title: ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¿Ð¾ÑÐ¾ÐºÐ¾Ð²ÑÑ Ð³ÑÐ°ÑÐ¾Ð² Ð´Ð»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ½Ð¾-Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÑ Ñ Ð°ÑÐ°ÐºÑÐµÑÐ¸ÑÑÐ¸Ðº Ð¿ÑÐ¾ÑÐµÑÑÐ°
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: Application of flowgraphs for the study of probabilistic characteristics of the process
Creators: name: ÐÐ°Ð¿Ð¾Ð½ÐµÐ½ÐºÐ¾, ÐÐ°ÑÑÑ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2021
Subjects: Ð¡Ð»ÑÑÐ°Ð¹Ð½ÑÐµ Ð¿ÑÐ¾ÑÐµÑÑÑ (Ð¼Ð°Ñ.)
ÐÑÐ°ÑÐ¾Ð² ÑÐµÐ¾ÑÐ¸Ñ
Ð¿ÑÐ¾Ð¸Ð·Ð²Ð¾Ð´ÑÑÐ°Ñ ÑÑÐ½ÐºÑÐ¸Ñ Ð¼Ð¾Ð¼ÐµÐ½ÑÐ¾Ð²
ÑÑÐ½ÐºÑÐ¸Ñ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÐ¸ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ
moment generating function
probability distribution function

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description: The subject of the graduate qualification work is Â«Application of flowgraphs for the study of probabilistic characteristics of the processÂ». Flowgraph models are a useful decision support tool that can be applied in a variety of fields such as reliability theory, power systems, and medical statistics. The known analyzing flowgraphs methods are characterized by a significant limitation: simultaneously active parallel branches are not allowed in a flowgraph. The work is devoted to the methods study for the distribution finding of the process duration with some operations performed simultaneously. In this case, the process is defined by a flowgraph, in which the presence of simultaneously active parallel branches is allowed. An algorithm for processing such a graph by complex convolution with the use of residue theory is proposed. To expand the scope of the transition method from the flowgraph to the density function of the process duration, the approximation of the initial operation duration distribution by the two-phase Cox one is used. The algorithm for the flowgraph with parallel branches calculating is implemented, which allows us to obtain the moment generating function and the density function of the transition duration between the flowgraph nodes.