Maintenance optimization of periodic replacement for mono-unit production system is a widely discussed topic.In practice,the replacement for a parallel production system with multi-unit served by one repairman is univ...Maintenance optimization of periodic replacement for mono-unit production system is a widely discussed topic.In practice,the replacement for a parallel production system with multi-unit served by one repairman is universal.The replacement action is often implemented in a maintenance window at random,although the replacement period appears as a quasi-periodic event.To optimize these maintenance policies,this study analyzes a bivariate quasi-periodic replacement policy (T,W) for a two-unit parallel production system with a maintenance window and one repairman.One unit of the system is replaced when either a failure occurs or a replacement plan comes in the maintenance window,whichever comes first.If one of the two units is in the replacement,the other may continue operating or waiting until the replacement is completed.An optimal replacement window [T*,T* + W*] can be obtained by jointly considering the system's long-running cost rate and the availability using the genetic algorithm.This study also introduces three examples of the production system with different types of units to illustrate the proposed policy.展开更多
A notable portion of cachelines in real-world workloads exhibits inner non-uniform access behaviors.However,modern cache management rarely considers this fine-grained feature,which impacts the effective cache capacity...A notable portion of cachelines in real-world workloads exhibits inner non-uniform access behaviors.However,modern cache management rarely considers this fine-grained feature,which impacts the effective cache capacity of contemporary high-performance spacecraft processors.To harness these non-uniform access behaviors,an efficient cache replacement framework featuring an auxiliary cache specifically designed to retain evicted hot data was proposed.This framework reconstructs the cache replacement policy,facilitating data migration between the main cache and the auxiliary cache.Unlike traditional cacheline-granularity policies,the approach excels at identifying and evicting infrequently used data,thereby optimizing cache utilization.The evaluation shows impressive performance improvement,especially on workloads with irregular access patterns.Benefiting from fine granularity,the proposal achieves superior storage efficiency compared with commonly used cache management schemes,providing a potential optimization opportunity for modern resource-constrained processors,such as spacecraft processors.Furthermore,the framework complements existing modern cache replacement policies and can be seamlessly integrated with minimal modifications,enhancing their overall efficacy.展开更多
To investigate the effects of various random factors on the preventive maintenance (PM) decision-making of one type of two-unit series system, an optimal quasi-periodic PM policy is introduced. Assume that PM is per...To investigate the effects of various random factors on the preventive maintenance (PM) decision-making of one type of two-unit series system, an optimal quasi-periodic PM policy is introduced. Assume that PM is perfect for unit 1 and only mechanical service for unit 2 in the model. PM activity is randomly performed according to a dynamic PM plan distributed in each implementation period. A replacement is determined based on the competing results of unplanned and planned replacements. The unplanned replacement is trigged by a catastrophic failure of unit 2, and the planned replacement is executed when the PM number reaches the threshold N. Through modeling and analysis, a solution algorithm for an optimal implementation period and the PM number is given, and optimal process and parametric sensitivity are provided by a numerical example. Results show that the implementation period should be decreased as soon as possible under the condition of meeting the needs of practice, which can increase mean operating time and decrease the long-run cost rate.展开更多
Named Data Networking(NDN)is one of the most excellent future Internet architectures and every router in NDN has the capacity of caching contents passing by.It greatly reduces network traffic and improves the speed of...Named Data Networking(NDN)is one of the most excellent future Internet architectures and every router in NDN has the capacity of caching contents passing by.It greatly reduces network traffic and improves the speed of content distribution and retrieval.In order to make full use of the limited caching space in routers,it is an urgent challenge to make an efficient cache replacement policy.However,the existing cache replacement policies only consider very few factors that affect the cache performance.In this paper,we present a cache replacement policy based on multi-factors for NDN(CRPM),in which the content with the least cache value is evicted from the caching space.CRPM fully analyzes multi-factors that affect the caching performance,puts forward the corresponding calculation methods,and utilize the multi-factors to measure the cache value of contents.Furthermore,a new cache value function is constructed,which makes the content with high value be stored in the router as long as possible,so as to ensure the efficient use of cache resources.The simulation results show that CPRM can effectively improve cache hit ratio,enhance cache resource utilization,reduce energy consumption and decrease hit distance of content acquisition.展开更多
