Abstract: The quality of some complex manufacturing or service processes might be characterized by the functional relationship referred to as a profile. To monitor the ordinal response profile, a generalized likelihood ratio control chart was proposed based on a nonparametric regression model. In practice, the in-control(IC) model was usually unknown and needed to be estimated. Three model estimation methods, including the local linear kernel estimation, spline, and Newton Raphson, were proposed to study the effects of model estimation on the performance of the control chart, considering different sample sizes and different parameter settings of the estimation method. The simulation results and case study show that, the sample size has a significant effect on the IC performance of the control chart, but when the sample size exceeds a certain value, the performance of the control chart no longer changes with the sample size. When the IC model is a generalized linear model, all three estimation methods have a significant impact on the out-of-control performance of the control chart, where the Newton Raphson method performs better. When the IC model is unknown, the local linear kernel estimation method is better.

Key words: statistical process control, ordinal profile monitoring, model estimation, nonparametric regression, generalized likelihood ratio statistics

摘要： 复杂制造或服务过程的质量特性可用函数关系即轮廓描述。针对序数响应轮廓的监控，基于非参数回归模型提出了广义似然比控制图。在受控模型未知且需要估计的现实情况下，采用局部线性核估计、样条和Newton Raphson 3种模型估计方法，并考虑不同的样本量、估计方法的不同参数设置，研究模型估计对控制图性能的影响。仿真以及案例分析的结果表明，样本量对受控状态下的控制图性能有显著影响，但当样本量超过一定值时，控制图的受控性能不再随样本量的增加而变化。另外，当受控模型为广义线性模型时，3种估计方法均对失控状态下的控制图性能有明显影响，Newton Raphson方法表现较好，而当受控模型不明确时，局部线性核估计方法更优。

关键词: 统计过程控制, 序数轮廓监控, 模型估计, 非参数回归, 广义似然比统计量