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...
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.
Journal of Mathematical and Computational Science, Feb 15, 2014
Studies on reliability characteristics of a redundant repairable warm standby system involving co... more Studies on reliability characteristics of a redundant repairable warm standby system involving common cause failure are numerous. Little attention is paid on the effect of common cause failure, individual unit failure and repair rates on mean time to system failure and which among the common cause failure and individual unit failure will reduce the life span of the system than the other. In the present paper, we developed the explicit the expression for mean time to system failure (MTSF) for 3-out-of-5 warm standby system using kolmogorov’s forward equations method and perform graphical analysis to see the behavior of common cause failure, individual unit failure and repair rates on mean time to system failure. The results have indicated that common cause failure decreases the life span (MTSF) earlier than the individual unit failure rates. The developed model helps in determining the maintenance policy, which will ensure the maximum overall mean time to system failure (MTSF) of the system.
In this paper, we study the reliability and availability characteristics of two-stage deteriorati... more In this paper, we study the reliability and availability characteristics of two-stage deterioration reinforce concrete structure .Failure and repair times are assumed exponential. The explicit expressions of reliability and availability characteristics such as mean time to system failure (MTSF), steady-state availability and busy period are derived using Kolmogorov forward equations method. Various cases are analyzed graphically to investigate the impact of system parameters on MTSF, availability and busy period
In this paper stochastic models for identical two unit parallel system are developed in which the... more In this paper stochastic models for identical two unit parallel system are developed in which the system is subjected to two types of failure. In the model I, the proposed system works in three modes: normal, deterioration and failure. In the deterioration mode, the system can be in slow, mild or fast deterioration. Model II is a special case of Model I in which the system works in two modes: normal and failure no deterioration is allowed. The two models are developed using linear differential equations. Graphs are plotted to highlight the effect of deterioration, the behavior of mean time to system failure (MTSF) and availability. The results indicate that MTSF and availability of the system exposes to various degree of deterioration decreases more that the system without deterioration.
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...
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.
Journal of Mathematical and Computational Science, Feb 15, 2014
Studies on reliability characteristics of a redundant repairable warm standby system involving co... more Studies on reliability characteristics of a redundant repairable warm standby system involving common cause failure are numerous. Little attention is paid on the effect of common cause failure, individual unit failure and repair rates on mean time to system failure and which among the common cause failure and individual unit failure will reduce the life span of the system than the other. In the present paper, we developed the explicit the expression for mean time to system failure (MTSF) for 3-out-of-5 warm standby system using kolmogorov’s forward equations method and perform graphical analysis to see the behavior of common cause failure, individual unit failure and repair rates on mean time to system failure. The results have indicated that common cause failure decreases the life span (MTSF) earlier than the individual unit failure rates. The developed model helps in determining the maintenance policy, which will ensure the maximum overall mean time to system failure (MTSF) of the system.
In this paper, we study the reliability and availability characteristics of two-stage deteriorati... more In this paper, we study the reliability and availability characteristics of two-stage deterioration reinforce concrete structure .Failure and repair times are assumed exponential. The explicit expressions of reliability and availability characteristics such as mean time to system failure (MTSF), steady-state availability and busy period are derived using Kolmogorov forward equations method. Various cases are analyzed graphically to investigate the impact of system parameters on MTSF, availability and busy period
In this paper stochastic models for identical two unit parallel system are developed in which the... more In this paper stochastic models for identical two unit parallel system are developed in which the system is subjected to two types of failure. In the model I, the proposed system works in three modes: normal, deterioration and failure. In the deterioration mode, the system can be in slow, mild or fast deterioration. Model II is a special case of Model I in which the system works in two modes: normal and failure no deterioration is allowed. The two models are developed using linear differential equations. Graphs are plotted to highlight the effect of deterioration, the behavior of mean time to system failure (MTSF) and availability. The results indicate that MTSF and availability of the system exposes to various degree of deterioration decreases more that the system without deterioration.
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Papers by Ibrahim Yusuf