Reliability analysis of a repairable system with step-by-step maintenance policy

This paper devotes to studying reliability of a bicycle repairable model with step-by-step maintenance policy by C₀ semigroup theory. Firstly, we get that the system has a unique nonnegative time-dependent solution. Moreover, we obtain that the time-dependent solution exponentially converges to the steady-state solution, which is the positive eigenfunction corresponding to the simple eigenvalue 0. Finally, we discuss some steady-state reliability indices of the system, and make a comparison of the repair costs between step-by-step maintenance policy and non-step-by-step maintenance policy.