Water scarcity is the major problem confronting both urban and rural dwellers in Enugu State. This scarcity emanated from indiscriminate pipe failure, lack of adequate maintenance, uncertainty on the time of repair or...Water scarcity is the major problem confronting both urban and rural dwellers in Enugu State. This scarcity emanated from indiscriminate pipe failure, lack of adequate maintenance, uncertainty on the time of repair or replacement of pipes etc. There is no systematic approach to determining replacement or repair time of the pipes. Hence, the rule of thumb is used in making such a vital decision. The population is increasing, houses are built but the network is not expanded and the existing ones that were installed for no less than two to three decades ago are not maintained. These compounded the problem of scarcity of water in the state. Replacement or repair of water pipes when they are seen spilling water cannot solve this lingering problem. The solution can be achieved by developing an adequate predictive model for water pipe replacement. Hence, this research is aimed at providing a solution to this problem of water scarcity by suggesting a policy that will be used for better planning. The interests in this paper were to obtain a water pipe failure model, the intensity function λ(t) [failure rate], the reliability R(t) and the optimal time of replacement and they were achieved. It was observed that the failure rate of the pipes increases with time while their reliability deteriorates with time. Hence, the Optimal replacement policy is that each pipe should be replaced after 4th break when the reliability = 0.0011.展开更多
As the big data era is coming, it brings new challenges to the massive data processing. A combination of GPU and CPU on chip is the trend to release the pressure of large scale computing. We found that there are diffe...As the big data era is coming, it brings new challenges to the massive data processing. A combination of GPU and CPU on chip is the trend to release the pressure of large scale computing. We found that there are different memory access characteristics between GPU and CPU. The most important one is that the programs of GPU include a large number of threads, which lead to higher access frequency in cache than the CPU programs. Although the LRU policy favors the programs with high memory access frequency, the programs of GPU can’t get the corresponding performance boost even more cache resources are provided. So LRU policy is not suitable for heterogeneous multi-core processor. Based on the different characteristics of GPU and CPU programs on memory access, this paper proposes an LLC dynamic replacement policy--DIPP (Dynamic Insertion / Promotion Policy) for heterogeneous multi-core processors.The core idea of the replacement policy is to reduce the miss rate of the program and enhance the overall system performance by limiting the cache resources that GPU can acquire and reducing the thread interferences between programs. Experiments compare the DIPP replacement policy with LRU and we conduct a classified discussion according to the program results of GPU. Friendly programs enhance 23.29% on the average performance (using arithmetic mean).Large working sets programs can improve 13.95%, compute-intensive programs enhance 9.66% and stream class programs improve 3.8%.展开更多
The replacement problem can be modeled as a finite, irreducible, homogeneous Markov Chain. In our proposal, we modeled the problem using a Markov decision process and then, the instance is optimized using linear progr...The replacement problem can be modeled as a finite, irreducible, homogeneous Markov Chain. In our proposal, we modeled the problem using a Markov decision process and then, the instance is optimized using linear programming. Our goal is to analyze the sensitivity and robustness of the optimal solution across the perturbation of the optimal basis ?obtained from the simplex algorithm. The perturbation ?can be approximated by a given matrix H?such that . Some algebraic relations between the optimal solution and the perturbed instance are obtained and discussed.展开更多
Hardware prefetching and replacement policies are two techniques to improve the performance of the memory subsystem.While prefetching hides memory latency and improves performance,interactions take place with the cach...Hardware prefetching and replacement policies are two techniques to improve the performance of the memory subsystem.While prefetching hides memory latency and improves performance,interactions take place with the cache replacement policies,thereby introducing performance variability in the application.To improve the accuracy of reuse of cache blocks in the presence of hardware prefetching,we propose Prefetch-Adaptive Intelligent Cache Replacement Policy(PAIC).PAIC is designed with separate predictors for prefetch and demand requests,and uses machine learning to optimize reuse prediction in the presence of prefetching.By distinguishing reuse predictions for prefetch and demand requests,PAIC can better combine the performance benefits from prefetching and replacement policies.We evaluate PAIC on a set of 27 memory-intensive programs from the SPEC 2006 and SPEC 2017.Under single-core configuration,PAIC improves performance over Least Recently Used(LRU)replacement policy by 37.22%,compared with improvements of 32.93%for Signature-based Hit Predictor(SHiP),34.56%for Hawkeye,and 34.43%for Glider.Under the four-core configuration,PAIC improves performance over LRU by 20.99%,versus 13.23%for SHiP,17.89%for Hawkeye and 15.50%for Glider.展开更多
The West Development Policy being implemented in China causes significant land use and land cover (LULC) changes in West China, of which the two most important types of LULC change are replacing farmland and re-greeni...The West Development Policy being implemented in China causes significant land use and land cover (LULC) changes in West China, of which the two most important types of LULC change are replacing farmland and re-greening the desertification land with forest or grass. This paper modifies the prevailing regional climate model (RCM) by updating its lower boundary conditions with the up-to-date satellite database of the Global Land Cover Characteristics Database (GLCCD) created by the United States Geological Survey and the University of Nebraska-Lincoln. The modified RCM is used to simulate the possible regional climate changes due to the LULC variations. The preliminary results can be summarized as that the two main types of LULC variation, replacing farmland and greening the desertification lands with forest or grass in west China, will affect the regional climate mostly in northwest and north China, where the surface temperature will decrease and the precipitation will increase. The regional climate adjustments in South, Southwest China and on the Tibet Plateau are uncertain.展开更多
