International Journal of Operational Research, 2021
The paper deals with the availability analysis of a series-parallel system consisting of four sub... more The paper deals with the availability analysis of a series-parallel system consisting of four subsystems: A11, B, C and A12. Subsystem B contains units' b11 and b12 arranged in active parallel, subsystem C contains units' c11 and g12 arranged in active parallel. The system is exposed to two types of failure. Type I failure is a unit failure called partial failure where the failed unit is replaced with new and identical one while type II is a common cause failure to either subsystem B or C in which the failed subsystem is replaced with new one. Two probabilistic models are discussed. In model I (system without common cause failure), the system has type I failure while in model II (system with common cause failure) the system has both type I and II failure. In both models, the system has three modes: full capacity, reduced capacity and failure mode. Failure and replacement rate were assumed to be exponentially distributed. Through the transition diagram, system of first order linear differential equations were developed and solved to obtain the explicit expressions for steady-state availability. At last, some numerical examples have been taken to clarify the results.
International Journal of Quality & Reliability Management, 2021
PurposeThis paper analyzed a complex system consisting n-identical units under a k-out-of-n: G; c... more PurposeThis paper analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The computed results are more supportable for repairable system performability analysis.Design/methodology/approachIn this paper, the authors have analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The supplementary variable technique has employed for analyzing the performance of the system.FindingsReliability measures have been computed for different types of configuration. It generalized the results for purely series and purely parallel configurations.Research limitations/implicationsThis research may be beneficial for industrial system performances whereas a k-out-of-n-type configuration exists.Practical implicationsNot sure as it is a theoretical assessment.Social implicationsThis research may n...
International Journal of Quality & Reliability Management, 2021
PurposeThe purpose of this paper is to model and to improve the stability and long-lasting operat... more PurposeThe purpose of this paper is to model and to improve the stability and long-lasting operation of the small home solar system configuration regarding the reliability, availability, sensitivity, cost analysis and mean time to failure (MTTF).Design/methodology/approachA model of a small home solar system is designed in this write up. It is designed in a series–parallel configuration, such that four panels are arranged in parallel, working under 1-out-of-4: G; policy and two batteries configured in parallel also, working under 1-out-of-2: G; policy. The panels are connected to a charge controller, then to the batteries and lastly to an inverter, all connected together in series configuration. Different types of system reliability such as reliability, sensitivity, availability, MTTF and cost analysis for particular values of the failure and repair rates have been evaluated by using a supplementary variable and Laplace transforms and demonstrated the computed results on tables and ...
Life Cycle Reliability and Safety Engineering, 2020
This paper deals with the reliability modelling and performance evaluation of three configuration... more This paper deals with the reliability modelling and performance evaluation of three configurations arranged in series–parallel. Configuration I consist of six units in which four are on operational while two are on standby. Configuration II consist of seven units with three of the units are on standby while the remaining four are on operation. Configuration III comprises of two subsystems C and D with three unit in each subsystem with a unit on standby. Units in each configuration provide 25 MW. The failure and repair times are assumed to be exponentially distributed. Through the transition diagram, system of first-order linear differential difference equations are derived for each configuration and are used to obtain the corresponding explicit expressions of system availability and mean time to failure. Cost–benefit analysis is examined and compared among the configuration through numerical examples to determine the optimal configuration and it was found to be configuration I. This study is important to system designers and developers, maintenance personnel, engineers and plant management in the suitable in designing and analysis of maintenance policy and processes and also the assessment of performance and the safety of the systems in general during and after the burn-in period.
Life Cycle Reliability and Safety Engineering, 2021
The present paper deals with the reliability analysis of a computer network system as series para... more The present paper deals with the reliability analysis of a computer network system as series parallel system consisting of two subsystems. Subsystem I consist of four homogeneous clients while subsystem II consist of two homogeneous servers. Both clients and servers have exponential failure whereas repairs follow two types of distributions that are general and Gumbel–Hougaard family copula. The network under consideration has three states: normal, partial failure state and complete failure state. From the transition diagram, the system of first-order partial differential equations is derived and solved using a supplementary variable technique and Laplace transforms. The system is analyzed using Laplace transforms to solve the mathematical equations. The results obtained are presented in tables and graphs. Some important measures of reliability such as availability of system, reliability of the system, MTTF, sensitivity and cost analysis have been discussed. Some particular cases have also been derived and examined to see the practical effect of the model.
