Search

This paper models a warm standby system where a single element is online performing a specified mission task (e.g., a computing task) and subject to corrective replacement (CR) by an available standby element upon its failure. During the mission, preventive replacements (PRs) are also performed to renew the aged or worn online operating element before its actual failure according to a predetermined policy. In addition, to facilitate an effective restoration of system function in case of CR or PR happening, backups are also performed periodically so that the mission task can be resumed from the last successful backup point instead of from scratch. The mission succeeds if the specified mission task is accomplished; in other words, the mission fails when no operating elements remain prior to the mission task completion. In this paper, we make new contributions by first proposing an event transition-based numerical method to evaluate mission performance indices of the considered standby system subject to periodic backups, CR and PR. Mission success probability (MSP), expected mission completion time, expected mission operation cost (EMC), and expected uncompleted work fraction are evaluated. Based on the suggested evaluation algorithm, we make another contribution by formulating and solving optimization problems that help to determine the optimal backup-PR policy or the optimal combination of element activation sequencing and backup-PR policy to maximize MSP or minimize EMC. Influence of element performance and reliability parameters, data backup and retrieval complexity parameters on the optimal operation policy is investigated. Findings from this paper can guide the optimal decision making on policies related to element sequencing, backups as well as preventive maintenance planning, contributing toward reliable and cost-effective design and operation of standby computing systems. [ABSTRACT FROM AUTHOR]

This paper models a hybrid standby system subject to periodic inspections and condition-based standby mode transfers during a mission. At the beginning of the mission only one element is online and operating. The second element waits in a hot standby mode being ready to replace the failed online element at any time. Other elements wait in less-stressful and less-costly warm standby mode. During the mission periodic inspections are performed for checking conditions of the online and hot standby elements and subsequently triggering necessary mode transfer(s) of available warm standby element(s) to replace the failed hot standby element and/or online element. We suggest an efficient numerical method to assess availability and expected total mission cost (including standby cost, operation cost and mode transfer cost of system elements, inspection cost, system interruption or idle cost) of the considered system. The algorithm is flexible and applicable to arbitrary type of time-to-failure distributions. Then we formulate and solve new optimization problems that identify the optimal combination of inter-inspection interval and element activation sequence to minimize expected total mission cost while satisfying a certain constraint on system availability. As illustrated through examples, the optimization results can facilitate cost-effective and availability-aware planning of system inspection and operation. [ABSTRACT FROM AUTHOR]

This paper considers 1-out-of- N : G warm standby (WS) systems subject to multiple-phased mission requirements, where performance, failure behavior, operation cost, replacement time, and cost of system elements can vary from phase to phase due to changing working conditions and stress levels. The system succeeds if its elements can accomplish a specified mission task within the maximum allowed time. A numerical algorithm is proposed for evaluating mission indices, including system reliability, expected mission cost, and expected uncompleted work of the heterogeneous, dynamic standby system considered. The influence of the maximum allowed mission time on mission indices is investigated. As demonstrated through examples, the proposed algorithm can also facilitate a determination of mission interruption based on reliability or cost-oriented criteria. Based on the proposed algorithm, an unconstrained optimal standby element sequencing problem is then formulated and solved for heterogeneous WS multiphase systems. The problem is to find the optimal activation sequence of system elements maximizing system reliability, or minimizing expected mission cost, or minimizing expected uncompleted work. The constrained optimization problems of minimizing expected mission cost subject to providing a desired level of mission reliability or uncompleted work are also solved. Illustrative examples of these optimization problems and their applications in estimating the role of each element in the mission success are presented. [ABSTRACT FROM PUBLISHER]

Motivated by practical applications (for example production systems, flow transmission systems, and transportation systems), this paper considers 1-out-of-N: G warm standby systems subject to periodic inspections. Periodic inspections are performed to detect failures of system components. If an online operating component failure is detected during inspection, an available warm standby component is activated to take over the mission task. The mission succeeds if system components can complete a pre-specified amount of work. A state space event transition based numerical algorithm is first suggested for evaluating important mission performance indices including mission success probability, expected mission cost, expected mission time, expected mission completion delay over a desired time, and expected uncompleted work of the considered standby system. Based on the proposed evaluation algorithm, inspection interval optimization problems are formulated and solved, which find the optimal value of the inspection interval to minimize the expected total mission cost subject to providing a desired level of mission success probability, expected completion time, and delay. Further, combined component sequencing and inspection interval optimization problems are solved, for minimizing the expected total mission cost, or maximizing the mission success probability. As illustrated through examples, the proposed methodology can also facilitate solving dynamic optimization problems that update the optimal solution after each component failure, leading to further improvements of various mission indices. [ABSTRACT FROM PUBLISHER]

