Multistate Markov models for systems with dependent units

A system that can be described by a homogeneous continuous-time discrete-state Markov process is treated. The case in which transition rates for each unit depend on the current state of the system is considered. The condition in which the transition-rate matrix of the system has the form of a modified Kronecker sum of transition-rate matrices of its units is investigated. An algorithm based on the Kronecker algebra is introduced for determining the transition-rate matrix of the system. its use is particularly efficient during construction of machines when reliability is evaluated for several systems with the same structure but different transition rates.