Economic-statistical design of effective variance control charts, /Sp/ ^1/p

Multivariate Statistical Process Control (MSPC) is to control several quality characteristics simultaneously during a production process. When a process is statistically under control, only common causes of variability affect the process. The MSPC techniques help to detect the special causes of variability on the process. In the last few years multivariate quality control has been thoroughly studied and there are different but those charts don't let control de multivariate dispersion on process. Recently the generalized variance control chart /S/, has been develop to control multivariate dispersion. Nevertheless, this chart is unhelpful to work with incomplete databases or with missing data, that are commonly found in a great deal of processes due to the failure of certain sensors. In this sense, Garcia-Diaz developed the effective variance control chart, /Sp/^1/p, to control multivariate dispersion with missing data. To design the economic-statistical of the Variance Effective control chart, attempting to obtain the values of the parameters in the sampling plan that minimize the expected operation costs by time unit, according to the restrictions of a minimum ARL value under control, and a maximum ARL value when the process is out of control.