Wireless local area networks (WLANs) which are based on IEEE 802.11 standard are used widely in existing local area network configurations. IEEE 802.11 offers multiple non-overlapping channels to increase the capacity of the network. There are strong evidences that WLANs are prone to impairments. In order to improve the quality of service (QoS) and to evaluate the performance of WLANs realistically, the availability of the systems should be considered. This paper studies performability evaluation of a multi-channel WLAN using analytical modelling approach. Unlike the existing studies, the failures of the overall system, where a critical function unit fails making all the channels unavailable are considered. A new term is introduced as global failures. It is possible to solve the models considered using matrix geometric method where system parameters and minimal non negative solution R is computed by an iterative method. However spectral expansion method is a well-known alternative where the iterative calculations for solving R is avoided using eigenvalues and eigenvectors. The exact spectral expansion method is employed to obtain performability measures such as mean queue length and blocking probability. Iterative refinements are employed in solution of simultaneous equations.