Health and safety is a problem that is intensively discussed nowadays. The failures in healthcare are called medical errors: if the patient’s condition worsens or he/she contracts an illness, then the actions that led to this are interpreted as medical errors. Medical errors can be the result of new procedures, extremes of age, complex or urgent care, improper documentation, illegible hand-writing, or patient actions. One of the ways to reduce medical error is an evaluation of its possibility, and then using the result of this evaluation to improve the medical organization units and processes in patient diagnosis, treatment, and care. This evaluation is possible based on methods of reliability engineering. The reliability engineering methods allow evaluating of different systems’ reliability and the influence of external and internal factors on system reliability. These methods’ application needs the system to be investigated or objective interpretation in terms of reliability engineering. Therefore, such a system in healthcare, for the diagnosis of disease, a patient’s treatment, the influence of different factors on a patient’s condition, and others, should be presented according to the rules and demands of reliability engineering. The first step is development of the mathematical representation of the investigated system or object according to the demands of the reliability analysis. One of the often-used mathematical representations in the reliability analysis of a system is the structure function. However, this mathematical representation needs completely specified initial data. The initial data from the healthcare domain for medical error analysis is uncertain and incompletely specified. Therefore, the development of this mathematical representation needs special methods. In this paper, a new method for the mathematical representation of system development based on uncertain and incompletely specified data is proposed. The system evaluation based on the structure function allows computing of many reliability indices and measures used in reliability engineering. The approbation of this method is considered based on an example of COVID-19 patients.
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