The relationship between the response variable and one or more independent variables refers to the quality characteristic in some statistical quality control applications, which is called profile. Most research dealt with the monitoring of profiles in single-stage processes considering a basic assumption of normality. However, some processes are made up of several sub-processes; thus, the effect of cascade property in multistage processes should be considered. Moreover, sometimes in practice, the assumption of normally distributed data does not hold. This paper first examines the effect of non-normal data to monitor simple linear profiles in two-stage processes in Phase II. We study non-normal distributions such as the skewed gamma distribution and the heavy-tailed symmetric t-distribution to measure the non-normality effect using the average run length criterion. Next, generalized linear models have been used and a monitoring approach based on generalized likelihood ratio (GLR) has been developed for gamma-distributed responses as a remedial measure to reduce the detrimental effects of non-normality. The results of simulation studies reveal that the performance of the GLR procedure is satisfactory for the multistage non-normal linear profiles. Finally, the simulated and real case studies with gamma-distributed data have been provided to show the application of the competing monitoring approaches.

响应变量与一个或多个自变量之间的关系是指一些统计质量控制应用中的质量特征，称为轮廓。大多数研究都是在考虑正常性的基本假设的情况下处理单阶段过程中的剖面监测。但是，有些流程是由几个子流程组成的；因此，应考虑多级过程中级联特性的影响。此外，有时在实践中，数据正态分布的假设并不成立。本文首先研究了非正态数据对第二阶段两阶段过程中简单线性剖面的监测效果。我们研究非正态分布，例如偏态 gamma 分布和重尾对称t-分布以使用平均运行长度标准测量非正态性效应。接下来，已使用广义线性模型，并开发了一种基于广义似然比 (GLR) 的监测方法，用于伽马分布响应，作为减少非正态性不利影响的补救措施。仿真研究结果表明，对于多级非正态线性剖面，GLR 程序的性能是令人满意的。最后，提供了具有伽马分布数据的模拟和真实案例研究，以展示竞争监测方法的应用。