Reliability of consecutive k-out-of-n: F system under incomplete information

Most studies of consecutive k-out-of-n: F system assume that the component lifetime distributions are known precisely, this implies the reliability of component is known. However it is difficult to expect this assumption is fulfilled, (such as software, human-machine systems). Therefore the paper considers the reliability of consecutive k-out-of-n: F system by using imprecise probability theory under the condition, that there is only some partial information about the component lifetime distribution. The exact formulas are obtained when k is 2; an algorithm is put forward. Finally an example is illustrated.