In this paper, mission reliability, expected mission completion time, and cost of non-repairable 1-out-of-N: G warm standby sparing systems subject to uneven backup actions are modeled and optimized. The backup actions are used to facilitate the data recovery process in the case of an online operating element failure, which enables an activated standby element to take over the mission task through subsequent data retrievals. Both data backup and retrieval times are dynamic, and physically dependent on the amount of work performed. The system elements are not necessarily identical; each element can be characterized by a different time-to-failure distribution, a different performance, and a different level of readiness to take over the system task during the warm standby mode. An iterative numerical method is first proposed to simultaneously evaluate mission reliability, expected mission completion time, and the cost of the considered heterogeneous warm standby systems. Due to the non-monotonic effect of the backup distribution on the mission reliability, time, and cost, we formulate and solve the optimal backup distribution problem considering different combinations of optimization objectives and constraints. In the case of system elements being non-identical, their activation order can influence the mission reliability, expected mission completion time, and mission cost significantly. Therefore, we also formulate and solve the optimal element sequencing problem for the considered system. Furthermore, new integrated optimization problems are formulated and addressed. The integrated optimization aims to identify the optimal combination of backup distribution and element activation order that maximizes the mission reliability, or minimizes the expected mission time or mission cost. As shown through examples, the proposed methodology can implement a tradeoff analysis among the three mission requirements of reliability, cost, and completion time, leading to the optimal decision on both backup and standby policies of warm standby systems. [ABSTRACT FROM PUBLISHER]

Standby redundancy is a design technique that has been widely adopted to enhance system reliability and achieve fault tolerance in many critical applications. In this paper, we consider a 1-out-of-N: G hybrid standby redundant system with unrepairable elements being subject to delayed failure-driven standby mode transfers. Specifically, in the considered system, all the standby elements are initially in a warm standby mode (WSM) but can be transferred to a hot standby mode (HSM) so as to be ready to replace the online operating element when it fails. The WSM to HSM transfer is performed with a fixed time delay after no element resides in HSM either due to the element failure or because the element leaves the HSM to replace the failed online element for operation. A new iterative numerical algorithm is first proposed for evaluating reliability and expected mission cost (relevant to elements’ standby expense, operation expense, as well as mode transfer expense) of the considered hybrid standby system. The algorithm has no restriction on element time-to-failure distribution types. Based on the proposed evaluation algorithm, we further formulate and solve a new optimization problem that finds the optimal delay and optimal sequence of standby elements with the objective to minimize expected mission cost while satisfying a certain level of mission reliability constraint. Examples are presented to demonstrate applications of the proposed methodology. [ABSTRACT FROM AUTHOR]

This paper considers the modelling and optimization of 1-out-of-N: G cold standby (CS) systems with non-repairable components functioning at different levels of productivity or load. The productivity heterogeneity leads to difference in component failure behaviour as well as in operational and replacement costs. Thus, the choice of load or productivity of components can greatly affect the system reliability and mission cost. To make the optimal choice of component loading, we first suggest a method for analysing the reliability and expected mission cost of 1-out-of-N: G non-repairable CS systems with heterogeneous components. The optimal dynamic load distribution problem is then formulated and solved, in which the component loading is chosen depending on the amount of work completed prior to the component activation. The optimal loading is aimed at minimizing the expected mission cost, while meeting a certain system reliability constraint. Examples are given to demonstrate the proposed methodology and the improvement in the optimal design solution through introducing the component productivity’s dependence on the completed work. [ABSTRACT FROM AUTHOR]

This paper considers nonrepairable 1-out-of- N : G cold standby (CS) systems subject to uneven backup actions as well as dynamic backup and retrieval times. In such systems, only one element is online and operates with the rest of the elements waiting in the unpowered CS mode. The operating element performs data backup actions when certain fractions of the mission task are accomplished. The backup actions facilitate data recovery in case of an operating element failure, which allows an activated standby element to take over the task through data retrieval. Backup distribution can have a nonmonotonic effect on mission reliability, time, and cost, leading to the optimal backup distribution problem. In this paper, we first suggest a numerical method to model and evaluate mission reliability, expected time, and cost simultaneously for the considered CS systems with uneven backup actions and dynamic backup and retrieval times. Based on the suggested evaluation method and genetic algorithm, the optimal backup distribution problem is then formulated and solved with the objective to minimize the expected mission cost subject to meeting certain levels of mission reliability and expected mission time. Examples show that the proposed methodology can facilitate a tradeoff study between mission reliability, and time and cost, which assists in the optimal decision-making for the backup policy used in the practical design of CS systems. [ABSTRACT FROM AUTHOR]