Life Cycle Reliability and Safety Engineering, 2019
This paper deals with the reliability modelling and evaluation of a linear consecutive 2-out-of-4... more This paper deals with the reliability modelling and evaluation of a linear consecutive 2-out-of-4 system under online and offline preventive maintenance. The failure and repair time are assumed exponentially distributed. Through the transition diagrams, a system of first-order linear differential difference equations is obtained. Explicit expressions of system availability, mean time to failure busy period of repairman and profit function using probabilistic approach have been developed. Impacts of online preventive maintenance, offline preventive maintenance, and failure and repair rate on system availability, profit and mean time to failure have been investigated. The results of this paper will enhance the system performance and will be useful for timely execution of proper maintenance improvement, decision, planning and optimisation.
We proposed a matrix-free direction with an inexact line search technique to solve system of nonl... more We proposed a matrix-free direction with an inexact line search technique to solve system of nonlinear equations by using double direction approach. In this article, we approximated the Jacobian matrix by appropriately constructed matrix-free method via acceleration parameter. The global convergence of our method is established under mild conditions. Numerical comparisons reported in this paper are based on a set of large-scale test problems and show that the proposed method is efficient for large-scale problems.
ABSTRACT In this paper, three probabilistic models for a redundant system with three identical un... more ABSTRACT In this paper, three probabilistic models for a redundant system with three identical units have been developed to analyze and compare some reliability characteristics. Model II and model III are special cases of model I. In each model, the system is under three types of failures and attended by one repairman. Model I is under preventive maintenance before failure, while model II and III are analyzed without preventive maintenance, and in addition model III is viewed as linear consecutive 2-out-of-3. The objective is to see the effect of preventive maintenance and system design of 2-out-of-3. Mean time to system failure, availability, busy period and profit function for the three models are analyzed using Kolmogorov’s forward equations method. Furthermore, we compare these reliability characteristics for the three models and found that model I is more reliable and efficient than the remaining models.
The determination of this paper is to study reliability measures and routine analysis of computer... more The determination of this paper is to study reliability measures and routine analysis of computer network, which is a combination of four subsystems A, B, C and D and all the subsystem connected in series parallel pattern, the subsystem A is client, the subsystem B is load balancer and subsystem C is servers which is divided in to two subsystem (i.e. subsystem C1 and subsystem C2) and C1andC2 served as computer servers together with two unit each and working 1-out-of-2: G policy, and subsystem D is centralized server. The system has two types of failure, degraded and complete failure. The system can completely fail due to failure of one of the following subsystems A, B, C and D. The system is at partial failed state if at least one unit is working in either subsystem C1 or subsystem C2.The system is examined using supplementary variables techniques and Laplace transform. General distribution and copula family are employed to restore degraded and complete failed state respectively. C...
In this paper, we study some reliability characteristics of a repairable linear consecutive 2-out... more 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.
The paper presents the explicit expressions for measuring reliability parameter of systems, Grap... more The paper presents the explicit expressions for measuring reliability parameter of systems, Graphs were plotted to highlight important results. Results have shown that measures of system effectiveness such MTSF, system availability and profit increases with repair rates and decreases with failure rates.The developed model helps in determining the optimal maintenance strategies which ensure the maximum overall availability of the system. The optimum values of failure and repair rates for each subsystem were given. It is observed that the first subsystem is having the maximum availability with (97%). The optimum values of failure and repair rates for maximum availability level for each subsystem is also shown. Keywords : Mean time to system failure, Availability, Reliability, Maintenance and Subsystem.
International Journal of Applied Mathematical Research, 2017
The paper deals with modeling and performance evaluation of a series-parallel system using Markov... more The paper deals with modeling and performance evaluation of a series-parallel system using Markov Birth-Death process and probabilistic approach. The system consists of four subsystems arranged in series-parallel with three possible states, working with full capacity, reduced capacity and failed. Through the transition diagrams, systems of differential equations are developed and solved recursively via probabilistic approach. Explicit expressions for steady-state availability are de-rived. Availability matrices for each subsystem have been developed to provide various performance values for different combinations of failure and repair rates of all subsystems. The results from this paper will enhance the system performance and useful for timely execution of proper maintenance improvement, decision, planning and optimization.
