Transient analysis of a repairable system, using phase-type distributions and geometric processes

The transient behavior of a system with operational and repair times distributed following phase-type distributions is studied. These times are alternated in the evolution of the system, and they form 2 separate geometric processes. The stationary study of this system when the repair times form a renewal process has been made . This paper also considers that operational times are partitioned into two well-distinguished classes successively occupied: good, and preventive. An algorithmic approach is performed to determine the transition probabilities for the Markov process which governs the system, and other performance measures beyond those in are calculated in a well-structured form. The results are applied to a numerical example, and the transient quantities are compared with the ones obtained in the stationary case. The computational implementation of the mathematical expressions formulated are performed using the Matlab program.