This paper considers 1-out-of-N:G heterogeneous fault-tolerant systems that are designed with a mix of hot and cold standby redundancies to achieve the tradeoff between restoration and operation costs of standby elements. In such systems, the way in which the elements are distributed between hot and cold standby groups and the initiation sequence of all the cold standby elements can greatly affect the system reliability and mission cost. Therefore, it is significant to solve the optimal standby element distributing and sequencing problem (SE-DSP). The failure that occurs in a system element can propagate, causing the outage of other system elements, which complicates the solution to the SE-DSP problem. In this paper, we first propose a numerical method for evaluating the reliability and expected mission cost of 1-out-of-N:G systems with mixed hot and cold redundancy types and propagated failures. Two different failure propagation modes are considered: an element failure causing the outage of all the system elements, and an element failure causing the outage of only working or hot standby elements but not cold standby elements. A genetic algorithm is utilized as an optimization tool for solving the formulated SE-DSP problem, leading to a solution that can minimize the expected mission cost of the system while providing a desired level of the system reliability. Effects of the failure propagation probability on the system reliability, expected mission cost, as well as the optimization results are investigated. The suggested methodology can facilitate a reliability-cost tradeoff study of the considered systems, thus assisting in optimal decision making regarding the system's standby policy. Examples are provided for illustrating the considered problem as well as the proposed solution methodology. [ABSTRACT FROM PUBLISHER]

The paper proposes a new fault tolerant system design model, in particular a 1-out-of-N:G hybrid redundant system with standby elements subject to state-dependent standby mode transfers. Specifically, in such systems, one standby element always resides in the hot standby mode, and thus is ready to replace the failed online element at any time to make the system dependable. If the online operating element or the hot standby element fails, one of the warm standby elements is immediately transferred to the hot standby mode. A numerical algorithm is first suggested for evaluating the reliability and the expected mission cost of the considered system. The algorithm is based on a discrete approximation of element time-to-failure distributions, and can work with any type of distribution. Furthermore, based on the suggested algorithm, the problem of optimal sequencing of standby elements initiation is formulated and solved. The objective of this optimization problem is to minimize the expected mission cost associated with elements' standby and operation expenses, as well as the mode transfer expenses, while meeting a certain system reliability constraint. Illustrative examples are provided. [ABSTRACT FROM PUBLISHER]

In this paper, mission cost and reliability of 1-out-of- $N$ : G nonrepairable warm standby systems with imperfect switching are modeled and analyzed using an iterative method. A general switching structure is considered, which consists of an overall fault detection mechanism (FDM) and a set of individual switches (one for each standby element). The failure of the FDM prevents the replacement of the failed online element by any standby element while the failure of an individual switch only makes the corresponding standby element unavailable. The entire mission fails either when the FDM fails before the failure of the online element during the mission, or when all the system elements have failed or become unavailable before the mission completion. Based on the proposed algorithm for the mission cost and reliability analysis, the optimal element sequencing problem is further formulated and solved for 1-out-of- $N$ : G nonrepairable warm standby systems with nonidentical elements and imperfect switching mechanisms. The objective of the problem is to find the optimal initiation sequence of system elements that can minimize the expected mission cost while providing a certain level of system reliability. Examples are given to illustrate the considered problem and the proposed solution methodology. [ABSTRACT FROM AUTHOR]

Thek-out-of-n: G heterogeneous cold-standby system structure is a widely used fault-tolerant system design method, where the sequence in which the different system elements are initiated can greatly affect the system reliability and mission cost. This paper considers the optimal standby element sequencing problem (SESP) for such systems. Given the desired cold-standby redundancy level and fixed set of element choices, the objective of the optimal system design is to select the initiation sequence of the system elements so as to minimize the expected system mission cost while meeting a certain level of system reliability constraint. Based on a discrete approximation of time-to-failure distributions of the system elements, the system reliability and expected mission cost are evaluated simultaneously using a numerical method. A genetic algorithm is used as an optimization tool for solving the formulated SESP problem fork-out-of-n: G heterogeneous cold-standby systems. Examples are given to illustrate the considered problem and the proposed solution methodology. [ABSTRACT FROM AUTHOR]

