Unavailability of a repairable system with one or two replacement options

The Submarine Line Terminal Equipment (SLTE) is part of the land-based equipment of a submarine network. It is considered to be a repairable system and is housed in the Terminal Station (TS). This study is concerned with (he methodology for the calculation of the unavailability of the SLTE. The traditionally-accepted method of calculating the unavailability of the SLTE is to assume an unlimited number of spares in the TS. Because of the rapidly increasing capacity of submarine networks, it is becoming more important to quantify accurately the unavailability of the equipment, taking into account the exact limited number of spares provided. Furthermore, the spares replacement policy has a bearing on unavailability. For example, a Central Store (CS) may be provided in order to reduce the effective Mean Time To Repair (MTTR). The terminal equipment considered comprises m independent sub-systems in series, each of which comprises ni, i=1,m identical units following the same distribution, taken to be exponential. The problem is then reduced to calculating the unavailability of a repairable series system composed of n(1) independent, identically distributed units, taking into account the different replacement options. The first replacement option takes into account the spares in the TS only. The second replacement option includes both the spares in the TS and in the CS. The Markov method is used to model these systems and to calculate their unavailability, the results are supported using Monte-Carlo simulations. Simplified formulae are derived to approximate the results. Numerical examples are presented to show the advantage of introducing a central store and to validate the approximations.