This chapter considers a consecutive r-out of-k-from n: G system taken for the study. The considered system works if at least r elements out of k consecutive elements within n elements work. The consecutive r-out of-k-from n: G system is special case of linear consecutive k-out-of-r-from-n:G system. A technique is applied for analyzing fuzzy reliability of the system using universal generating function and fuzzy set theory. At the end of the chapter, the proposed technique is demonstrated from a numerical example.
The prime factorization theorem states that every integer greater than 1 can be expressed as a product of primes. Goldbach conjecture states that every even number greater than 2 can be expressed as a sum of 2 primes. In this paper we study the proof of prime factorization theorem using hypergraphs and we show that every sum of two or more primes gives a composite number.
KEY WORDSprime factorization theorem, complete prime vertex composite edge weighted hypergraph
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