A New Iterative Approach to Evaluate the Reliability of a Combined Consecutive k and v-Out-Of-n System

doi:10.23940/ijpe.18.12.p8.29832993

Abstract

Abstract:

Consecutive k-out-of-n: F systems have applications in the fields of telecommunications and oil pumping. A consecutive k-out-of-n: F system fails if at least consecutive k components fail. However, practical systems may fail due to either the failure of a number ofconsecutive components or the failure of a total number of components. In this paper, we consider a system with linearly arranged components, where the system fails if at least a pre-specified number of consecutive components fail or a pre-specified total number of components fail. The system is termed as a combined consecutive k and v-out-of-n system. The iterative relationship between the failure probability of a consecutive k-out-of-n: F system has been proposed. This paper focuses on the iterative relationship between the success probabilities and proposes the detailed calculation process for illustrative purposes.

Key words: k-out-of-n system, failure model, iterative approach, combined consecutive k and v-out-of-n system

Kaiye Gao, Xuejuan Liu, Huiying Wang, Xiaoyang Ma, and Rui Peng. A New Iterative Approach to Evaluate the Reliability of a Combined Consecutive k and v-Out-Of-n System [J]. Int J Performability Eng, 2018, 14(12): 2983-2993.

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References 27

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n	Total numbers of components
p	Fault detection process
k	The number of the consecutive failed components that lead to the failure of the whole system
v	The number of the failed components in arbitrary position that lead to the failure of the whole system
$R(n,k,v,p)$	The reliability of the whole system that have two types of failure modes
${{R}_{C}}(n,k,p)$	The reliability of the whole system that fails if k consecutive components fail
${{R}_{A}}(n,v,p)$	The reliability of the whole system that fails if v components in arbitrary positions fail
m	The index of the first component that does not fail
$Q(m)$	The probability that the first working component is the No. m in the whole system
${{N}_{C}}(j,k,n-m)$	The number of ways to arrange j failed components within n-m linearly ordered components under the condition that no k or more failed components are consecutive
$j/k$	The maximum integer no largerthan$j/k$
$C(n,k,v)$	The complexity of calculating the reliability of a combined consecutive k and v-out-of-n system

k	$R(5,k,3,0.1)$
1	0.59045
2	0.96228
3	0.99104

v	$R(5,2,v,0.1)$
1	0.91845
2	0.96228
3	0.96309

p	$R(5,2,3,p)$
0.1	0.96228
0.2	0.88704
0.5	0.495
0.8	0.103