Analysis of the EWMA-algorithm Properties for Detecting Disorder by Mathematical Expectation оf the Gaussian Time Series of a Moving Average

The article addresses a study of the statistical characteristics of the exponentially weighted moving average (EWMA) algorithm, which is one of the most popular algorithms for detecting spontaneous changes in the properties (disorder) of random processes in real time. The purpose of the work is to determine this kind of characteristics under the conditions of correlated values of a controlled time series, namely, when the process belongs to the category of moving average series. Using simulation, relationships have been found that make it possible to synthesize a controlling EWMA algorithm with preset properties, namely, to select a decisive threshold h for a given value of the mean time between false alarms  depending on the exponential smoothing parameter λ of the EWMA algorithm for various values of the order d of the controlled moving average process. In a similar way, for a number of  values, the dependences of the average delay time  in detecting a disorder and the efficiency indicator Е =  as a function of λ and the relative disorder value r were found. The possibility of synthesizing the EWMA algorithm with the highest response speed has been established by choosing the optimal value of the parameter λ for various combinations of the r and  values. A comparison of the effectiveness of EWMA algorithms for uncorrelated and correlated observations was carried out, as well as a comparison of the effectiveness of the EWMA algorithm with the effectiveness of a similar procedure of the MA algorithm.