TY - JOUR
T1 - On reliability of parallel and series systems of two three-state components with dependent functioning-state lifetimes
AU - Li, Chen
AU - Li, Xiaohu
N1 - Publisher Copyright:
© IMechE 2025.
PY - 2025
Y1 - 2025
N2 - In the Markov model of degraded multi-state systems, instantaneous degradation rates are constant and their functioning state lifetimes are semi-independent. This note attempts to study systems of two independent three-state components with arbitrary degradation rates and any statistical dependence between functioning state lifetimes. In particular, we derive nonparametric reliability functions for functioning state lifetimes of both parallel and series systems of the two components. Moreover, we investigate how the statistical dependence impacts the system lifetime through conducting nonparametric stochastic comparison on system functioning state lifetimes. Some numerical examples are presented to illustrate the results as well.
AB - In the Markov model of degraded multi-state systems, instantaneous degradation rates are constant and their functioning state lifetimes are semi-independent. This note attempts to study systems of two independent three-state components with arbitrary degradation rates and any statistical dependence between functioning state lifetimes. In particular, we derive nonparametric reliability functions for functioning state lifetimes of both parallel and series systems of the two components. Moreover, we investigate how the statistical dependence impacts the system lifetime through conducting nonparametric stochastic comparison on system functioning state lifetimes. Some numerical examples are presented to illustrate the results as well.
KW - Copula
KW - increasing convex order
KW - increasing failure rate
KW - positively quadrant dependent
KW - usual stochastic order
UR - https://www.scopus.com/pages/publications/105002993126
UR - https://www.scopus.com/inward/citedby.url?scp=105002993126&partnerID=8YFLogxK
U2 - 10.1177/1748006X251324967
DO - 10.1177/1748006X251324967
M3 - Article
AN - SCOPUS:105002993126
SN - 1748-006X
JO - Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
JF - Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability
ER -