Reliability of systems with random arrival of multi-staged customers

The paper is concerned with reliability of systems whose sequence of waiting and busy modes makes an alternating process and a customer of $n$ steps is processed in the busy mode. Assuming that flows of failures and faults of the system are Poisson and all the remaining distributions are arbitrary a mathematical model is obtained for changes of states in a system which is described as a semi-Markov process. Laplace-Stieltjes transforms are found for functions of time to functioning failure distribution, the mean values of those times, asymptotic distribution of time to functioning failureswhich depends on failures and faults in the system.