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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 Applied Mathematical Research
Availability evaluation of repairable system requiring two types of supporting device for operations2017 •
With advancement of modern science and technology, complex systems connected to an external supporting device for their operations have been manufactured to meet the demand of industries, economic growth and populace in general. Companies and organizations heavily rely on these systems to conduct their business. This study presents the availability assessment of a single unit system connected to two types of an external supporting device for its operation. Each type of supporting device has two copies I and II. First order differential equations method is used to obtain the explicit expression for the steady-state availability. Based on assumed numerical values given to system parameters, graphical illustrations are given to highlight important results. Comparisons are performed to highlight the impact of unit failure and repair rates.
This paper presents a Markov model of a computer networking system. It consists of four subsystems: z client, router, load balancer, and two distributed data based servers. They are arranged in a series-parallel configuration and integrated with a switch. The paper research objectives include evaluating the system for various dependability metrics and to see the effect of the repairs. Unit failure is presumed to be continuous and follows exponential distribution, and two repairs are available: general repair addresses partially failed states while copula repair addresses the system failure. The derived equations are studied utilising supplementary variables techniques and Laplace conversion procedures in order to obtain dependability metrics expressions such as reliability, availability, MTTF, sensitivity, and costs. The results were justified using numerical examples and presented in Tables and Figures. It was observed that copula repair produces better outcomes than general repair and therefore recommended for optimal performance of the system.
2019 •
This paper deals with the reliability analysis of a complex system consisting of a two dissimilar unit' in a parallel configuration with correlated lifetime distribution. The system stops functioning when both units stop working. Both units are inspected periodically as well as being examined before assigning to repair facility. Under consideration of the system have two states: Normal and failed. Regenerative point technique has been used for the mathematical formulation of the model. The system is analyzed using Laplace transforms to solve the mathematical equations. Reliability, Availability, MTSF, Busy Period of repairmen and Cost-effectiveness of the system has been computed. The computed results have been demonstrated by tables and graphs. The repair time of both the units follows the negative exponential distribution with different parameters in a joint probability density function. The inspection times are assumed to follow the general distribution. Some particular cases of the system have also been derived from seeing the practical importance of the model.
Journal of Industrial Engineering International
Comparative analysis of profit between three dissimilar repairable redundant systems using supporting external device for operation2014 •
2020 •
Redundancy is commonly employed to improve system reliability. In most situations, components in the standby configurations are assumed statistically similar but independent. In many realistic models, all parts in standby are not treated as identical as they have different failure possibilities. The operational structure of the system has subsystem-1 with five identical components working under 2-out-of-5: G; policy, and the subsystem-2 has two units and functioning under 1-out-of-2: G; policy. Failure rates of units of subsystems are constant and assumed to follow an exponential distribution. Computed results give a new aspect to the scientific community to adopt multi-dimension repair in the form of the copula.
2017 •
The twenty first century is a century of technologies. Today, everyone has impact of these technologies, even industries, which are totally dependent on machines for their chores. Now, the great challenge for researchers/engineers is to produce highly reliable products at minimum cost. Thus, the fastest growing industries need to select highly reliable systems. The aim of present paper is to analyze the reliability and the behavior of mean time to system failure, availability, busy period and profit function with respect to systems parameters (failure rate, repair rate, service rate, etc). A tabular and graphical study also has been done to highlight the important results.
2020 •
Reliability is a performance factor applied to multi-computer network system consisting of devices such as active parallel or redundant hosts (clients), distributed database servers with replication, and a central server. For reliability evaluation and performance of such a system, this study analyzed a computer network system consisting of hosts (clients) connected to two distributed database servers in replication to each other. The system is configured as a series-parallel system consisting of two subsystems, namely A and B. Subsystem A consists of three clients in active parallel while subsystem B consists od two distributed database servers in replication to each order. Both clients and server failure and repair time are to be exponentially distributed The system is analyzed using first-order differential-difference equations to derive the expressions for the availability, mean time to failure, probability of a busy period of repairman due to partial or complete failure. The re...
International Journal of Mathematical, Engineering and Management Sciences
Effectiveness Analysis of a Two Non-Identical Unit Standby System with Switching Device and Proviso of Rest2019 •
This paper deals with two-unit cold standby system with switching device and proviso of rest. The system consists of two non-identical units which are connected in parallel redundancy. Initially, the first unit is in operative mode and second is kept in cold standby mode. There is also a proviso for rest for the first unit after a random time from its starting operation. For operation and repair, priority is always given to first unit. A switching device is used to shift the failed unit to repair mode. If the switching device is found non-operational then priority is given to it for repair provided that system is in functional mode. The effectiveness of the proposed system has been carried out by determining various reliability characteristics of the proposed model.
