We use a Poisson imbedding technique to investigate the possibilities of generalizing some pathwise and stochastic monotonicity results from the M/M/k queues to systems with monotone failure rate service time distribution. A dichotomy between the decreasing failure rate (DFR) and the increasing failure rate (IFR) cases is revealed: In the DFR case, we achieve that the number of customers in the systems is stochastically increasing if it is idle at time 0, whereas in the IFR case, there is an alternating character that renders a bound between two identical systems that have different initial conditions. We also explore how our methods work in a comparison between systems with different numbers of stations but the same maximal capacity.