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The article presents a cumulative sum algorithm intended to detect a sudden step-like change in the probabilistic characteristics of a monitored time series when such a change (“disorder”) is associated with a simultaneous change in both the location characteristics and the dispersion characteristics of the corresponding distribution functions. In the general case of a multidimensional time series, the disorder is associated with a jump in the values of the mathematical expectation vector (the vector of means) and covariance matrix entries. To solve this problem, it is proposed to use a preliminary linear transformation of the time series values, as a result of which the covariance matrix is transformed to the unity form before disordering and to the diagonal form after disordering. The change in the vector of means is analyzed, and the main relations describing the considered detection algorithm are derived. It is noted that by using the above-mentioned linear transformation it is possible to simplify the obtaining of the reference data necessary for synthesizing the monitoring algorithm with the predetermined properties. As an example, a particular case of a one-dimensional time series and a disorder in the form of a simultaneous change in the mean and variance is considered. For this case, reference data obtained by applying the simulation method are given, using which it is possible to find the monitoring algorithm triggering threshold and estimate the average delay time of detecting the specified disorder from the given interval between false alarms. This study is a logical continuation and further development of the approach to construction of multidimensional algorithms for detecting disorders [1].

The solution of the problem of detecting, in the online mode, a spontaneous change in the probabilistic characteristics (“disorder” or “breakdown”) of a time series is given. It is pointed out that there is a growing interest in the development of so-called nonparametric disorder detection methods, i.e., methods the application of which does not require the knowledge of the probability distribution function of the controlled process values. It is stated that the majority of the known versions of such methods are based on using a number of standard nonparametric criteria transformed for solving disorder detection problems. It is proposed to use the signs criterion, the series criterion, and the Ramachandran–Ranganathan criterion as a basis for construction of disorder detection algorithms. The methodical aspects of studying the statistical properties and efficiency of the disorder detection algorithms built on their basis are considered. The simulation method was used as a study tool. The plan of carrying out simulation experiments was developed separately for each of the proposed algorithms, taking into account their individual characteristics, but based on the general requirement of fully reproducing the monitoring algorithm performance dynamics under real conditions, when a disorder can appear at any time and there is a transient in the values of the decisive function. By using a simulation experiment for each of the algorithms under consideration, data on their statistical characteristics were obtained and systematized in a scope sufficient for synthesizing a monitoring procedure with the specified properties.