Journal of Systems Engineering and Electronics ›› 2021, Vol. 32 ›› Issue (3): 711-721.doi: 10.23919/JSEE.2021.000061

• RELIABILITY • Previous Articles     Next Articles

Reliability modelling based on dependent two-stage virtual age processes

Qingan QIU*(), Lirong CUI()   

  1. 1 School of Management and Economics, Beijing Institute of Technology, Beijing 100081, China
  • Received:2020-03-22 Online:2021-06-18 Published:2021-07-26
  • Contact: Qingan QIU;
  • About author:|QIU Qingan was born in 1991. He received his M.S. and Ph.D. degrees in 2020 from the School of Management and Economics, Beijing Institute of Technology. He participated in the joint Ph.D. program in University of Pittsburgh from 2018 to 2019. Now he is a postdoctor in Beijing Institute of Technology. His research interests include maintenance optimization, degradation modeling, and risk analysis. E-mail:||CUI Lirong was born in 1960. He received his Ph.D. degree in probability and statistics from University of Wales in 1994. Now he is a professor in the School of Management and Economics, Beijing Institute of Technology. In 2005, he received the award for New Century Excellent Talents in China. His research interests mainly focus on reliability modeling, quality engineering, simulation and optimization, operations, and applied probability. E-mail:
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (72001026).


This paper proposes reliability and maintenance models for systems suffering random shocks arriving according to a non-homogeneous Poisson process. The system degradation process include two stages: from the installation of a new system to an initial point of a defect (normal stage), and then from that point to failure (defective stage), following the delay time concept. By employing the virtual age method, the impact of external shocks on the system degradation process is characterized by random virtual age increment in the two stages, resulting in the corresponding two-stage virtual age process. When operating in the defective state, the system becomes more susceptible to fatigue and suffers from a greater aging rate. Replacement is carried out either on failure or on the detection of a defective state at periodic or opportunistic inspections. This paper evaluates system reliability performance and investigates the optimal opportunistic maintenance policy. A case study on a cooling system is given to verify the obtained results.

Key words: reliability evaluation, delay-time model, virtual age process, opportunistic maintenance