Reliability for sparsely connected consecutive-k systems
We introduce the system of consecutive failures with sparse d which is a natural extension of consecutive-k systems. Then a series of generalizations of consecutive-k systems are discussed, such as consecutive-k-out-n:F systems with sparse d, M consecutive-k-out-of-n:F systems with sparse d, and (n, f, k):F systems with sparse d. We present the formulation for the system reliability of these generalized consecutive-k systems with various component settings in terms of the finite Markov Chain imbedding idea, along with two numerical examples.
system reliability consecutive-k system with sparse d finite markov chain imbedding approach