International Journal of Reliability, Risk and Safety: Theory and Application
The recursive approach for assessing the reliability, availability, maintainability, and dependab... more The recursive approach for assessing the reliability, availability, maintainability, and dependability (RAMD) of five subsystems in a reverse osmosis (RO) machine was investigated in this study. The components include the raw water tank, precision filter, carbonated filter, reverse osmosis membrane, and water producing tank. Furthermore, the efficacy of a reverse osmosis (RO) unit, mean time to failure (MTTF), mean time to repair (MTTR), and dependability ratio were also assessed. The major aim is to maximize efficiency and identify the critical subsystem or component of the reverse osmosis machine. And finding out how to fix the problem. We utilized data from the RO unit with a repair rate and a failure rate over a 100-day period to validate the technique. There were numerical numbers for each subsystem's dependability, as well as comparisons between subsystem dependability and total system dependability.
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.
Life Cycle Reliability and Safety Engineering, 2019
Series system is having the shortest optimal replacement time among the other systems. And someti... more Series system is having the shortest optimal replacement time among the other systems. And sometimes, the components (similar or non-similar) that formed the series system may have different failure rates due to some factors. In this paper, we considered a series system with six components, such that, all the six components are subjected to two types of failures, which are type I and type II failures. Therefore, we can say the system is also subjected to two types of failures (type I and type II). If the system fails due to type I, the system is minimal repair. But if the system fails due to type II, the system is replaced completely with a new one. We developed a discounted age replacement models with minimal repair for a series system. Two discounted age replacement model with minimal repair based on two decisions are proposed in the study. Finally, some numerical examples are given to obtain the optimal replacement times for the series system from the three replacement models constructed.
International Journal of Mechanisms and Robotic Systems, 2018
This paper deals with evaluation of cost of four dissimilar configurations with mixed standby uni... more This paper deals with evaluation of cost of four dissimilar configurations with mixed standby units. The standby units exist as warm and cold standby. It is assumed that failure and repair time of all units are assumed to be exponentially distributed. Explicit expressions for busy period of repairmen, steady-state availability and profit function are derived using linear first order differential equations. Several cases are analysed graphically to investigate the effects of various system parameters on profit. The paper also presents graphical comparison for specific values of system parameters and finds that the optimal system configuration is configuration I.
Journal of Mathematical and Computational Science, Feb 3, 2013
In this paper, two different systems both are requiring a supporting unit for their operation are... more In this paper, two different systems both are requiring a supporting unit for their operation are studied. The first system consist of 3-out-of-4 subsystem requiring its support from 2-out-of-4 subsystem for its operation while the other system is two unit cold standby system where each unit is attached to its supporting unit for its operation. Each system is attended by two repairmen, one repairing the main unit and the other repairing the supporting unit. Explicit expressions for mean time to system failure (MTSF) and steady-state availability are developed. We analyzed the system by using linear differential equations. Effect of failure and repair rates on mean time to system failure and steady-state availability have also been discussed graphically. Comparisons are made graphically for specific values of parameters. Furthermore, we compare these reliability characteristics for the two models and found that model I is more reliable and efficient than the remaining models.
Journal of Mathematical and Computational Science, Feb 3, 2013
Most of the researches done on repairable systems assumed that when the system failed, it is repa... more Most of the researches done on repairable systems assumed that when the system failed, it is repaired by repairman or repairmen. Little literature is found in the use of repair machines to repair the failed unit. In this study, stochastic analysis of a repairable 2-out-of-4 system is presented. The system comprises of two subsystems A and B arranged in series. Subsystems A and B are two units warm standby. The system is attended by two repair machines assigned to each subsystem to repair any failed unit. Explicit expressions for mean time to system failure (MTSF), the steady-state availability, busy period of repair machines, and profit function of the system are analyzed stochastically using Kolmogorov's forward equation method. Analytical and numerical results giving some particular values to the costs and other parameters have been obtained.
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 Mathematics in Operational Research, 2015
Many engineering systems are subjected to deterioration, meaning that during the course of time t... more Many engineering systems are subjected to deterioration, meaning that during the course of time their conditions fall to failure levels. Such systems and their components are either repaired at failure or replaced before or after failure. However not every deterioration can bring about sudden failure of the system. Some deterioration can slightly reduce the strength of the system until at some point failure occurs. Such deterioration is said to be minor deterioration. This paper deals with the modelling and evaluation of availability of a system subjected to minor deterioration under imperfect repair. In this paper, we developed the explicit expression of system availability using probabilistic approach and determine the effect of failure, repair rate and number of states on system availability. The optimal availability level the system can attain is also determined. The results of this paper will enhance the system performance and useful for timely execution of proper maintenance improvement, decision, planning and optimisation.