The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ fai...The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ failure occurs,the system will be repaired immediately,which is failure repair(FR).Between the(n-1)th and the nth FR,the system is supposed to be preventively repaired(PR)as the consecutive working time of the system reaches λ^(n-1) T,where λ and T are specified values.Further,we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type Ⅰ failure or the occurrence of the first type Ⅱ failure,whichever occurs first.In practice,the system will degrade with the increasing number of repairs.That is,the consecutive working time of the system forms a decreasing generalized geometric process(GGP)whereas the successive repair time forms an increasing GGP.A simple bivariate policy(T,N)repairable model is introduced based on GGP.The alternative searching method is used to minimize the cost rate function C(N,T),and the optimal(T,N)^(*) is obtained.Finally,numerical cases are applied to demonstrate the reasonability of this model.展开更多
In this paper,the optimal maintenance policy is investigated for a system with stochastic lead time and two types of failures. The system has two types of failures, one type is repairable, when the repairable failure ...In this paper,the optimal maintenance policy is investigated for a system with stochastic lead time and two types of failures. The system has two types of failures, one type is repairable, when the repairable failure occurs, the system will be repaired by repairman, and the system after repair is not“as good as new". The other type of failure is unrepairable, and when the unrepairable failure occurs the system must be replaced by a new and identical one. The spare system for replacement is available only by order, and the lead time for delivering the spare system is stochastic. The successive survival times of the system form a stochastically decreasing geometric process, the consecutive repair times after failures of the system form a renewal process. By using the renewal process theory and geometric process theory, the explicit expression of the long-run average cost per unit time under ordering policy (N-1) is derived, and the corresponding optimal can be found analytically. Finally, the numerical analyses are given.展开更多
Most of the spare ordering policies treated up to now have assumed that preventive and corrective replacement costs are equal, which implies in essential that there is no significant need for preventive replacement. T...Most of the spare ordering policies treated up to now have assumed that preventive and corrective replacement costs are equal, which implies in essential that there is no significant need for preventive replacement. This paper presents an ordering policy for preventive age replacement with minimal repair. Introducing the replacement, repair, inventory holding and shortage costs, the expected cost rate is derived. A procedure to determine jointly the ordering time for a spare and the preventive replacement time for the operating unit so as to minimize the expected cost rate is proposed. To explain the ordering policy and the optimization procedure, a numerical example is also included.展开更多
This study considers an age replacement policy(ARP) for a repairable product with an increasing failure rate with and without a product warranty. As for the warranty policy to consider in association with such an age ...This study considers an age replacement policy(ARP) for a repairable product with an increasing failure rate with and without a product warranty. As for the warranty policy to consider in association with such an age replacement policy, we adapt a renewable minimal repair-replacement warrant(MRRW) policy with 2D factors of failure time of the product and its corresponding repair time. The expected cost rate during the life cycle of the product is utilized as a criterion to find the optimal policies for both with and without the product warranty. We determine the optimal replacement age that minimizes the objective function which evaluates the expected cost rate during the product cycle and investigate the impact of several factors on the optimal replacement age. The main objective of this study lies on the generalization of the classical age replacement policy to the situation where a renewable warranty depending on 2D factors is in effect. We present some interesting observations regarding the effect of relevant factors based on numerical analysis.展开更多
基金the National Natural Science Foundation of China(No.71561016)the China Postdoctoral Science Foundation(Nos.2017M613297XB , 2019T120964)。
文摘Maintenance optimization of periodic replacement for mono-unit production system is a widely discussed topic.In practice,the replacement for a parallel production system with multi-unit served by one repairman is universal.The replacement action is often implemented in a maintenance window at random,although the replacement period appears as a quasi-periodic event.To optimize these maintenance policies,this study analyzes a bivariate quasi-periodic replacement policy (T,W) for a two-unit parallel production system with a maintenance window and one repairman.One unit of the system is replaced when either a failure occurs or a replacement plan comes in the maintenance window,whichever comes first.If one of the two units is in the replacement,the other may continue operating or waiting until the replacement is completed.An optimal replacement window [T*,T* + W*] can be obtained by jointly considering the system's long-running cost rate and the availability using the genetic algorithm.This study also introduces three examples of the production system with different types of units to illustrate the proposed policy.
