Reliability of Combined $k{\hbox {-out-\of-}}n$ and Consecutive $k_{c}{\hbox {-out-\of-}}n$

A combined k-out-of-n :F(G) & consecutive kc-out-of-n:F(G) system fails (functions) iff at least k components fail (function), or at least kc consecutive components fail (function). These models involve two common failure criteria, and can be used in various situations depending on the actual failure criteria involving consecutive components, or all components. Explicit formulas for the reliabilities of these systems are obtained for Markov dependent components using the distribution theory of runs. Some numerical results are also presented.