Self-starting Statistical Control Charts For High-dimensional Process Mean And Covariance Matrix

In the industrial production, statistical process control (SPC) is tokeep the process stability and the quality of the products. And with thedevelopment the production skills, the structures of the products becomeintensively complicated. This requires us to monitor more parameters ofthe products simultaneously, which lead to the development of variousmultivariate control charts. So far there has been a lot of research onmonitoring multivariate data. However, using the multivariate methodson high-dimensional data can lead to a lot of problems. For example, weneed to collect quite large samples with the traditional methods inhigh-dimensional situation, which often cannot be realized in a realproduction line. Besides, high dimensional data can produce a lot of noise,which would certainly affect the monitoring greatly.Aimed at the problems listed above, we develop self-starting controlcharts for monitoring process mean and covariance separately.Self-starting control charts monitor the data at the very beginning of theprocess and update the estimation of the parameters rather than use twophases separately to estimate the process parameters and monitor the data.In this way, our methods can have the quick-detecting abilityIn this paper, we use Monte Carlo simulation to compare themonitoring ability of process mean and covariance matrix of the self-starting control charts that we built and the traditional methods. Inthe end we show the values of our methods in the real production data.Our methods can be used to the quick detection of the deviation of thehigh-dimensional production data. Our method shows its advantageespecially when sufficient sample data cannot be easily gathered, such asif the test is a destructive one or the test costs are too high.