Study of Dynamic Solutions for Human–Machine System with Human Error and Common-Cause Failure

This work investigates a dynamic solution of human–machine systems with human error and common-cause failure. By means functional analysis, it is proved that the semigroup generated by underlying operator converges exponentially to projection analyzing spectral property operator, asymptotic expressions system’s time-dependent solutions are presented. We also provide numerical examples illustrate effects different parameters on system theoretical analysis’s validity.