2021 •
This paper discusses the reliability analysis of repairable complex system comprising of two subsystems in series configuration together with the controllers. The two subsystems, consisting of three undistinguishable units in a parallel arrangement and functioning under 1-out-of-3: G operational policy. Controllers control both the subsystems and can be unstable, and the malfunction result in the controller prevents system operation. The system may have an unforeseeable catastrophic failure due to which the system may not perform its function once the situation arises. The failure rate of the units is constant, and the exponential distribution is assumed to obey. The two forms of repair namely general repair and Goumbel-Hougard copula repair are used to restore the existing failed units of the system. The supplementary variable technique with Laplace transformation is used to evaluate the output of the system. Using Stochastic theory, differential equations are derived to obtain ess...
Life Cycle Reliability and Safety Engineering
Stochastic analysis of a two units’ complex repairable system with switch and human failure using copula approach2019 •
Journal of Applied Mathematics and Physics
Reliability Modelling and Analysis of Redundant Systems Connected to Supporting External Device for Operation Attended by a Repairman and Repairable Service Station2014 •
International Journal of Mathematics in Operational Research
Availability analysis for repairable system with warm standby, switching failure and reboot delay2013 •
Cogent Engineering
An analysis to multi-state manufacturing system with common cause failure and waiting repair strategy2016 •
International Journal of Applied Mathematical Research
Availability comparison between three dissimi-lar photovoltaic configurationsSN Computer Science
Performance Analysis of Multi-computer System Consisting of Three Subsystems in Series Configuration Using Copula Repair Policy2020 •
American Journal of Operational Research
Evaluation Some Reliability Characteristics of a System under Three Types of Failures with Repair-Replacement at Failure2013 •
International Journal of Operational Research
Transient analysis of a machine repair system with standby, two modes of failure, discouragement and switching failure2014 •
International Journal of Engineering
Maintainability Policy for Deteriorating System with Inspection and Common Cause Failure2013 •
Life Cycle Reliability and Safety Engineering
Reliability analysis of repairable network system of three computer labs connected with a server under 2- out- of- 3 G configuration2020 •
International Journal of Advanced Statistics and Probability
Comparative analysis of some reliability characteristics between two dissimilar redundant systems with replacement at common cause failure2013 •
Mathematical Problems in Engineering
Availability and Reliability Analysis of a k-Out-of-n Warm Standby System with Common-Cause Failure and Fuzzy Failure and Repair Rates2022 •
Journal of Applied Sciences
Profit Analysis of a Serial-parallel System under Partial and Complete Failures2019 •
Applied Mathematics
Analysis of Stochastic Reliability Characteristics of a Repairable 2-out-of-3 System with Minimal Repair at Failure2013 •
American Journal of Applied Mathematics and Statistics
Availability and Profit Analysis of a linear Consecutive 2-out-of-4 Repairable System with Units Exchange2014 •
2017 •
American Journal of Computational and Applied Mathematics
Stochastic Modeling of Repairable Redundant System Comprising One Big Unit and Three Small Dissimilar Units2012 •
2013 •
Journal of Mathematics and Statistics
Evaluation of Reliability and Availability Characteristics of Two Different Systems by Using Linear First Order Differential Equations2005 •
Journal of Mathematical and Computational Science
Comparison of some reliability characteristics between redundant systems requiring supporting units for their operations2013 •
Journal of Reliability and Statistical Studies
Analysis of a Stochastic Model with Rework System2021 •
Journal of Mathematical and Computational Science
Reliability analysis of a complex repairable system in series configuration with switch and catastrophic failure using copula repair2021 •
International Journal of Engineering, Transactions B: Applications
Availability of k-out-of-n: F Secondary Subsystem with General Repair Time DistributionJournal of Applied Mathematics and Physics
Assessment of Profit of a Two-Stage Deteriorating Linear Consecutive 2-out-of-3 Repairable System2013 •
Journal of Industrial Engineering International
Comparison between four dissimilar solar panel configurations2017 •
Journal of Statistics Applications & Probability
Profit Evaluation of a Repairable System with Three-Stage Deterioration2016 •
International Journal of Mathematics in Operational Research
Threshold N-policy for (M, m) degraded machining system with K-heterogeneous servers, standby switching failure and multiple vacations2013 •
International Journal of Basic and Applied Sciences
Mean Time to System Failure and Availability Modeling of a Repairable non Identical Three Unit Warm Standby Redundant System2012 •
2021 •
International Journal of Applied Mathematical Research
Availability and Profit Analysis of 3-out-of-4 Repairable System with Preventive Maintenance2012 •
International Journal of Reliability and Safety
Performance assessment of repairable system in series configuration under different types of failure and repair policies using copula linguistics2018 •