Mathematical Modeling Approach to Analyzing Mean Time to System Failure of Two Unit Cold Standby System with A Supporting Device and Repairable Service Station

The main purpose of this paper is to study the reliability and availability of a system with M operating devices, m spares, and an imperfect service station that takes vacations. Specifically, once there are no failed devices in the system, the service station takes consecutive vacations until there is at least one failed device upon its return from vacation. The service station may break down and require repair at a repair facility. This paper derives the reliability, the mean time to system failure, the availability, and failure frequency of the K-out-of-M + m system. Numerical simulation of the impacts of system parameters as well as sensitivity analysis for the reliability, the mean time to system failure, the availability and failure frequency is performed.

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Reliability Analysis of a Cold Standby System with Imperfect Repair and under Poisson Shocks

Mathematical Problems in Engineering ◽

10.1155/2014/507846 ◽

2014 ◽

Vol 2014 ◽

pp. 1-11 ◽

Cited By ~ 1

Author(s):

Yutian Chen ◽

Xianyun Meng ◽

Shengqiang Chen

Keyword(s):

Poisson Process ◽

Reliability Analysis ◽

System Availability ◽

Reliability Indices ◽

Intrinsic Factors ◽

Cold Standby ◽

Tauberian Theory ◽

The Mean ◽

Standby System ◽

Mean Time

This paper considers the reliability analysis of a two-component cold standby system with a repairman who may have vacation. The system may fail due to intrinsic factors like aging or deteriorating, or external factors such as Poisson shocks. The arrival time of the shocks follows a Poisson process with the intensityλ>0. Whenever the magnitude of a shock is larger than the prespecified threshold of the operating component, the operating component will fail. The paper assumes that the intrinsic lifetime and the repair time on the component are an extended Poisson process, the magnitude of the shock and the threshold of the operating component are nonnegative random variables, and the vacation time of the repairman obeys the general continuous probability distribution. By using the vector Markov process theory, the supplementary variable method, Laplace transform, and Tauberian theory, the paper derives a number of reliability indices: system availability, system reliability, the rate of occurrence of the system failure, and the mean time to the first failure of the system. Finally, a numerical example is given to validate the derived indices.

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Reliability Analysis of Cold Standby Parallel System Possessing Failure And Repair Rate Under Geometric Distribution

Recent Advances in Computer Science and Communications ◽

10.2174/2666255813666191219110504 ◽

2019 ◽

Vol 13 ◽

Author(s):

Jasdev Bhatti ◽

Mohit Kumar Kakkar

Keyword(s):

Failure Rate ◽

Geometric Distribution ◽

Discrete Distribution ◽

Maintenance Cost ◽

Discrete Problem ◽

New Techniques ◽

Testing Strategies ◽

Cold Standby ◽

Mean Time ◽

Iteration Technique

Background and Aim: With an increase in demands about reliability of industrial machines following continuous or discrete distribution, the important thing to be noticed is that in all previous researches where systems are having more than one failure no iteration technique has been studied to separate the failed unit on basis of its failure. Therefore, aim of our paper is to analyze the real industrial discrete problem following cold standby units arranged in parallel manner with newly concept of inspection procedure for failed units to inspect the exact failure and being communicator to the repairman for repairing exact failed part of unit for saving time and maintenance cost. Methods: The geometric distribution and regenerative techniques had been applied for calculating different reliability measures like mean time to system failure, availability of a system, inspection, repair and failed time of unit. Results: Graphical and analytical study had also been done to analyze the increasing/decreasing behavior of profit function w.r.t repair and failure rate. The system responded properly in fulﬁlling his basic needs. Conclusion: The calculated value of all reliability parameter is helpful for studying any other models following same concept under different environmental conditions. Thus, it concluded that, reliability increases/decreases with increase in repair/failure rate. Also, the evaluated results by this paper provides the better reliability testing strategies that helps to develop new techniques which leads to increase the effectiveness of system.

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Inspecting Briquette Machine with Different Faults

Recent Advances in Computer Science and Communications ◽

10.2174/2666255813999200909110603 ◽

2020 ◽

Vol 13 ◽

Author(s):

Divesh Garg ◽

Reena Garg ◽

Vanita Garg

Keyword(s):

Failure Rate ◽

Rate Increase ◽

Practical Importance ◽

System Failure ◽

Regenerative Point ◽

Semi Markov Process ◽

Major Fault ◽

Environment Study ◽

Burning Coal ◽

Mean Time

Background: A briquette machine can be considered very useful in modern times as the need of energy consumption is increasing rapidly. Considering the harm to environment, study of briquette machine is the need of present times. In this paper, the operative unit is considered as briquette machine also known as bio-coal which is used for agroforestry waste. Objective: A single operative unit has been analyzed stochastically. The inspection of breakdown of a unit reveals the feasibility of the unit under the supervision of either ordinary or expert repairmen. Two types of fault are revealed by the repairmen either minor or major fault. Minor faults are repaired immediately by the same repairmen but whenever major fault held, the machine’s fault will be handled by expert person. Method: It is assumed that the repair needs no modification once served. Availability, Mean-time for system failure, and profits are analyzed by utilizing the Regenerative point graphical technique and semi-Markov process. Result: Study reveals that the Mean-time for system failure of the system model go on decreasing as failure rate increase and availability goes on decreasing as failure-rate increase. Moreover, the study shows that the systems profit goes down on increase of Failure-rate. Conclusion: Findings of the study supports the hypothesis that the limits of failure/repair/inspection rate will surely have effective profitability. Moreover, it is found that the utility of scale of operation can easily be derived. The practical importance of biomass briquettes for burning coal or wood is very well appreciated.

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