Abstract
We investigate Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations. By using C0-semigroup theory of linear operators in the functional analysis, we prove well-posedness and the existence of the unique positive dynamic solution of the system.
Highlights
The study of repairable systems is an important topic in reliability
In [4], the authors used the dynamic solution in calculating the availability and the reliability
We study in this paper the well-posedness and the existence of a unique positive dynamic solution of the system, by using C0 -semigroup theory of linear operators
Summary
The study of repairable systems is an important topic in reliability. The Gaver’s Parallel system is one of the classical repairable systems in reliability. In [4], the authors studied Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations and obtained some reliability expressions such as the Laplace transform of the reliability, the mean time to the first failure, the availability and the failure frequency of the system. We study in this paper the well-posedness and the existence of a unique positive dynamic solution of the system, by using C0 -semigroup theory of linear operators. The Gaver’s parallel system attended by a cold standby unit and a repairman with multiple vacations can be described by the following equations (see [4]). (2015) Well-Posedness of Gaver’s Parallel System Attended by a Cold Standby Unit and a Repairman with Multiple Vacations.
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