International Journal of Operational Research, 2021
The paper deals with the availability analysis of a series-parallel system consisting of four sub... more The paper deals with the availability analysis of a series-parallel system consisting of four subsystems: A11, B, C and A12. Subsystem B contains units' b11 and b12 arranged in active parallel, subsystem C contains units' c11 and g12 arranged in active parallel. The system is exposed to two types of failure. Type I failure is a unit failure called partial failure where the failed unit is replaced with new and identical one while type II is a common cause failure to either subsystem B or C in which the failed subsystem is replaced with new one. Two probabilistic models are discussed. In model I (system without common cause failure), the system has type I failure while in model II (system with common cause failure) the system has both type I and II failure. In both models, the system has three modes: full capacity, reduced capacity and failure mode. Failure and replacement rate were assumed to be exponentially distributed. Through the transition diagram, system of first order linear differential equations were developed and solved to obtain the explicit expressions for steady-state availability. At last, some numerical examples have been taken to clarify the results.
International Journal of Quality & Reliability Management, 2021
PurposeThis paper analyzed a complex system consisting n-identical units under a k-out-of-n: G; c... more PurposeThis paper analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The computed results are more supportable for repairable system performability analysis.Design/methodology/approachIn this paper, the authors have analyzed a complex system consisting n-identical units under a k-out-of-n: G; configuration via a new method which has not been studied by previous researchers. The supplementary variable technique has employed for analyzing the performance of the system.FindingsReliability measures have been computed for different types of configuration. It generalized the results for purely series and purely parallel configurations.Research limitations/implicationsThis research may be beneficial for industrial system performances whereas a k-out-of-n-type configuration exists.Practical implicationsNot sure as it is a theoretical assessment.Social implicationsThis research may n...
International Journal of Quality & Reliability Management, 2021
PurposeThe purpose of this paper is to model and to improve the stability and long-lasting operat... more PurposeThe purpose of this paper is to model and to improve the stability and long-lasting operation of the small home solar system configuration regarding the reliability, availability, sensitivity, cost analysis and mean time to failure (MTTF).Design/methodology/approachA model of a small home solar system is designed in this write up. It is designed in a series–parallel configuration, such that four panels are arranged in parallel, working under 1-out-of-4: G; policy and two batteries configured in parallel also, working under 1-out-of-2: G; policy. The panels are connected to a charge controller, then to the batteries and lastly to an inverter, all connected together in series configuration. Different types of system reliability such as reliability, sensitivity, availability, MTTF and cost analysis for particular values of the failure and repair rates have been evaluated by using a supplementary variable and Laplace transforms and demonstrated the computed results on tables and ...
Life Cycle Reliability and Safety Engineering, 2020
This paper deals with the reliability modelling and performance evaluation of three configuration... more This paper deals with the reliability modelling and performance evaluation of three configurations arranged in series–parallel. Configuration I consist of six units in which four are on operational while two are on standby. Configuration II consist of seven units with three of the units are on standby while the remaining four are on operation. Configuration III comprises of two subsystems C and D with three unit in each subsystem with a unit on standby. Units in each configuration provide 25 MW. The failure and repair times are assumed to be exponentially distributed. Through the transition diagram, system of first-order linear differential difference equations are derived for each configuration and are used to obtain the corresponding explicit expressions of system availability and mean time to failure. Cost–benefit analysis is examined and compared among the configuration through numerical examples to determine the optimal configuration and it was found to be configuration I. This study is important to system designers and developers, maintenance personnel, engineers and plant management in the suitable in designing and analysis of maintenance policy and processes and also the assessment of performance and the safety of the systems in general during and after the burn-in period.
Life Cycle Reliability and Safety Engineering, 2021
The present paper deals with the reliability analysis of a computer network system as series para... more The present paper deals with the reliability analysis of a computer network system as series parallel system consisting of two subsystems. Subsystem I consist of four homogeneous clients while subsystem II consist of two homogeneous servers. Both clients and servers have exponential failure whereas repairs follow two types of distributions that are general and Gumbel–Hougaard family copula. The network under consideration has three states: normal, partial failure state and complete failure state. From the transition diagram, the system of first-order partial differential equations is derived and solved using a supplementary variable technique and Laplace transforms. The system is analyzed using Laplace transforms to solve the mathematical equations. The results obtained are presented in tables and graphs. Some important measures of reliability such as availability of system, reliability of the system, MTTF, sensitivity and cost analysis have been discussed. Some particular cases have also been derived and examined to see the practical effect of the model.
