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A preventive maintenance of circular consecutive-k-out-of-n: F systems

Alfonsus Julanto Endharta (Department of Industrial Engineering, Pusan National University, Busan, Republic of Korea)
Won Young Yun (Department of Industrial Engineering, Pusan National University, Busan, Republic of Korea)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 5 June 2017




The purpose of this paper is to develop a preventive maintenance policy with continuous monitoring for a circular consecutive-k-out-of-n: F systems. A preventive maintenance policy is developed based on the system critical condition which is related to the number of working components in the minimal cut sets of the system. If there is at least one minimal cut set which consists of only one working component, the system is maintained preventively (PM) after a certain time interval and the failed components are replaced with the new ones to prevent the system failures. If the system fails prior to the preventive maintenance, the system is correctively maintained (CM) immediately by replacing the failed components.


The mathematical function of the expected cost rate for the proposed maintenance policy is derived. The costs of PM, CM, and replacement per component are considered. The optimal maintenance parameter, which is the PM interval, is obtained by enumeration, and the numerical studies are shown with various system and cost parameters. The performance of the proposed policy is evaluated by comparing its expected cost rate to those of the no-PM and age-PM policies. The percentage of cost increase from the no-PM and age-PM policies to the proposed PM policy is calculated and this value can represents how important the continuous monitoring in this policy.


The proposed policy outperforms other policies. When the cost of CM is high and the cost of PM is low, the proposed PM policy is more suitable.

Research limitations/implications

The system consists of identical components and the component failure times follow an exponential distribution. Continuous monitoring is considered, which means that the component states can be known at any time. Three cost parameters, cost of PM, CM, and replacement per component, are considered.


This paper shows a maintenance problem for circular consecutive-k-out-of-n: F systems. Many studies on this system type focused on the reliability estimation or system design problem. Previous study with this policy (Endharta and Yun, 2015) has been developed for linear systems, although the study used a simulation approach to estimate the expected cost rate. Also, Endharta et al. (2016) considered a similar method for the different types of system, which is linear consecutive-k-out-of-n: F system.



This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1D1A1A09919337).


Endharta, A.J. and Yun, W.Y. (2017), "A preventive maintenance of circular consecutive-k-out-of-n: F systems", International Journal of Quality & Reliability Management, Vol. 34 No. 6, pp. 752-769.



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