Study On Statistical Process Control Methods In Auto-correlated Processes

Traditional statistical process control (SPC) theory is based on a fundamental assumption that the process data are statistically independent. However, in many conditions the process data are autocorrelated, not independent. Under the circumstances, the traditional SPC theory becomes invalid.The basic theory and knowledge of the characteristics and identification methods of auto-correlated process, process capability analysis and control charts are first introduced in this paper. When the observations can be fitted by an AR(1) model in time series models, a method about calculating process capability indices is introduced. If there is trended term in the process, the in-control process can be wrongly judged to be out of control. Considering the trended term, the variability of the tool wear process is classified into three components, and capability indices are proposed to distinguish these different components. The C_p and C_pk confidence intervals of stationary auto-correlated processes are also calculated to monitor the processes.When the processes are auto-correlated, traditional control charts are not adequate and can lead to false alarms. When the observations can be fitted by an AR(2) model in time series models, the control limits of X|- - s chart are modified. Based on sample auto-correlated function, the control limits are modified to be used in all stationary processes. At the same time, the Typeâ… andâ…¡error probability of X|- chart are calculated in auto-correlated process. The parameters of economic control charts are designed when the failure mechanism distribution is Weibull process. Also, the parameters of economic statistical control charts are designed when the failure mechanism distribution is Weibull process and the time interval that the process remains in control is an exponential random variable. Economic statistical designs are slightly more costly than economic designs due to the added constraints. However, the statistical properties of economic statistical designs are improved and more useful in industry.Non-random patterns on a control chart suggest the presence of assignable-cause variations. However, there are processes where the presence of trend patterns is unavoidable and is well understood. In this paper, the trended term is fitted into simple linear model. The process capability indices and process yield of the trended process with the same variance of residuals are calculated. To solve the phenomena of...