Control charts for monitoring two-dimensional spatial count data with spatial correlations. (November 2019) - Shang, Yanfen; Li, Tao; Song, Lisha; Wang, Zhiqiong
Highlights: The two-dimensional (2D) spatial count data are demonstrated by wafer map data. The 2D spatial count data are modelled by hierarchical IGMRF model. The MCMC method is adopted to estimate the model parameters. Four MEWMA control schemes are developed for monitoring spatial count data. A real example from wafer production process is tested and analyzed. Abstract: The quality characteristic of some manufacturing processes is represented by two-dimensional (2D) spatial count data in which spatial correlations are commonly observed. Statistical process control (SPC) is important and challenging for monitoring such kind of data. However, there is a scarcity of methods for monitoring spatial count data in SPC. In this paper, we integrate an intrinsic Gaussian Markov random field (IGMRF) with the hierarchical Bayesian model for modelling 2D spatial count data. Then, we adopt the Markov chain Monte Carlo (MCMC) method to tackle the issue of hierarchical model parameter estimation. Moreover, based on the estimates, we develop corresponding monitoring schemes utilizing the multivariate exponentially weighted moving average (MEWMA) procedure to detect shifts in the general trend and the spatial correlation. Extensive numerical results are presented with regard to the performance of the proposed schemes for detecting changes in the coefficient and the random spatial error. Finally, a real example from the wafer manufacturing process is used to illustrate the implementation and effectiveness of the proposed approach.