This paper presents a mathematical model for analyzing computer networks in production systems. The manufacturing facility, which is considered to be the main part of a production system is controlled by a computer network. Every station within a production system is assumed to have a computer and a network interface unit (NIU) as part of the overall computer network. For the system to remain operational, the computer network along with the manufacturing facilities should be extremely reliable. In this paper, we studied the reliability of the former, the computer network. The manufacturing facility is assumed to be reliable. Since every station must be operational for the whole system to function, failure in any network unit (computer of NIU) will halt the system production. For such systems the topology is logically equivalent to that of a system whose stations are connected in series. Hence, series reliability formulae is appropriate for these systems. In other systems, back-up (or stand-by) units are added to the computer and/or to the NIU to enhance the reliability. We consider our model to be a generic one because the reliability analysis it uses is independent of the network topology. It assumes constant failure rates for network components and uses a two-pass procedure in determining the effect of network reliability on the total system cost. A case study is presented to illustrate the importance of reliability considerations during the network design phase. Our analysis of the network reliability reveals that, in most cases, the incremental cost due to network failures will justify the additional units.