In this paper the transition probability matrix is used to tackle the problem of the availability of repairable systems. The method is applicable to a system governed by a two-parameter distribution for the life-time and repair-time. It will be concentrated on the Weibull and Gamma distributions without and/or with singularities. The method is involving matrices multiplication of massive size. ...

The inventory management of multi-echelon repairable items systems is a major problem as these items are relatively expensive and slow-moving, so, inventory management can be a real problem due to mathematical complexities. In this work, a study was performed in a complex high-value products manufacturer, whose repairable items are both expensive and critical. Data of parts’ failure, storage an...

Recently, locally repairable codes has gained significant interest for their potential applications in distributed storage systems. However, most constructions in existence are over fields with size that grows with the number of servers, which makes the systems computationally expensive and difficult to maintain. Here, we study linear locally repairable codes over the binary field, tolerating m...

Operational systems consist of components that deteriorate and eventually fail. Upon failure, components are either repaired or replaced. Cheap and critical components are usually replaced, while expensive and non-critical components are repaired several times before complete replacement. In this research work, repairable systems undergoing imperfect repair are examined. In this type of repair,...

A series repairable system not only is one of the classical reliability models but is also the usually used model in practice. In this paper, a method for calculating system availability for series repairable system is studied. From the states of components, this methodology uses a gamma distribution to model the material degradation, and the impact of imperfect maintenance actions on the syste...

The availability equivalence factors of a general repairable parallel-series system are discussed in this paper considering the availability function of the system. The system components are assumed to be repairable and independent but not identical. The life and repair times of the system components are exponentially distributed with different parameters. Two types of availability equivalent f...

This paper presents a decomposition technique for the service station reliability in a discrete-time repairable Geom/G/1 queueing system, in which the server takes exhaustive service and multiple adaptive delayed vacation discipline. Using such a novel analytic technique, some important reliability indices and reliability relation equations of the service station are derived. Furthermore, the s...

This paper introduces a Markov model for a multi-state repairable system in which some states are changeable in the sense that whether those states are up or down depends on the recent system evolution history. Several reliability indexes, such as availability, mean up time, steady-state reliability, are calculated using the matrix method. A sufficient condition under which the availabilities o...