文摘A notable portion of cachelines in real-world workloads exhibits inner non-uniform access behaviors.However,modern cache management rarely considers this fine-grained feature,which impacts the effective cache capacity of contemporary high-performance spacecraft processors.To harness these non-uniform access behaviors,an efficient cache replacement framework featuring an auxiliary cache specifically designed to retain evicted hot data was proposed.This framework reconstructs the cache replacement policy,facilitating data migration between the main cache and the auxiliary cache.Unlike traditional cacheline-granularity policies,the approach excels at identifying and evicting infrequently used data,thereby optimizing cache utilization.The evaluation shows impressive performance improvement,especially on workloads with irregular access patterns.Benefiting from fine granularity,the proposal achieves superior storage efficiency compared with commonly used cache management schemes,providing a potential optimization opportunity for modern resource-constrained processors,such as spacecraft processors.Furthermore,the framework complements existing modern cache replacement policies and can be seamlessly integrated with minimal modifications,enhancing their overall efficacy.
基金The National Natural Science Foundation of China(No.51275090,71201025)the Program for Special Talent in Six Fields of Jiangsu Province(No.2008144)+1 种基金the Scientific Research Foundation of Graduate School of Southeast University(No.YBJJ1302)the Scientific Innovation Research of College Graduates in Jiangsu Province(No.CXLX12_0078)
文摘To investigate the effects of various random factors on the preventive maintenance (PM) decision-making of one type of two-unit series system, an optimal quasi-periodic PM policy is introduced. Assume that PM is perfect for unit 1 and only mechanical service for unit 2 in the model. PM activity is randomly performed according to a dynamic PM plan distributed in each implementation period. A replacement is determined based on the competing results of unplanned and planned replacements. The unplanned replacement is trigged by a catastrophic failure of unit 2, and the planned replacement is executed when the PM number reaches the threshold N. Through modeling and analysis, a solution algorithm for an optimal implementation period and the PM number is given, and optimal process and parametric sensitivity are provided by a numerical example. Results show that the implementation period should be decreased as soon as possible under the condition of meeting the needs of practice, which can increase mean operating time and decrease the long-run cost rate.
基金This research was funded by the National Natural Science Foundation of China(No.61862046)the Inner Mongolia Natural Science Foundation of China under Grant No.2018MS06024+2 种基金the Research Project of Higher Education School of Inner Mongolia Autonomous Region under Grant NJZY18010the Inner Mongolia Autonomous Region Science and Technology Achievements Transformation Project(No.CGZH2018124)the CERNET Innovation Project under Grant No.NGII20180626.
文摘Named Data Networking(NDN)is one of the most excellent future Internet architectures and every router in NDN has the capacity of caching contents passing by.It greatly reduces network traffic and improves the speed of content distribution and retrieval.In order to make full use of the limited caching space in routers,it is an urgent challenge to make an efficient cache replacement policy.However,the existing cache replacement policies only consider very few factors that affect the cache performance.In this paper,we present a cache replacement policy based on multi-factors for NDN(CRPM),in which the content with the least cache value is evicted from the caching space.CRPM fully analyzes multi-factors that affect the caching performance,puts forward the corresponding calculation methods,and utilize the multi-factors to measure the cache value of contents.Furthermore,a new cache value function is constructed,which makes the content with high value be stored in the router as long as possible,so as to ensure the efficient use of cache resources.The simulation results show that CPRM can effectively improve cache hit ratio,enhance cache resource utilization,reduce energy consumption and decrease hit distance of content acquisition.