As a common practice in computing-related applications, checkpointing is used to facilitate an effective system recovery in the case of the occurrence of failures. Checkpoints are performed to save data associated with completed portion of a mission task. In the case of a failure, through rollback and data retrieval the system can resume the mission task from the last successful checkpoint instead of from the very beginning of the mission, saving time and cost. This paper models and optimizes 1-out-of- N : G warm standby systems subject to uneven online checkpointing, where checkpoints can be performed in parallel with execution of the primary mission task for improving efficiency of computing elements. Both data checkpoint and retrieval take dynamic time, depending on the amount of work completed. System elements can be heterogeneous in the time-to-failure distribution, performance, and level of readiness to take over the mission task during the warm standby mode. A numerical method is first suggested to evaluate mission performance indices including mission success probability, expected mission completion time, and expected mission operation cost. Examples are provided to demonstrate influence of mission deadline and element resource sharing parameter (i.e., CPU time distribution between the checkpointing procedure and the primary mission task) on the mission performance metrics. The optimal checkpoint distribution and optimal element activation sequencing problems are considered for different combinations of optimization objectives and constraints. A co-optimization problem is further addressed, which aims to find the optimal combination of checkpoint distribution and element activation sequence. Example optimization solutions illustrate the tradeoff among the three mission requirements (reliability, completion time, operation cost) for warm standby systems with online checkpoints. [ABSTRACT FROM AUTHOR]

This paper considers single-component repairable systems performing backup procedures to avoid repeating the entire work from scratch and thus facilitate fast system recovery in the case of failures. The mission succeeds if a specified amount of work can be accomplished within the maximum allowed mission time or deadline. The repair time is randomly distributed within a specified interval. Both failure and repair times are represented by known distributions. We first suggest a numerical algorithm to evaluate mission reliability, conditional expected cost and completion time of a successful mission. The backup frequency optimization problem is then formulated and solved for finding the inter-backup interval that maximizes mission reliability or minimizes expected mission cost while satisfying a desired level of mission reliability. Impacts of parameters including the maximum allowed mission time, data backup and retrieval times, repair and failure time distributions, and repair efficiency on mission reliability, cost and time as well as on the optimal solution are investigated through examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the optimal choice of productivity (load) of components in 1-out-of-N non-repairable cold standby systems. It is assumed that each system component can function at different levels of productivity (load) and that the life time acceleration factor as well as operational and replacement costs of each component are affected by its productivity. We present a model for evaluating the standby system reliability and expected mission cost. Furthermore, we formulate and solve the optimal load distribution problems in which the mission cost is minimized subject to system reliability constraint. Both fixed and variable sequences of component initiation are considered. Illustrative examples are provided. [Copyright &y& Elsevier]

Abstract: This paper considers the optimal standby component sequencing problem (SESP) for 1-out-of-N: G heterogeneous cold-standby systems. Given the desired cold-standby redundancy level and a fixed set of components, the objective of the optimal system operation scheduling is to select the initiation sequence of the system components so as to minimize the expected mission cost of the system. Based on a discrete approximation of time-to-failure distributions of the system components, the mission reliability and expected mission cost are simultaneously evaluated using the universal generating function technique. A genetic algorithm is used as an optimization tool for solving the formulated SESP problem for the 1-out-of-N: G heterogeneous cold-standby systems. Several examples are given to illustrate the considered problem and the proposed solution methodology. [Copyright &y& Elsevier]

This paper considers a new type of optimization problems, the optimal standby mode selection problem in 1-out-of- N : G warm standby systems where multiple standby mode choices are available to provide different levels of operation readiness of standby elements and further to achieve a balance between fast restoration and low operation cost. Given the desired redundancy level and a fixed set of standby mode choices, the objective of the optimal system design is to choose a standby mode for each of redundant elements so as to minimize expected mission cost of the system subject to a certain reliability constraint. An iterative procedure is first suggested to evaluate system reliability and expected mission cost simultaneously. Based on the suggested evaluation algorithm, a genetic algorithm is then used as an optimization tool for solving the formulated optimal standby mode selection problem in 1-out-of- N : G warm standby systems. Examples are given to illustrate the considered evaluation and optimization problems as well as the proposed solution methodology. [ABSTRACT FROM AUTHOR]