Reliability and failure functions of some weighted systems

In modern systems, not only the number and the position of the functioning or the failed components are the main factors that keep the system into the functioning state or transform it into failure state, but the contribution or the working probability of the component is also a very important one. This contribution is usually called the component weight. In this paper, the reliability and the failure functions of the consecutive weighted k-out-of-n: F linear and circular system, the weighted f-out-of-n: F system, the weighted (n,f,k) linear and circular system and the weighted linear and circular system are obtained.