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Reliability analysis of repairable consecutive‐k‐out‐of‐n: G systems with sensor and repairmen

Ragi Krishnan (Department of Mathematics, RVS College of Engineering and Technology, Coimbatore, India)
S. Somasundaram (Department of Mathematics, Coimbatore Institute of Technology, Coimbatore, India)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 6 September 2011




The purpose of this paper is to study repairable consecutive‐k‐out‐of‐n: systems with r repairmen and a sensing device.


The system can either be a circular C(k, n: G) system or a linear C(k, n: G) system. The working time and the repair time of each component in the system and the sensor detection time are exponentially distributed. Every component after repair is perfect. Each component is classified as either a key component, or an ordinary one according to its priority role to system's repair. A sensing device is introduced to detect the failure of each component in the system in advance and completion of repair of components. If the repair is completed, the sensor will send the component to standby according to its priority. The state transition probabilities of the system are derived using the definition of generalized transition probability. To obtain the reliability and availability Laplace transform techniques have been used.


The Kolmogorov‐Feller forward equations are derived for both linear and circular systems. Reliability and MTTF of both the systems are derived using Laplace transforms. Numerical examples are given in detail to demonstrate the theoretical results and these verify the validity of the studied system.

Research limitations/implications

A consecutive‐k‐out‐of‐n system consists of a sequence of n‐ordered components along a line or a circle such that the system is good if and only if at least k consecutive components in the system are good. Each component in the system is classified as key component or ordinary component according to its priority in system functioning. By using a sensing device the failure can be detected in advance.


This study indicates that by using a sensing device we can detect the failure in advance. Thus, the reliability and MTTF of the system can be improved.



Krishnan, R. and Somasundaram, S. (2011), "Reliability analysis of repairable consecutive‐k‐out‐of‐n: G systems with sensor and repairmen", International Journal of Quality & Reliability Management, Vol. 28 No. 8, pp. 894-908.



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Copyright © 2011, Emerald Group Publishing Limited

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