Study On Statistical Process Control Method For Spatial Discrete Data

With the rapid development of the economy and society,the variety of products is largely increasing.The quality of products has attracted more attention.Therefore,companies have to improve and control the product quality if they want to stand out in the increasingly fierce market competition.Statistical Process Control?SPC?is a statistical technique for monitoring the production processes to ensure stable operation of the production process.it is one of the most important tools for quality management and control.In previous studies,quality characteristics of a product or a production process were usually univariate or multiple variables.With the advancement of industrial technology,the complexity of products has also increased.The quality of some products needs to be characterized by two-dimensional?2-D?spatial discrete data.In this case,traditional SPC theory is no longer applicable.In this study,we first introduce some fundamental theories of the characteristics of 2-D spatial discrete data,modeling methods and control chart methods.The 2-D spatial discrete data that characterizes adjacent spatial relationships are usually spatially correlated,then the intrinsic Gauss Markov random field?IGMRF?is used to model the spatial correlation.According to the different transmission modes of spatial information in adjacent spatial structures,three kinds of relative spatial distances are constructed to simulate the transmission of spatial information in adjacent spatial structures.Based on Bayes'theorem and Markov Chain Monte Carlo?MCMC?method,the Gibbs sampling is used to estimate the posterior distribution of the parameters in the hierarchical Bayesian model.The Deviance Information Criterion?DIC?was introduced to investigate the goodness of fit of different models for specific data sets.In order to monitor the 2-D spatial discrete data,four Multi-variate exponential weighted moving average?MEWMA?control charts,i.e.(2,(2,(2and(2are constructed for the mean and covariance of the coefficientand the spatial correlation variablerespectively.Based on the simulation results,we can conclude that the(2chart exhibits better performance than(2for detecting the large shift inand any magnitude of shifts occurring in.Overall,the(2chart performance better than(2in detecting shifts inandsimultaneously.When the spatial correlation variableshifts,the(2scheme is more sensitive in monitoring small and moderate shifts,while the(2chart is more sensitive to the large shifts.Finally,the effectiveness and robustness of the proposed modeling and monitoring methods are verified by an example of wafer map.