On reliability of parallel and series systems of two three-state components with dependent functioning-state lifetimes

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.