Statistical methods dealing with change detection and isolation in dynamical systems are based on algorithms deriving from hypothesis testing. As for any statistical test, the problem of threshold choice has to be addressed by taking into account the constraints fixed by the supervisors and the nonstationary nature of the stochastic systems under supervision. A procedure for obtaining adaptive thresholds in change detection or diagnosis algorithms of CUSUM-type rules is proposed. This procedure is carried out through a large number of simulations. The advantage of such an adaptive threshold, when compared with a fixed threshold, is its adaptation to the time evolution of the probability distribution of the test statistic, in order to guarantee constant rates of false alarm or false diagnosis, fixed by the supervisor.