AbstractA new approach to the study of a consecutive-k-out-of-r-from-n:F system with any component reliability is presented. A random variable describing the behaviour of this general system is defined. Its probability density function, mean, and variance, system reliability, and the Bimbaum importance of system components are investigated by simulation for a variety of values ofn, randk.The analysis is supported by graphs and tables. Easily computed bounds on system reliability in the independent and identically distributed case are given. The proposed simulation method is compared to other existing methods associated with several failure systems.