A lattice system in this paper is a system whose components are ordered like the elements of (m, n) matrix. A representative example of a lattice system is a connected-(r, s)-out-of-(m, n):F lattice system which is treated as a model of supervision system. It fails if and only if all components in an (r, s) sub lattice fail. We modify the lattice system so as to include a maintenance action and a restriction on the number of failed components. Then, this paper presents availability and MTBF of the repairable system, and reliability when the system stocks spare parts on hand to ensure the specified reliability level.

Mean Time Between Failures (MTBF) is an important measure of practical repairable systems, but it has not been obtained for a repairable linear consecutive-k-out-of-n: F system. We first present a general formula for the (steady-state) availability of a repairable linear consecutive-k-out-of-n: F system with nonidentical components by employing the cut set approach or a topological availability method. Second, we present a general formula for frequency of system failures of a repairable linear consecutive-k-out-of-n: F system with nonidentical components. Then the MTBF for the repairable linear consecutive-k-out-of-n: F system is shown by using the frequency of system failure and availability. Lastly, we derive some figures which show the relationship between the MTBF and repair rate µorρ(=λ/µ) in the repairable linear consecutive-k-out-of-n: F system. The figures can be easily used and are useful for reliability design.