Journal of Industrial Engineering International, 2014
The importance in promoting, sustaining industries, manufacturing systems and economy through rel... more The importance in promoting, sustaining industries, manufacturing systems and economy through reliability measurement has become an area of interest. The profit of a system may be enhanced using highly reliable structural design of the system or subsystem of higher reliability. On improving the reliability and availability of a system, the production and associated profit will also increase. Reliability, availability and profit are some of the most important factors in any successful industry and manufacturing settings. In this paper, we compare three different repairable redundant systems using an external supporting device for operation based on the profit. Explicit expressions for the busy period of repairmen, steady-state availability and profit function are derived using linear first-order differential equations. Furthermore, we compare the profit for the three systems and find that system I is more profitable than systems II and III.
In this paper, we study the reliability and availability characteristics of a repairable 2-out-of... more In this paper, we study the reliability and availability characteristics of a repairable 2-out-of-3 system. 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, busy period and profit function are derived using Kolmogorov's forward equations method. Various cases are analyzed graphically to investigate the impact of system parameters on MTSF, availability, busy period and profit function.
In this paper, probabilistic models for three redundant configurations have been developed to ana... more In this paper, probabilistic models for three redundant configurations have been developed to analyze and compare some reliability characteristics. Each system is connected to a repairable supporting external device for operation. Repairable service station is provided for immediate repair of failed unit. Explicit expressions for mean time to system failure and steady-state availability for the three configurations are developed. Furthermore, we compare the three configurations based on their reliability characteristics and found that configuration II is more reliable and efficient than the remaining configurations.
Most of the researches on profit and cost evaluation of redundant system focus on the effect of f... more Most of the researches on profit and cost evaluation of redundant system focus on the effect of failure and repair on revenue generated. However, as these systems continue to work, their strength gradually deteriorates. Where such deterioration occurs, minor and major maintenance is employed to remedy the deterioration. Little or no attention is paid on the effect of deterioration on the impact of deterioration and their maintenance on the revenue generated. In this paper, we study the profit generated of two-stage deteriorating linear consecutive 2-out-of-3 system. Failure, repair and deterioration time are assumed exponential. The explicit expressions of availability, busy period of a repairman and profit function are derived using Kolmogorov's forward equations method. Various cases are analyzed graphically to investigate the effect of deterioration parameters such as slow deterioration, fast deterioration, and their maintenance such as minor and major minimal maintenance on profit generated.
International Journal of Reliability, Risk and Safety: Theory and Application
The recursive approach for assessing the reliability, availability, maintainability, and dependab... more The recursive approach for assessing the reliability, availability, maintainability, and dependability (RAMD) of five subsystems in a reverse osmosis (RO) machine was investigated in this study. The components include the raw water tank, precision filter, carbonated filter, reverse osmosis membrane, and water producing tank. Furthermore, the efficacy of a reverse osmosis (RO) unit, mean time to failure (MTTF), mean time to repair (MTTR), and dependability ratio were also assessed. The major aim is to maximize efficiency and identify the critical subsystem or component of the reverse osmosis machine. And finding out how to fix the problem. We utilized data from the RO unit with a repair rate and a failure rate over a 100-day period to validate the technique. There were numerical numbers for each subsystem's dependability, as well as comparisons between subsystem dependability and total system dependability.
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.
Life Cycle Reliability and Safety Engineering, 2019
Series system is having the shortest optimal replacement time among the other systems. And someti... more Series system is having the shortest optimal replacement time among the other systems. And sometimes, the components (similar or non-similar) that formed the series system may have different failure rates due to some factors. In this paper, we considered a series system with six components, such that, all the six components are subjected to two types of failures, which are type I and type II failures. Therefore, we can say the system is also subjected to two types of failures (type I and type II). If the system fails due to type I, the system is minimal repair. But if the system fails due to type II, the system is replaced completely with a new one. We developed a discounted age replacement models with minimal repair for a series system. Two discounted age replacement model with minimal repair based on two decisions are proposed in the study. Finally, some numerical examples are given to obtain the optimal replacement times for the series system from the three replacement models constructed.
International Journal of Mechanisms and Robotic Systems, 2018
This paper deals with evaluation of cost of four dissimilar configurations with mixed standby uni... more This paper deals with evaluation of cost of four dissimilar configurations with mixed standby units. The standby units exist as warm and cold standby. It is assumed that failure and repair time of all units are assumed to be exponentially distributed. Explicit expressions for busy period of repairmen, steady-state availability and profit function are derived using linear first order differential equations. Several cases are analysed graphically to investigate the effects of various system parameters on profit. The paper also presents graphical comparison for specific values of system parameters and finds that the optimal system configuration is configuration I.
