OPTIMAL DESIGN OF TWO K-OUT-OF-N SYSTEMS CONNECTED IN SERIES

Abstract

The safety monitoring system in an underground mine consists of mainly methane sensors and smoke sensors. It can be described as a k-out-of-n:F system with dual failure modes. This paper is to determine the values of k*1 and k*2 that maximize system reliability and minimize average system cost for fixed n1 and n2 values; and the values of n*1 and n*2 that maximize system reliability and minimize average system cost for fixed k1 and k2 values. Two approaches to find n*1 and n*2 for fixed k1 and k2 values by explicitly considering the constraint n*1 +n*2 ≤ n will also be illustrated. The results presented in this paper are useful for optimal design of safety monitoring systems in underground mines.