Distributed systems potentially provide high reliability owing to the program and data-file redundancy possible. In many applications, high reliability is the major consideration for system design. Previous work has shown that the distribution of programs and data-files can affect the system reliability appreciably, and that redundancy in resources such as computers, programs, and data-files can improve the reliability of a distributed system. This work formulates a practical application for a reliability-oriented distributed task assignment problem which is NP-hard. Then, to cope with this challenging problem, a greedy algorithm is proposed, based on some heuristics, to find an approximate solution. The simulation shows that, in most cases tested, the algorithm finds suboptimal solutions efficiently; therefore, it is a desirable approach to solve these problems. ? 1993 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.?