A note on parametric availability

Availability of a binary repairable system is generalised on the case when the quality of the system's operation is characterised by some decreasing in time (since the latest renewal) function of performance. The corresponding equation for the time-dependent availability is derived and the stationary characteristic is considered as well. The probability of exceeding the fixed level of performance for an arbitrary instant of time is also obtained. A further generalisation is performed by assuming the possibility of a gradual repair. This means that the system can be partly available (with the decreased level of performance) during the process of repair. Finally, the specific case of imperfect repair is treated. Possible generalisations of the last approach are discussed.