Journal of Mathematical and Computational Science, Feb 3, 2013
In this paper, two different systems both are requiring a supporting unit for their operation are... more In this paper, two different systems both are requiring a supporting unit for their operation are studied. The first system consist of 3-out-of-4 subsystem requiring its support from 2-out-of-4 subsystem for its operation while the other system is two unit cold standby system where each unit is attached to its supporting unit for its operation. Each system is attended by two repairmen, one repairing the main unit and the other repairing the supporting unit. Explicit expressions for mean time to system failure (MTSF) and steady-state availability are developed. We analyzed the system by using linear differential equations. Effect of failure and repair rates on mean time to system failure and steady-state availability have also been discussed graphically. Comparisons are made graphically for specific values of parameters. Furthermore, we compare these reliability characteristics for the two models and found that model I is more reliable and efficient than the remaining models.
Journal of Mathematical and Computational Science, Feb 3, 2013
Most of the researches done on repairable systems assumed that when the system failed, it is repa... more Most of the researches done on repairable systems assumed that when the system failed, it is repaired by repairman or repairmen. Little literature is found in the use of repair machines to repair the failed unit. In this study, stochastic analysis of a repairable 2-out-of-4 system is presented. The system comprises of two subsystems A and B arranged in series. Subsystems A and B are two units warm standby. The system is attended by two repair machines assigned to each subsystem to repair any failed unit. Explicit expressions for mean time to system failure (MTSF), the steady-state availability, busy period of repair machines, and profit function of the system are analyzed stochastically using Kolmogorov's forward equation method. Analytical and numerical results giving some particular values to the costs and other parameters have been obtained.
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 Mathematics in Operational Research, 2015
Many engineering systems are subjected to deterioration, meaning that during the course of time t... more Many engineering systems are subjected to deterioration, meaning that during the course of time their conditions fall to failure levels. Such systems and their components are either repaired at failure or replaced before or after failure. However not every deterioration can bring about sudden failure of the system. Some deterioration can slightly reduce the strength of the system until at some point failure occurs. Such deterioration is said to be minor deterioration. This paper deals with the modelling and evaluation of availability of a system subjected to minor deterioration under imperfect repair. In this paper, we developed the explicit expression of system availability using probabilistic approach and determine the effect of failure, repair rate and number of states on system availability. The optimal availability level the system can attain is also determined. The results of this paper will enhance the system performance and useful for timely execution of proper maintenance improvement, decision, planning and optimisation.
Journal of Industrial Engineering International, 2014
The importance in promoting, sustaining industries, manufacturing systems and economy through rel... more The importance in promoting, sustaining industries, manufacturing systems and economy through reliability measurement has become an area of interest. The profit of a system may be enhanced using highly reliable structural design of the system or subsystem of higher reliability. On improving the reliability and availability of a system, the production and associated profit will also increase. Reliability, availability and profit are some of the most important factors in any successful industry and manufacturing settings. In this paper, we compare three different repairable redundant systems using an external supporting device for operation based on the profit. Explicit expressions for the busy period of repairmen, steady-state availability and profit function are derived using linear first-order differential equations. Furthermore, we compare the profit for the three systems and find that system I is more profitable than systems II and III.
In this paper, we study the reliability and availability characteristics of a repairable 2-out-of... more In this paper, we study the reliability and availability characteristics of a repairable 2-out-of-3 system. 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, busy period and profit function are derived using Kolmogorov's forward equations method. Various cases are analyzed graphically to investigate the impact of system parameters on MTSF, availability, busy period and profit function.
In this paper, probabilistic models for three redundant configurations have been developed to ana... more In this paper, probabilistic models for three redundant configurations have been developed to analyze and compare some reliability characteristics. Each system is connected to a repairable supporting external device for operation. Repairable service station is provided for immediate repair of failed unit. Explicit expressions for mean time to system failure and steady-state availability for the three configurations are developed. Furthermore, we compare the three configurations based on their reliability characteristics and found that configuration II is more reliable and efficient than the remaining configurations.
Most of the researches on profit and cost evaluation of redundant system focus on the effect of f... more Most of the researches on profit and cost evaluation of redundant system focus on the effect of failure and repair on revenue generated. However, as these systems continue to work, their strength gradually deteriorates. Where such deterioration occurs, minor and major maintenance is employed to remedy the deterioration. Little or no attention is paid on the effect of deterioration on the impact of deterioration and their maintenance on the revenue generated. In this paper, we study the profit generated of two-stage deteriorating linear consecutive 2-out-of-3 system. Failure, repair and deterioration time are assumed exponential. The explicit expressions of availability, busy period of a repairman and profit function are derived using Kolmogorov's forward equations method. Various cases are analyzed graphically to investigate the effect of deterioration parameters such as slow deterioration, fast deterioration, and their maintenance such as minor and major minimal maintenance on profit generated.
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Papers by Ibrahim Yusuf