The generalized linear mixed model (GLMM) becomes very popular in profile monitoring, especially when the production processes follow nonnormal distribution. In most of the real‐life applications in industry, medicine, biology…and so on researchers assume that the response variable follows a Bernoulli or Binomial distribution. The majority of previous studies in profile monitoring focused on parametric modeling using the logistic regression model, with both fixed or random effects, under the assumption of correct model specification. This research considers those cases where the parametric logistic regression model for the family of profiles is unknown or at least uncertain. Consequently, we propose two mixed model methods to monitor profiles from the exponential family: a nonparametric (NP) regression method based on the penalized spline regression technique and a semiparametric method (model robust profile monitoring for the generalized linear mixed model) which combines the advantages of both the parametric and NP methods. Several Hotelling T2 charts that have been studied for a binary response variable with replicates for Phase I profile monitoring. The performance of the proposed method is evaluated by using mean squares of errors and probability of signals criteria. The results showed satisfactory performance of the proposed control charts.

中文翻译：

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用于I期分析的广义线性混合模型的模型鲁棒轮廓监视

广义线性混合模型（GLMM）在轮廓监测中非常受欢迎，尤其是当生产过程遵循非正态分布时。在工业，医学，生物学等大多数现实生活中的应用中，研究人员都假定响应变量遵循伯努利分布或二项分布。在正确的模型规范的假设下，大多数先前的轮廓监测研究都集中在使用逻辑回归模型的参数建模中，该模型具有固定或随机影响。这项研究考虑了那些关于轮廓族的参数对数回归模型未知或至少不确定的情况。因此，我们提出了两种混合模型方法来监视指数族的轮廓：基于惩罚样条回归技术的非参数（NP）回归方法和结合了参数和NP方法优点的半参数方法（针对广义线性混合模型的模型鲁棒轮廓监视）。研究了几个Hotelling T2图表，以研究二元响应变量，并复制了第一阶段配置文件。通过使用误差的均方和信号概率标准来评估所提出方法的性能。结果表明所提出的控制图性能令人满意。研究了几个Hotelling T2图表，以研究二元响应变量，并复制了第一阶段配置文件。通过使用误差的均方和信号概率标准来评估所提出方法的性能。结果表明所提出的控制图性能令人满意。研究了几个Hotelling T2图表，以研究二元响应变量，并复制了第一阶段配置文件。通过使用误差的均方和信号概率标准来评估所提出方法的性能。结果表明所提出的控制图性能令人满意。