This paper considers the problem of determining the optimal number of spare modules in a dynamic redundant system. Two versions of the problem are treated. First, it is shown how to minimize the average system cost. Second, it is shown how to maximize the reliability of the system with imperfect coverage. Some numerical examples are also obtained to illustrate the results. 1 NOTATION a d E(T~) P R(s) S Ts Cost of each module Cost of system failure Average system cost Module reliability System reliability Number of spares System cost for a system of size S + 1
2 Introduction
In many critical applications of computer systems, fault tolerance has been an essential architectural attribute for achieving high reliability. It is universally accepted that computers cannot achieve the intended reliability in operating systems, 1 application programs, control programs or commercial systems such as nuclear power plant control, 2 space shuttle, etc., without employing redundancy.
Consider a system with dynamic redundancy which consists of several modules but with only one operating at a time. Various fault detection schemes are used to determine when a module has become faulty, and fault location is used to determine exactly which module, if any, is faulty. If a fault is detected and located, the faulty module is removed from operation and. replaced by a spare. Thus dynamic redundancy requires consecutive actions of fault