Investigations of the Potential Application of <i>k</i>-out-of-<i>n</i> Systems in Oil and Gas Industry Objects

Abstract

The purpose of this paper was to demonstrate the possibilities of assessing the reliability of oil and gas industry structures with the help of mathematical models of k-out-of-n systems. We show how the reliability of various structures in the oil and gas complex can be described and investigated using k-out-of-n models. Because the initial information about the life and repair time of components of systems is only usually known on the scale of one and/or two moments, we focus on the problem of the sensitivity analysis of the system reliability indices to the shape of its components repair time distributions. To address this problem, we used the so-called markovization method, based on the introduction of supplementary variables, to model the system behavior with the help of the two-dimensional Markov process with discrete-continuous states. On the basis of the forward Kolmogorov equations for the time-dependent process’ state probabilities, relevant balance equations for the process’ stationary probabilities are presented. Using these equations, stationary probabilities and some reliability indices for two examples from the oil and gas industry were calculated and their sensitivity to the system component’s repair time distributions was analyzed. Calculations show that under “rare” component failures, most system reliability indices become practically insensitive to the shape of the components repair time distributions.

Keywords

• <i>k</i>-out-of-<i>n</i>-type systems
• reliability
• probability of system failure
• failure-free time
• repair time
• stationary mode