In this paper, some joint probabilities have been defined with a view to extract more information about the behaviour of a complex system havingn components, which has sufferedN failures by the timet under the assumption of exponential failure time distributions with constant rates $$\lambda _1 ,\lambda _2 ,...,\lambda _n $$ and general waiting and repair time distributions with probability densities $$S_1 \left( x \right),S_2 \left( x \right),...,S_n \left( x \right)$$ and $$\Phi _1 \left( y \right),\Phi _2 \left( y \right),...,\Phi _n \left( y \right)$$ respectively. It is assumed that the system fails if any one of then components fails. The Laplace transforms of various joint probabilities have been obtained for the general case and the corresponding results for some particular cases are then reduced. The mean number of a failures upto timet have also been derived. In the end, the behaviour of the complex system under steady state has been examined. The supplementary variable techniques [1, 5] have been employed to obtain the solution.