A level-dependent general discrete system involving phase-type distributions

Abstract

A discrete repairable redundant n-system with one online unit and the others in warm standby is presented. The operational and repair times follow general distributions and the phase-type representation is considered. It is shown that the process governing the system is a discrete level-dependent M/G/1 process. For this system, the stationary distribution, performance reliability measures in transient and stationary regime, the up period and the involved costs are worked out in a matrix and algorithmic form. The presented results have been computationally implemented using Matlab. An application illustrates the developed model.

Keywords:

• Phase-type distribution
• stationary distribution
• reliability
• reward
• up period

Acknowledgements

The authors are very grateful to the two referees and the Associate Editor, whose comments have greatly improved the paper. The work reported in this paper was partially supported by the Ministerio de Educación y Ciencia, España, under grant MTM2004-03672.