文摘Water scarcity is the major problem confronting both urban and rural dwellers in Enugu State. This scarcity emanated from indiscriminate pipe failure, lack of adequate maintenance, uncertainty on the time of repair or replacement of pipes etc. There is no systematic approach to determining replacement or repair time of the pipes. Hence, the rule of thumb is used in making such a vital decision. The population is increasing, houses are built but the network is not expanded and the existing ones that were installed for no less than two to three decades ago are not maintained. These compounded the problem of scarcity of water in the state. Replacement or repair of water pipes when they are seen spilling water cannot solve this lingering problem. The solution can be achieved by developing an adequate predictive model for water pipe replacement. Hence, this research is aimed at providing a solution to this problem of water scarcity by suggesting a policy that will be used for better planning. The interests in this paper were to obtain a water pipe failure model, the intensity function λ(t) [failure rate], the reliability R(t) and the optimal time of replacement and they were achieved. It was observed that the failure rate of the pipes increases with time while their reliability deteriorates with time. Hence, the Optimal replacement policy is that each pipe should be replaced after 4th break when the reliability = 0.0011.
文摘As the big data era is coming, it brings new challenges to the massive data processing. A combination of GPU and CPU on chip is the trend to release the pressure of large scale computing. We found that there are different memory access characteristics between GPU and CPU. The most important one is that the programs of GPU include a large number of threads, which lead to higher access frequency in cache than the CPU programs. Although the LRU policy favors the programs with high memory access frequency, the programs of GPU can’t get the corresponding performance boost even more cache resources are provided. So LRU policy is not suitable for heterogeneous multi-core processor. Based on the different characteristics of GPU and CPU programs on memory access, this paper proposes an LLC dynamic replacement policy--DIPP (Dynamic Insertion / Promotion Policy) for heterogeneous multi-core processors.The core idea of the replacement policy is to reduce the miss rate of the program and enhance the overall system performance by limiting the cache resources that GPU can acquire and reducing the thread interferences between programs. Experiments compare the DIPP replacement policy with LRU and we conduct a classified discussion according to the program results of GPU. Friendly programs enhance 23.29% on the average performance (using arithmetic mean).Large working sets programs can improve 13.95%, compute-intensive programs enhance 9.66% and stream class programs improve 3.8%.
文摘The replacement problem can be modeled as a finite, irreducible, homogeneous Markov Chain. In our proposal, we modeled the problem using a Markov decision process and then, the instance is optimized using linear programming. Our goal is to analyze the sensitivity and robustness of the optimal solution across the perturbation of the optimal basis ?obtained from the simplex algorithm. The perturbation ?can be approximated by a given matrix H?such that . Some algebraic relations between the optimal solution and the perturbed instance are obtained and discussed.
基金supported by the Natural Science Foundation of Beijing under Grant No.4192007the National Natural Science Foundation of China under Grant No.61202076.
文摘Hardware prefetching and replacement policies are two techniques to improve the performance of the memory subsystem.While prefetching hides memory latency and improves performance,interactions take place with the cache replacement policies,thereby introducing performance variability in the application.To improve the accuracy of reuse of cache blocks in the presence of hardware prefetching,we propose Prefetch-Adaptive Intelligent Cache Replacement Policy(PAIC).PAIC is designed with separate predictors for prefetch and demand requests,and uses machine learning to optimize reuse prediction in the presence of prefetching.By distinguishing reuse predictions for prefetch and demand requests,PAIC can better combine the performance benefits from prefetching and replacement policies.We evaluate PAIC on a set of 27 memory-intensive programs from the SPEC 2006 and SPEC 2017.Under single-core configuration,PAIC improves performance over Least Recently Used(LRU)replacement policy by 37.22%,compared with improvements of 32.93%for Signature-based Hit Predictor(SHiP),34.56%for Hawkeye,and 34.43%for Glider.Under the four-core configuration,PAIC improves performance over LRU by 20.99%,versus 13.23%for SHiP,17.89%for Hawkeye and 15.50%for Glider.
