ABSTRACT
This chapter describes a multi-state complex k-out-of-n : G system, modelled in an algorithmic and computational form. The k-out-of-n system with loss of units is modelled by a vector Markov process with state space as described. The transition probability matrix is composed of various levels of matrix blocks. To build the matrix blocks, the auxiliary functions are incorporated, taking into account the phases of the operational units. The transient distribution and the long-run case have also been computed, and several interesting reliability measures obtained, for both transient and stationary regimes. The long-run distribution is obtained by matrix-analytic methods. Several measures associated with the system have been applied, including availability, reliability, and the conditional probability of failure. Various measures are applied in a Markov counting process is developed. The mean number of new systems per unit of time is calculated by means of a Markov counting process.
