© Science and Education Publishing DOI:10.12691/ajams-2-2-6 Availability and Profit Analysis of a linear Consecutive (original) (raw)
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American Journal of Applied Mathematics and Statistics, 2014
In this paper, we study some reliability characteristics of a repairable linear consecutive 2-out-of-4 system. The system work when to two units in a row (consecutive) works. The system is attended by three repairmen. When an operating unit failed, a standby is switched on or an idle operating unit is exchange with the failed unit. The explicit expressions of the reliability characteristics such availability, busy period of the repairmen and profit function are derived. Some cases are analyzed graphically to investigate the impact of system parameters on availability and profit.
Availability and Profit Analysis of 3-out-of-4 Repairable System with Preventive Maintenance
International Journal of Applied Mathematical Research, 2012
Studies on two unit repairable standby system dealing with availability and profit analysis involving preventive maintenance are numerous. However little attention is paid on the study of evaluation of reliability characteristics such as availability, busy period and profit function of multi component system such as 3-out-of-4 system involving four types of failures. In this paper, we studied the availability and profit analysis of a repairable redundant 3-out-of-4 system with preventive maintenance involving four types of failures and develop explicit expressions for steady-state availability and profit function for the system using Chapman-Kolmogorov equations. Some particular cases have also been obtained analytically and graphically to see the impact of preventive maintenance on some system measures of effectiveness .Certain important result have been evaluated as special cases. Results have shown that system with preventive maintenance is better in terms of system effectiveness than system without preventive maintenance.
International Journal of Engineering & Technology
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.
In this paper, we studied a series system consisting of single unit. The system is subjected to three types of failures. Type I failure is minor in which the system is imperfectly repaired. Type II failure is major in which the entire system is replaced. Type III failure is called a partial failure in which the system works in reduced capacity and is perfectly repaired. Failure and repair time are assumed exponential. We developed the explicit expressions for mean time to system failure (MTSF), steady-state availability, busy period and profit function using Kolmogorov forward equations method. Special cases are studied to determine the impact of various system parameters on MTSF, busy period, steady-state availability and profit function.
International Journal of System Assurance Engineering and Management, 2012
The purpose of this paper is to carry out the profit analysis of a three unit redundant system in which two units work in parallel and one unit is kept as spare in cold standby. Each unit has direct complete failure from normal mode. There is a single repairman (called server) who visits the system immediately to do repair, inspection and replacement of the units. The unit does not work as new after repair and so called a degraded unit. The degraded unit at its further failure undergoes for inspection to see the feasibility of its repair. If the repair is not feasible, it is replaced immediately by new unit. The system is considered in up-state if any two of original and/or degraded units are operative. The time to failure, repair and inspection of the units are taken as arbitrary with different probability density functions. By adopting semi-Markov process and regenerative point technique, the results for some measures of system effectiveness are obtained in steady state.
American Journal of Operational Research, 2013
In this paper, we studied a series system consisting of single unit. The system is subjected to three types of failures. Type I failure is minor in which the system is imperfect ly repaired. Type II failure is majo r in which the entire system is replaced. Type III failure is called a partial failure in wh ich the system works in reduced capacity and is perfectly repaired. Failure and repair t ime are assumed exponential. We developed the explicit exp ressions for mean time to system failure (MTSF), steady-state availability, busy period and profit function using Kolmogorov forward equations method. Special cases are studied to determine the impact of various system parameters on MTSF, busy period, steady-state availability and profit function.
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This investigation deals with the transient analysis of the machine repair system consisting of M-operating units operating under the care of single repairman. To improve the system reliability/availability, Y warm standby and S cold standby units are provided to replace the failed units. In case when all spares are being used, the failure of units occurs in degraded fashion. In such situation there is a facility of one additional repairman to speed up the repair. The lifetime and repair time of units are exponentially distributed. We use matrix method to solve the governing Chapman-Kolmogorov equations. Expressions for the system reliability, availability, mean time to system failure, etc. are established in terms of transient probability. Computational scheme is discussed to facilitate the numerical results. Sensitivity analysis is also carried out to depict the effect of various parameters on the system reliability.
International Journal for Research in Applied Science & Engineering Technology (IJRASET), 2022
In this paper we analyze the steady state availability of a series-parallel repairable system. In this system, the first unit is master control unit and other two are slave units and one single repairman who operates single vacation. Under that assumption each unit has arbitrary repair time distribution & a constant failure rate. Also, it is noted that to calculate the availability of the system it is required to obtain the explicit expression and for obtaining steady-state probabilities it is necessary to use "the supplementary variable" method as well as "Markov process theory".
Stochastic modelling and analysis of a repairable 2-out-of-4 system
International Journal of Mathematics in Operational Research, 2014
In this study, stochastic modelling and analysis of a repairable 2-out-of-4 system is presented. The system under study is exposed to four types of failures and is attended by four repairmen. The failure and repair time are assumed exponentially distributed. Explicit expressions for mean time to system failure (MTSF), the steady-state availability, and busy period of repairman and profit function of the system are analysed stochastically using Kolmogorov's forward equation method. Numerical results giving some particular values to the costs and other parameters have also been obtained. Graphical studies on MTSF, steady-state availability and profit has been shown with respect to both failure and repair rates.