Two models for a repairable two-system with phase-type sojourn time distributions

This paper investigates a general repairable two-system. The operational and repair times are general, but for applicability, are approached by phase-time distributions, given that this class is dense in the set of distribution functions on the positive real line. Two models are studied, depending on the remembering of the failure phase when the unit is repaired. The versatility of this class of functions is shown. For these models, the availability and the rate of occurrence of failures are calculated. These performance measures are presented in a well-structured form, and are computationally implemented. The method and results are illustrated by a numerical example. The present work generalizes others in the specialized literature, and completes the study of two-systems under the Markov system.