基金This study was supported bythe National Key Basic Research Development Programgranted by the Ministry of Science and Technology ofChina (MSTC) with project number G1999043500. Itwas also partly supported by the Innovation Program ofthe Chinese
文摘The West Development Policy being implemented in China causes significant land use and land cover (LULC) changes in West China, of which the two most important types of LULC change are replacing farmland and re-greening the desertification land with forest or grass. This paper modifies the prevailing regional climate model (RCM) by updating its lower boundary conditions with the up-to-date satellite database of the Global Land Cover Characteristics Database (GLCCD) created by the United States Geological Survey and the University of Nebraska-Lincoln. The modified RCM is used to simulate the possible regional climate changes due to the LULC variations. The preliminary results can be summarized as that the two main types of LULC variation, replacing farmland and greening the desertification lands with forest or grass in west China, will affect the regional climate mostly in northwest and north China, where the surface temperature will decrease and the precipitation will increase. The regional climate adjustments in South, Southwest China and on the Tibet Plateau are uncertain.
基金supported by the National Natural Science Foundation of China(61573014)the Fundamental Research Funds for the Central Universities(JB180702).
文摘The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ failure occurs,the system will be repaired immediately,which is failure repair(FR).Between the(n-1)th and the nth FR,the system is supposed to be preventively repaired(PR)as the consecutive working time of the system reaches λ^(n-1) T,where λ and T are specified values.Further,we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type Ⅰ failure or the occurrence of the first type Ⅱ failure,whichever occurs first.In practice,the system will degrade with the increasing number of repairs.That is,the consecutive working time of the system forms a decreasing generalized geometric process(GGP)whereas the successive repair time forms an increasing GGP.A simple bivariate policy(T,N)repairable model is introduced based on GGP.The alternative searching method is used to minimize the cost rate function C(N,T),and the optimal(T,N)^(*) is obtained.Finally,numerical cases are applied to demonstrate the reasonability of this model.
文摘In this paper,the optimal maintenance policy is investigated for a system with stochastic lead time and two types of failures. The system has two types of failures, one type is repairable, when the repairable failure occurs, the system will be repaired by repairman, and the system after repair is not“as good as new". The other type of failure is unrepairable, and when the unrepairable failure occurs the system must be replaced by a new and identical one. The spare system for replacement is available only by order, and the lead time for delivering the spare system is stochastic. The successive survival times of the system form a stochastically decreasing geometric process, the consecutive repair times after failures of the system form a renewal process. By using the renewal process theory and geometric process theory, the explicit expression of the long-run average cost per unit time under ordering policy (N-1) is derived, and the corresponding optimal can be found analytically. Finally, the numerical analyses are given.
文摘Most of the spare ordering policies treated up to now have assumed that preventive and corrective replacement costs are equal, which implies in essential that there is no significant need for preventive replacement. This paper presents an ordering policy for preventive age replacement with minimal repair. Introducing the replacement, repair, inventory holding and shortage costs, the expected cost rate is derived. A procedure to determine jointly the ordering time for a spare and the preventive replacement time for the operating unit so as to minimize the expected cost rate is proposed. To explain the ordering policy and the optimization procedure, a numerical example is also included.
基金the National Research Foundation of Korea Grant(NRF-2014S1A5A8012594)the 2014Hongik University Research Fund,the Basic Science Research Program Through the National Research Foundation of Korea(Nos.2013-2058436 and 2011-0022397)the Basic Science Research Program Through the National Research Foundation of Korea
文摘This study considers an age replacement policy(ARP) for a repairable product with an increasing failure rate with and without a product warranty. As for the warranty policy to consider in association with such an age replacement policy, we adapt a renewable minimal repair-replacement warrant(MRRW) policy with 2D factors of failure time of the product and its corresponding repair time. The expected cost rate during the life cycle of the product is utilized as a criterion to find the optimal policies for both with and without the product warranty. We determine the optimal replacement age that minimizes the objective function which evaluates the expected cost rate during the product cycle and investigate the impact of several factors on the optimal replacement age. The main objective of this study lies on the generalization of the classical age replacement policy to the situation where a renewable warranty depending on 2D factors is in effect. We present some interesting observations regarding the effect of relevant factors based on numerical analysis.