Renewal theory-based life-cycle analysis of deteriorating engineering systems

• We propose a model for the life-cycle analysis of deteriorating engineering systems.
• The model is based on renewal theory.
• It estimates the time dependent reliability and the life-cycle cost of systems.
• The model is used to analyze the life-cycle of a bridge located in a seismic region.

Engineering systems typically deteriorate due to regular use and exposure to harsh environment. Under such circumstances the owner of a system must take important decisions such as whether to repair, replace or abandon the system. Such decisions can affect the safety of, and the benefits to the users and the owner. Life-cycle analysis (LCA) provides a rational basis for such decision making process. In particular, LCA can provide helpful information on the performance of a system over its entire life-cycle, like its time-dependent reliability, the costs associated with its operation, and other quantities related to the service life of the system.This paper proposes a novel probabilistic formulation for LCA of deteriorating systems named Renewal Theory-based Life-cycle Analysis (RTLCA). The formulation includes equations to obtain important life-cycle variables such as the expected time lost in repairs, the reliability of the system and the cost of operation and failure. The proposed RTLCA formulation is based on renewal theory and proposes analytical solutions for the desired LCA variables using numerically solvable integral equations. As an illustration, the proposed RTLCA formulation is implemented to analyze the life-cycle of an example reinforced concrete (RC) bridge located in a seismic region. This analysis accounts for the accumulated seismic damage in the bridge columns caused by the earthquakes occurring during bridge’s life-cycle. The analysis results provide valuable insight into the importance of seismic damage in a bridge’s life-cycle performance and the strategies to operate a system in an optimal manner.