Stochastic analysis of A 1-server n-unit system subject to inspection and several failure modes

Abstract

The main intent of the paper is to investigate the stochastic behaviour of a single-server n-unit system subject to random inspection and several failure modes. The time between successive inspections is a random variable distributed exponentially. It is assumed that the life-time of a unit is arbitrarily distributed while all the other time distributicns involved are exponential. At any instant t, the system is characterized by the probabilities of its beinq in the ‘up’ or ‘down’ state . Integral equations are established for these probabilities by identifying the system at suitable regenerative epochs corresponding to different initial conditions. Various system parameters of significant importance, namely,

1. point-wise availability of the system at instant t,

2. steady-state availability of the system,

3. s-expected up-time of the system in [o, t],

4. s-expected inspection time of the server in [o, t],

5. s-expected repair time of type i (1 ≤ i ≤ r) in [o, t] and

6. s-expected net gain per unit time in [o, t], have been obtained.