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

## Kaiye Gaoa,b, Xuejuan Liub, Huiying Wangc, Xiaoyang Mad, and Rui Penge

aSchool of Economics and Management, Beijing Information Science and Technology University, Beijing, 100192, China
bDonlinks School of Economics and Management, University of Science and Technology Beijing, Beijing, 100083, China
cSchool of Public Administration, University of International Business and Economics, Beijing, 100029, China
dSchool of Information Management, Beijing Information Science and Technology University, Beijing, 100192, China
eSchool of Economics and Management, Beijing University of Technology, Beijing, 100124, China

(Submitted on September 23, 2018; Revised on October 16, 2018; Accepted on November 15, 2018)

## 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 of consecutive 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.

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