Abstract:Purpose -The purpose of this paper is to study repairable consecutive-k-out-of-n: systems with r repairmen and a sensing device. Design/methodology/approach -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 … Show more
This paper presents the Markov model for the reliability analysis of a linear consecutive 2-out-of-4 repairable system operating with the help of a linear consecutive 2-out-of-4 external supporting device. The system is analyzed using first order linear differential equation to develop the explicit expression for steady-state availability, busy period and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. In addition, the effect of failure and repair on availability and profit are researched.
This paper presents the Markov model for the reliability analysis of a linear consecutive 2-out-of-4 repairable system operating with the help of a linear consecutive 2-out-of-4 external supporting device. The system is analyzed using first order linear differential equation to develop the explicit expression for steady-state availability, busy period and profit function. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. In addition, the effect of failure and repair on availability and profit are researched.
“…They evaluated state transition probabilities and important reliability measures using a generalized transition probability definition. Krishnan and Somasundaram (2011) assessed the performance metrics of consecutive-k-out-of-n: G system having sensor and r repair persons. They used the Laplace transform and concluded that a use of sensor improves the system performance.…”
The concerned study pertains to the development of a new stochastic model for the reliability analysis of linear consecutive-k-out-of-n: G system, where k>n2. In the developed model, system may collapse as a result of common cause failure or hardware failure in its units. The system has exponentially distributed failure rates, and in case of breakdown, it is repaired with the copula method. The developed model has been examined through supplementary variable technique (SVT) along with Laplace transform. The current paper has specifically studied consecutive-(n-1)-out-of-n: G system. The performance of such system having ten components is explored and its various reliability measures have been obtained and discussed with the help of graphs. The originality of this work lies in incorporating common cause failure in conjunction with copula repair in the reliability modeling of consecutive systems through the SVT. The study confirms that an increase in failure rates and the number of components of the concerned system decreases mean time to failure (MTTF). The profit of linear consecutive-9-out-of-10: G system is examined with the help of a numerical example.
“…(1999) studied reliability for ( n , f , k ) system in which the system fails when consecutive k components out of n fail; Liang et al. (2010) studied exact reliability formula for consecutive k -out-of- n repairable systems; Krishnan and Somasundaram (2011) deliberated on reliability analysis of repairable consecutive k -out-of- n : G system sensor and repairman; Goyal et al. (2017) premeditated sensitivity analysis of a three-unit series system under k -out-of- n : G redundancy; Sharma and Kumar (2017) premeditated availability improvement for the successive k -out-of- n machine system using standby with multiple working vacations.…”
PurposeThe purpose of this paper is to deliberate the system reliability of a system in combination of three subsystems in a series configuration in which all three subsystems function under a k-out-of-n: G operational scheme. Based on computed results, it has been demonstrated that copula repair is better than general repair for system better performance. The supplementary variable approach with implications of copula distribution has been employed for assessing the system performance.Design/methodology/approachProbabilistic assessment of complex system consisting three subsystems, multi-failure threats and copula repair approach is used in this study. Abbas Jubrin Bin, V.V. Singh, D.K. Rawal, in this research paper, have analyzed a system consisting of three subsystems in a series configuration in which all three subsystems function under a k-out-of-n: G operational scheme. The supplementary variable approach with implications of copula distribution has been employed for assessing the system performance. Based on computed results, it has been demonstrated that copula repair is better than general repair for system better performance.FindingsIn this analysis, four different cases of availability are analysed for Gumbel–Hougaard family copula and also four cases for general repair with similar failure rates are studied. The authors found that when failure rates increase, the system availability decreases, and when the system follows copula repair distribution, the system availability is better than general repair.Research limitations/implicationsThis research may be implemented in various industrial systems where the subsystems are configured under k-out-of-n: G working policy. It is also advisable that copula repair is highly recommended for best performances from the system. On the basis of mean time to system failure (MTSF) computations, the failure rate which affects system failure more needs to be controlled by monitoring, servicing and replacing stratagem.Practical implicationsThis research work has great implications in various industrial systems like power plant systems, nuclear power plant, electricity distributions system, etc. where the k-out-of-n-type of system operation scheme is validated for system operations with the multi-repair.Originality/valueThis work is a new work by authors. In the previously available technical analysis of the system, the researchers have analyzed the repairable system either supplementary variable approach, supplementary variable and system which have two subsystems in a series configuration. This research work analyzed a system with three subsystems with a multi-repair approach and supplementary variables.
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