Combined $m_{1}$ -Consecutive-$k_{c1}$ -Out-of-$n$ and $m_{2}$ -Consecutive-$k_{c2}$ -Out-of-$n$ Systems

The commonly known m-consecutive-
kc
-out-of-
n
:F system consists of an ordered linear sequence of
n
components which fails if there exist at least
m
non-overlapping runs of
kc
consecutive failed components. A more general model is considered here such that the system fails if there exist at least
m
₁
non-overlapping runs of
kc
1 consecutive failed components, or
m
₂
non-overlapping runs of
kc
2 consecutive failed ones. The components are assumed to be i.i.d. An approach based on conditional probabilities is presented for evaluating the reliability of such systems. The computational times for various cases are presented. This model may be applied to various systems such as infrared (IR) detecting, and signal processing systems.