Some conditional reliability properties of k-out-of-n system composed of different types of components with discrete independent lifetimes

Abstract

AbstractIn this paper, we study reliability properties of k-out-of-n system consisting of l$$(1\le l\le n)$$ ( 1 ≤ l ≤ n ) different types of components with discrete, independent lifetimes. We obtain some conditional survival functions of lifetime of a used system. Next, we use them to calculate two conditional failure probabilities of k-out-of-n systems and show that they are equal to unconditional failure probability of a k-out-of-$$(n-r)$$ ( n - r ) system, $$r<n-k+1$$ r < n - k + 1 . These results are extended versions of the respective ones existing in the literature.