Life Cycle Reliability and Safety Engineering, 2019
This paper deals with the reliability modelling and evaluation of a linear consecutive 2-out-of-4... more This paper deals with the reliability modelling and evaluation of a linear consecutive 2-out-of-4 system under online and offline preventive maintenance. The failure and repair time are assumed exponentially distributed. Through the transition diagrams, a system of first-order linear differential difference equations is obtained. Explicit expressions of system availability, mean time to failure busy period of repairman and profit function using probabilistic approach have been developed. Impacts of online preventive maintenance, offline preventive maintenance, and failure and repair rate on system availability, profit and mean time to failure have been investigated. The results of this paper will enhance the system performance and will be useful for timely execution of proper maintenance improvement, decision, planning and optimisation.
We proposed a matrix-free direction with an inexact line search technique to solve system of nonl... more We proposed a matrix-free direction with an inexact line search technique to solve system of nonlinear equations by using double direction approach. In this article, we approximated the Jacobian matrix by appropriately constructed matrix-free method via acceleration parameter. The global convergence of our method is established under mild conditions. Numerical comparisons reported in this paper are based on a set of large-scale test problems and show that the proposed method is efficient for large-scale problems.
ABSTRACT In this paper, three probabilistic models for a redundant system with three identical un... more ABSTRACT In this paper, three probabilistic models for a redundant system with three identical units have been developed to analyze and compare some reliability characteristics. Model II and model III are special cases of model I. In each model, the system is under three types of failures and attended by one repairman. Model I is under preventive maintenance before failure, while model II and III are analyzed without preventive maintenance, and in addition model III is viewed as linear consecutive 2-out-of-3. The objective is to see the effect of preventive maintenance and system design of 2-out-of-3. Mean time to system failure, availability, busy period and profit function for the three models are analyzed using Kolmogorov’s forward equations method. Furthermore, we compare these reliability characteristics for the three models and found that model I is more reliable and efficient than the remaining models.
The determination of this paper is to study reliability measures and routine analysis of computer... more The determination of this paper is to study reliability measures and routine analysis of computer network, which is a combination of four subsystems A, B, C and D and all the subsystem connected in series parallel pattern, the subsystem A is client, the subsystem B is load balancer and subsystem C is servers which is divided in to two subsystem (i.e. subsystem C1 and subsystem C2) and C1andC2 served as computer servers together with two unit each and working 1-out-of-2: G policy, and subsystem D is centralized server. The system has two types of failure, degraded and complete failure. The system can completely fail due to failure of one of the following subsystems A, B, C and D. The system is at partial failed state if at least one unit is working in either subsystem C1 or subsystem C2.The system is examined using supplementary variables techniques and Laplace transform. General distribution and copula family are employed to restore degraded and complete failed state respectively. C...
In this paper, we study some reliability characteristics of a repairable linear consecutive 2-out... more 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.
The paper presents the explicit expressions for measuring reliability parameter of systems, Grap... more The paper presents the explicit expressions for measuring reliability parameter of systems, Graphs were plotted to highlight important results. Results have shown that measures of system effectiveness such MTSF, system availability and profit increases with repair rates and decreases with failure rates.The developed model helps in determining the optimal maintenance strategies which ensure the maximum overall availability of the system. The optimum values of failure and repair rates for each subsystem were given. It is observed that the first subsystem is having the maximum availability with (97%). The optimum values of failure and repair rates for maximum availability level for each subsystem is also shown. Keywords : Mean time to system failure, Availability, Reliability, Maintenance and Subsystem.
International Journal of Applied Mathematical Research, 2017
The paper deals with modeling and performance evaluation of a series-parallel system using Markov... more The paper deals with modeling and performance evaluation of a series-parallel system using Markov Birth-Death process and probabilistic approach. The system consists of four subsystems arranged in series-parallel with three possible states, working with full capacity, reduced capacity and failed. Through the transition diagrams, systems of differential equations are developed and solved recursively via probabilistic approach. Explicit expressions for steady-state availability are de-rived. Availability matrices for each subsystem have been developed to provide various performance values for different combinations of failure and repair rates of all subsystems. The results from this paper will enhance the system performance and useful for timely execution of proper maintenance improvement, decision, planning and optimization.
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