Standby Components Research Articles

Multi-objective optimization in the design of load sharing systems with mixed redundancy strategies under random shocks

The redundancy allocation problem (RAP) focuses on assigning one or more components in parallel to enhance the overall reliability of a system. Selecting a redundancy type (active or standby) for each component is a critical challenge in system design. Active components can share the load among themselves (unlike standby components), and standby components are not subjected to shock attacks (unlike active components). This research presents a multi-objective optimization model to enhance system reliability and minimize costs. The proposed model is designed for a load-sharing system with a series-parallel structure, subject to shock attacks. Reliability (availability) is calculated using a stochastic approach based on the Markov chain, and the NSGA-II algorithm solves the multi-objective optimization problem. Two numerical examples investigate the proposed approach, identifying appropriate solutions through Pareto frontiers and analyzing the impact of load-sharing and shock attacks on optimization results.

Reliability inference of stress-strength for a K-out-of-N: G mixed standby system with switching failure

In this paper, the statistical inference of the stress-strength reliability for a K-out-of-N: G mixed standby system with switching failure is investigated. It is assumed that the strength of the component itself and the external stress to which it is subjected are random variables that obey the same distribution. If an operating component fails, the warm standby component will be immediately switched to the operating one. During this switchover, the warm standby component is subject to switching failure with a certain probability. Based on Weibull distribution and generalized half-logistic distribution, the reliability indices of stress-strength model under two different distributions are derived, respectively. For the two types of distribution of stress and strength, the maximum likelihood estimator, maximum spacing estimator, Bayesian estimator, asymptotic confidence interval and bootstrap-p confidence interval of the reliability are obtained, respectively. The Monte Carlo method is applied in the numerical simulation to realize the simulation inference of the system reliability. The performance of the above inference methods is analyzed and compared. The influence of parameters of stress and strength on the system reliability is analyzed graphically.

A novel evolutionary strategy optimization algorithm for reliability redundancy allocation problem with heterogeneous components

The reliability-redundancy allocation problem (RRAP) is an optimization problem that maximizes system reliability under some constraints. In most studies on the RRAP, either active redundant components or cold standby components are used in a subsystem. This paper presents a new model for the RRAP of a system with a mixed redundancy strategy, in which all components can be heterogeneous. This formulation leads to a more precise solution for the problem; however, RRAP is an np-hard problem, and the new mixed heterogeneous model will be more complicated to solve. After formulating the issue, a novel design of an evolutionary strategy optimization algorithm is proposed to solve that. The problem consists of discrete and continuous variables, and different mutation strategies are designed for each. The new formulation of the problem and the new method for solving it lead to better results than those reported in other recent papers. We implement the new suggested heterogeneous model with the PSO and SPSO algorithms to better compare the proposed algorithm. Results show improvement in both system reliability and fitness evaluation count.

Cost optimization and reliability analysis of fault tolerant system with service interruption and reboot

Due to widespread usage in many real time systems, reliability modeling and cost optimization of fault tolerance system have drawn attention of the practitioners. The fault tolerance in these systems can be provided by the support of maintenance and redundant components that help in smooth operation of the system in spite of failure of some active components. This investigation deals with the performance modeling of a fault-tolerant system consisting of a finite number of active (online) and standby components. During the switching from active to standby, the recovery procedure is performed, which may be imperfect. In case of imperfect recovery, the system reboot takes place. The maintenance of all the components is managed by a repairman (server) which is subject to failure. When the server is interrupted for rendering the service, functioning does not get stopped due to the system switch-over from perfect working to working breakdown mode. The system works even when the server is on working vacation and performs repair jobs of the failed components. The machine repair model based on Markovian process is developed to derive the transient probabilities and other performance indices of the fault tolerant system using Laplace transforms and matrix analytical method. Using the direct search strategy and particle swarm optimization, the cost-benefit analysis is done. The optimal design of the control parameters for the fault-tolerant system are presented by framing a cost-effective ratio function. The model is examined computationally by performing the numerical simulation and cost optimization.

Statistical inference of reliability for a K-out-of-N: G system with switching failure under Poisson shocks

Based on the stochastic uncertainty of the system's operating environment, this research presents statistical inferences on the mean time to failure (MTTF) of a K-out-of-N: G non-repairable system model with switching failure under Poisson shocks. The standby component is switched to the operating component when an operating component fails, with a switching failure probability of p. The MTTF of the system is derived by using the Markov process theory and the Laplace transform for two cases where the shock threshold is a constant value or a random variable. The maximum likelihood estimator (MLE) of the MTTF is obtained, and based on this estimator, asymptotic confidence interval estimation and hypothesis testing are performed. Based on the setting of the basic parameter values, the MTTF under two different cases of the shock threshold is compared. The effect of each parameter on the MTTF is analyzed in numerical simulation. The effectiveness of the above statistical inference methods is also verified by numerical simulation.

