Substar reliability defined as the probability that a fault-free substar of a certain scale is still available in the star network \(S_n\) when the occurrence of faults. The substar reliability is one of the most practical reliability measures because a user in the current star multiprocessors is given a certain substar for the execution of his/her program. Wu and Latifi(Inf. Sci. 178 (2008)) derived upper-bound on the substar reliability of \(S_n\) by analysing the intersection of no more than three substars. Later, Li et al.(IEEE. Trans. Rel. 65 (2016)) derived lower-bound on the substar reliability of \(S_n\) by considering the intersection of no more than four substars. In the paper, we further derive the upper- and lower bounds on the substar reliability of \(S_n\) by taking into account the intersection of no more than five or four substars, respectively. At a result, we obtain more accurate value of the upper-bound on substar reliability of \(S_n\) . The experimental study indicates that both the upper- and lower bounds are very close to approximate results especially for the low value of the node reliability.
