Profile monitoring of residuals control charts under gamma regression model
Keywords:ARL, Control Charts, EWMA, GLM, Gamma Regression, Residuals
The statistical control chart is considered one of the superlative tools in quality control. Currently, control charts are being widely used in various areas, one of them being manufacturing processes. They are essential instruments that can impart crucial insights to quality controllers for maintaining productivity. The quality of a product or process can be characterized by a relationship between two or more variables, which is typically referred to as a profile. Also, public health surveillance is considered another important area that widely used control charts. In this regard, they are very useful and reliable tools for detecting outbreaks of infectious diseases. On the other hand, the gamma regression model (GRM) is a popular model considered in medical and other fields. It is applied when the response variable is continuous and positively skewed and well fitted to the gamma distribution. This paper presents a scheme for monitoring the profile. Based upon the generalized linear model (GLM) in the case of two link functions: identity and log link function. Exponentially weighted moving average control charts (EWMA) are proposed using deviance residuals and Pearson residuals for detecting any disturbance in the control variable of the gamma regression model. A detailed simulation study is designed to scrutinize and evaluate the performance of the control charts in phase I analysis and in phase II under parametric maximum likelihood estimation (MLE) using the average run length (ARL) measure. It turns out that using deviance residuals under the identity link function seems more suitable than Pearson residuals. Also, with increasing the sample size, the percentages of out-of-control (OC) samples increased which is theoretically acceptable
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