Bayesian Quality Control Model Based On Autocorrelation Stochastic Process

Quality control charts are used widely and extensively in quality management. If the control charts are used, the observations of the process must be independent identity distribution. In continuous production process, observations of the process always behave serial correlation, so it cannot be satisfied with the hypothesis of the control chart.When the serial is correlative, the monitoring capacity of quality control chart will be afected heavily, and it increases the probability of false alarm in normal process.Even worse, it will leave out the real alarm in abnormal process. In case that happened, the power of control charts will be discount. Not only the quality control cost will be increased because carried on the examination, which the unusual reason did not exist, the more important things is that will seriously affects the confidence of superintendent to the power of control chart, thus suspected, even gave up use this scientific management technique. In view of this actual problem, the technique that how to use control charts correctly under the autocorrelation production process has studied systematically. Furthermore, it provides guidance in using quality control charts in reality directly. It's good for studying the system of Bayesian control in theory and method, which is significant in theory and reality.Based on Bayesian inference of auto-regression model(AR),auto-regression moving average model(ARMA) and the vector auto-regression model (VAR)in time series., the Bayesian method is introduced. And the posterior distributions of parameters in quality model are simulated via the Monte Carlo Markov chain based Gibbs sampling. By which the representative AR(1) model, ARMA(1,1) model and VAR(2) model are used , that created in random simulation software, to building up Bayesian statistical quality control model. The Bayesian model can avoid alarming incorrectly when the process is in control, or not alarming when the process is out of control. The results show that the Bayesian method is an effective tool to monitor the quality control of autocorrelation process.