MTBF of a complex binary coherent system

It is noted that there has yet been no detailed study of the relationships between the MTBF (mean time between failures) of a system and the sequences of component failures, except for the case of a series system where every component failure causes a system failure. The author defines MTBF anew and derives relationships between the properties of the MTBF of a binary coherent system and the properties of the sequences of component failures, assuming that the lifetime distributions of the components are either new-better-than-used (NBU) exponential or increasing failure rate (IFR). Lower bounds of MTBF that can be used to predict the MTBF and to decide whether the system would satisfy the MTBF requirement are derived