Determination of failure rate function on the basis оf the markovian process

Abstract

The life cycle of a construction (or its element) is considered as markovian process with discrete states and continuous time. Five operational states have been accepted, in which the construction may be. The corresponding system of differential equations is obtained for the case of a homogeneous markovian process with a constant conversion rate (Kolmogorov system). The method of uncertain coefficients is applied to solve the system of equations in analytical form. The obtained solutions make it possible to determine the probability of finding the construction in a particular state as well as the most likely transition time from one operational state to another. Security function defined as the probability of not finding the construction in its last (inoperable) state and the failure rate function. The graphs of the probability of finding a construction in each of the five states, reliability and failure rate functions are presented and investigated. The obtained analytical dependences make it possible to determine the longevity and residual life of the work both individual elements and structures as a whole and optimize scheduling for ongoing maintenance work, significantly improve the performance of the structure, reduce the cost of repair work and extend the life of the structure.

Methodology for Assessing the Technical Condition and Durability of Bridge Structures

“…As we can see from (15), the failure intensity function does not depend on the initial reliability of the structure. If we assume that λ f r (t) does not depend on time (λ f r (t) = λ C = const), then from (15) we obtain the well-known exponential degradation law:…”

“…Lantukh-Lyashchenko in 1999 [13]. Subsequently, the model was further developed and improved in works [14,15] and was verified in practical applications as an updated nor-mative model for assessing and predicting the technical condition of bridge elements [16]. In the practices of Slovakia and the Czech Republic, a combined approach based on several models is used in the standards for assessing and predicting the condition of bridges [17].…”

“…Thus, the models and methods for assessing and predicting the technical condition of bridges identified in the studies [1][2][3][4][5][7][8][9][10][13][14][15][16][17]20,21] are not perfect, have limitations in their application, and require refinement. Additionally, the analysis of these studies has shown that adequate results cannot be obtained using traditional models.…”