Statistical Process Monitoring Ofautocorrelation Data From Multistage Processes

A multistage system refers to a system consisting of multiple components, stations or stages which were required to finish the final products or service. Multistage systems are very common in manufacture and service, but their complexity also brings great difficulties to us. Current research according to the multistage systems has achieved many results, but most of the methods assume that the sample data are independent of each other. However, in the actual production process, the pressure to meet the market demand quickly leads to the pace of production faster and faster, which results the output of the quality characteristics dependent on each other. So the quality data of production are auto-correlated.According to the characteristics of multistage process, we choose state space model and analysis the correlation of the model parameters, and then propose a formula about the correlated data of multistage processes by considering the correlated characteristic of failure source and noise. We also establish the linear relationship of the normal random variable with the fault source and noise, and then analysis how the normal random variable changed while the mean value of fault source changed. The change was monitored by using statistical process control (SPC) methods.As average run length is one of the most commonly used methods that evaluate control charts effectively, we also provide the formula of the type II error probability through the type I error probability. And then we calculate the theoretical value of average run length under in-control and out-of-control processes. This paper simulates the correlated data through Monte Carlo methods, and we achieve the simulated value of average run length, which verify the correctness of the formula. Finally, we demonstrate how to put this method into use in an actual multistage production processes.