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首页> 外文期刊>Journal of statistical computation and simulation >Phase I monitoring of generalized linear model-based regression profiles
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Phase I monitoring of generalized linear model-based regression profiles

机译：基于广义线性模型的回归配置文件的第一阶段监视

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摘要

In some industrial applications, the quality of a process or product is characterized by a relationship between the response variable and one or more independent variables which is called as profile. There are many approaches for monitoring different types of profiles in the literature. Most researchers assume that the response variable follows a normal distribution. However, this assumption may be violated in many cases. The most likely situation is when the response variable follows a distribution from generalized linear models (GLMs). For example, when the response variable is the number of defects in a certain area of a product, the observations follow Poisson distribution and ignoring this fact will cause misleading results. In this paper, three methods including a T-2-based method, likelihood ratio test (LRT) method and F method are developed and modified in order to be applied in monitoring GLM regression profiles in Phase I. The performance of the proposed methods is analysed and compared for the special case that the response variable follows Poisson distribution. A simulation study is done regarding the probability of the signal criterion. Results show that the LRT method performs better than two other methods and the F method performs better than the T-2-based method in detecting either small or large step shifts as well as drifts. Moreover, the F method performs better than the other two methods, and the LRT method performs poor in comparison with the F and T-2-based methods in detecting outliers. A real case, in which the size and number of agglomerates ejected from a volcano in successive days form the GLM profile, is illustrated and the proposed methods are applied to determine whether the number of agglomerates of each size is under statistical control or not. Results showed that the proposed methods could handle the mentioned situation and distinguish the out-of-control conditions.
机译：在某些工业应用中，过程或产品的质量以响应变量与一个或多个独立变量之间的关系（称为配置文件）为特征。文献中有许多方法可以监视不同类型的配置文件。大多数研究人员认为响应变量遵循正态分布。但是，在许多情况下都可能违反此假设。最可能的情况是响应变量遵循广义线性模型（GLM）的分布。例如，当响应变量是产品特定区域中的缺陷数时，观察结果遵循泊松分布，而忽略此事实将导致误导性结果。本文开发并修改了三种方法，包括基于T-2的方法，似然比检验（LRT）方法和F方法，以便将其应用于第一阶段的GLM回归剖面监测中。对于响应变量遵循泊松分布的特殊情况进行了分析和比较。针对信号准则的概率进行了仿真研究。结果表明，LRT方法在检测大小步长漂移和漂移方面比其他两种方法要好，而F方法比基于T-2的方法要好。此外，在检测异常值方面，F方法的性能优于其他两种方法，而LRT方法与基于F和T-2的方法相比性能较差。说明了一个真实案例，其中连续几天从火山喷出的团聚体的数量和数量形成了GLM轮廓，并采用了所提出的方法来确定每种尺寸的团聚体的数量是否处于统计控制之下。结果表明，所提出的方法可以处理上述情况并区分失控条件。

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