Model of item monitoring system under unreliable supervision

Aim. The conducted research aims to develop an analytical model of item dependability for situations of technical state monitoring with constant inspection frequency and subject to inspection errors and failures of various types. The primary purpose of the model is the calculation and prediction of dependability indicators that depend on specified conditions. Methods. The model is based on the Markovian process theory. Models of two types are used, i.e. the continuous-time discrete process model and semi-Markovian model. The mathematical operations involved in the model implementation were performed in matrix form. An items’ operation is presented in the form of recurrent cycles separated from each other by the recovery state. A continuous-time model allows obtaining state probabilities within the periods between inspections, mean active state times and state probabilities at the end of a period. The probabilities of entering states at the end of a period are a priori for the semi-Markovian model, using which the mean numbers of active states within one cycle were obtained. Results. The mean up and down time within a cycle were calculated using mean state frequency and mean time of active state. Based on those parameters, formulas were obtained for calculating the availability and non-availability coefficients. Out of the above model follows that the dependability indicators depend on the frequencies of explicit and hidden failures, inspection frequency and inspection errors. The paper sets forth the calculation data for the mean cycle duration and non-availability coefficient under various failure rates and various probabilities of inspection errors. It is shown that the mean cycle duration significantly depends on the probability of inspection errors of the I kind and practically does not depend on the probability of inspection errors of the II kind. However, the non-availability coefficient practically does not depend on the probability of inspection errors of the I kind, yet there is a strong dependence on the probability of inspection errors of the II kind. Conclusions. The presented model allows calculating and predicting dependability indicators taking into consideration explicit and hidden failures, as well as the monitoring system parameters. While designing new and improving the maintenance procedures of existing systems, the effect of various factors on the dependability level should to be taken into consideration.

item technical condition monitoring, explicit and hidden failures, inspection frequency, inspection errors

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