Charting techniques for monitoring a random shock process

Abstract

A modified geometric model is proposed for fitting data generated from a process where most of the samples are conforming and occasional samples are non-conforming. These near-zero-defect processes are classified as processes subjected to random shocks. A graphical comparison of the goodness of fit of industrial process data using modified geometric and modified Poisson models is performed. The geometric model is found to provide a better fit than the Poisson model. Based on the modified geometric model, a charting scheme consisting of two charts is developed to monitor a process subjected to random shocks. A cumulative count of conforming chart is used to monitor the frequency of random shocks and a geometric chart is used to monitor the count of non-conformities. The geometric chart performs better than the Poisson chart in terms of false alarm rate. The performance of the scheme is also evaluated.