Monitoring Poisson data of bivariate serially dependent response process Online publication date: Sat, 21-Feb-2015
by S. Lakshminarasimhan; S.M. Kannan
International Journal of Quality Engineering and Technology (IJQET), Vol. 2, No. 4, 2011
Abstract: Serially dependent multi-stage processes are monitored by cause selecting control charts based on regression models. In production processes, we come across instances where dependent stages have data modelled by the Poisson distribution. In such situations, the condition of homoscedasticity (constant variance) is not satisfied, as the process mean equals its variance. Pedagogy suggests remedying such cases by transforming a response variable with a square root transform and regressing it against independent variable(s). This work shows that transforming both the regressor and the response variable lends itself to a better regression model fit. A new power transform which is superior to the conventional square root transform has been proposed for improving the run length performance of the residuals control chart for response processes. Further, a run rule has been proposed to sensitise this control chart to enhance its average run length and detect data patterns.
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