Reliability evaluation of linear r -modified consecutive k -type systems

Consecutive k -type redundant systems, whose working/failure state is defined by the number of consecutive working/failed components, play an important role in reliability theory. In this work, we consider r -modified consecutive k -type systems from the viewpoint of energy/resource saving. Reliabilities of several r -modified consecutive k -type systems (namely, linear r -modified k -out-of- n : F systems, linear r -modified consecutive- k -out-of- n : F systems, linear r -modified m -consecutive- k -out-of- n : F systems, linear r -modified ( n , f , k ) : F systems and linear r -modified < n , f , k > : F systems) have all been evaluated by both finite Markov chain imbedding approach (FMCIA) and the combination method. Illustrative examples have also been provided to verify the correctness of the established results as well as the efficiency of the two methods of computation.