Stochastic Process Control (SPC) is used to detect changes in the performance parameters of interest from their target values, namely in industrial systems. Conversely, Stochastic Ordering (SO) is used to establish dominance relations between random variables and stochastic processes in stronger senses than a mere inequality between means. As the most important performance quantity in SPC is the time for a signal (TS) to be given and, the use of SO in SPC (namely, establishing stochastic order relations between TSs of different control procedures) is of great interest.

In this talk I will highlight joint work with M. Cabral Morais on the use of SO in two non-classical issues of SPC: run lengths to misleading signals in joint schemes for the mean and the variance, and the effect of autocorrelation in the performance of quality control schemes.The approach used relies heavily on the Markovian nature of the summary
statistics used to run the control procedure.