of the normal distribution parameters will always give a wrong conclusion at the PPM level. In view of the specific property of the data, a model of calculating Cpk based on non-linear least squares fitting are proposed. Due to the pathologic matrix of Gauss-Newton algorithm the Levenberg-Marquarat is used in the model. Also, the mathematic expectation formula is used to characterize the value of cumulative distribution function and the results are satisfactory in practical application.
出处
《工业工程与管理》
2008年第2期60-63,共4页
Industrial Engineering and Management
基金
模拟集成电路国家重点实验室基金资助项目(51439040103DZ0102)
关键词
非线性最小二乘法
工序能力指数
正态分布
标准偏差
样本容量
non-linear least squares
process capability index
normal distribution
standard deviation
sample size