Reliability modeling of [formula omitted]-out-of-[formula omitted]: [formula omitted] balanced systems with common bus performance sharing

This study examines the reliability of k-out-of-n: F balanced systems incorporating common bus performance sharing. The system comprises m sectors, with each sector containing n components. Each component has multiple performance levels to fulfill random demands. All components are interconnected through a common bus, enabling the surplus performance from certain components to be transmitted to deficient components via the bus. The system remains balanced as long as the difference in the number of functional components between any two sectors does not exceed a threshold d. A sector fails when the number of nonfunctional components reaches k, and the entire system fails if either Kf sectors fail or the system becomes unbalanced, whichever occurs first. Existing studies primarily focus on forcing-down functional components or activating standby components as the primary means of maintaining balance, which often leads to component wastage. However, performance sharing can also achieve rebalancing in practice. This study contributes by developing reliability models for performance sharing in balanced systems and proposing algorithms to determine the optimal performance sharing policy maximizing system reliability. The universal generating function is utilized to calculate the balance probability and system reliability. Furthermore, a case study involving a wing system in a Solar-powered Unmanned Aerial Vehicle is presented to illustrate the effectiveness of the proposed methodology.

Optimal maintenance policy considering imperfect switching for a multi‐state warm standby system

AbstractA novel maintenance policy for a two‐component warm standby system with multiple standby states is presented in this paper. Two standby states, that is, cold and warm standby, for components in the system are considered. Components can realize the transition from the cold standby to the warm standby state by periodic switching, intended to shorten recovery time and save system operating costs. Preventive maintenance (PM) and preventive switching (PS) of components are considered. In the PS strategy, the standby component can switch before the operating component fails. In addition, additional standby failure modes based on idle time are studied. Derive the long‐term average cost of the system through the semi‐regenerative process. A numerical example eventually verifies the feasibility of this paper's proposed maintenance and switching strategy.

1-out-of-n standby systems with storages and activation moment-dependent component operation time limit

This paper pioneers the modeling and optimization of a 1-out-of-n standby system with a required mission time and non-identical components, whose operation times are limited and dependent on their activation time and dynamic resource supply and storage units. Each component contains a main operating unit characterized by certain time-to-failure distribution and mode-dependent resource demands, a resource generator characterized by a time-varying resource generation rate, and a storage unit characterized by an initial amount of resource and the maximum capacity. The resource generator and storage interact collaboratively to supply the dynamic resource demand of the main unit. Based on an event transition probabilistic model, a new numerical algorithm is proposed for assessing the mission success probability (MSP) of the considered standby system. An optimization problem is further formulated and solved, which determines the activation sequence of standby components maximizing the MSP. A detailed case study of a standby sensor system with the photo-voltaic power supply source and battery storage is provided to demonstrate the proposed model and examine the effects of several system parameters on the MSP and optimization solutions. Several useful findings related to the MSP improvement are revealed from the case study.

A study on utilization of two cold standby components to increase reliability of a coherent system

. This article focuses on a specific type of coherent system in which, when the coherent system fails, either no active component remains or the remaining active components are connected in parallel. Roy and Gupta (2023) also considered the same type of coherent systems. We observe the restart of such a coherent system using two cold standby components. In our study, standbys are not placed into action simultaneously. They are put into action one by one. We compute the reliability function of the considered coherent system, which is equipped with two cold standby components. In addition, we show that when we use a stronger standby component (in the sense of failure rate order) at first, we get a longer system lifetime. Also, we compute three different mean residual life functions of the system. We have presented a few numerical results to illustrate the importance of our analysis.

The Frechet Reliability for (2+2) Cascade Model

In this paper, a reliability function for one of the cascade models was found; the model consists of two basic components (B_1 and B_2 ) and two spare components (B_3 and B_4 ), and it is sufficient for the model to be in a working state with the presence of two active components and, in case of failure of one of the two basic components, it is compensated with one of the two standby components to keep the model running. It was assumed that the strength-stress factors traced the Frechet, the parameters of the Frechet were estimated by three different estimation methods (Moments, Least Squares and Weighted Least Square,), after which the reliability of the model was estimated. Monte Carlo simulations were also conducted to compare the results and find out which estimation methods are the best to estimate the reliability of the model using two statistical criteria: MSE and MAPE, where it was presented that least square estimation is the preferred for estimating the function of reliability.

A new model for reliability redundancy allocation problem with component mixing

Reliability Redundancy Allocation Problem (RRAP) is a well-known problem in reliability optimization. In most of the previous research in RRAP, it is assumed that the components allocated to each subsystem are of the same type. This assumption limits the possible choices for the subsystem. In this paper, a new RRAP is proposed where the components allocated to each subsystem can be non-identical, and the redundancy strategy is a decision variable that can be active, standby, mixed, or none. In the proposed RRAP, both the active and the standby components can be independently of different types, which has not been considered in any of the previous studies. Since RRAP is an NP-hard problem, an adapted genetic algorithm is presented to search for the optimal solution of the proposed problem. Finally, some well-known problems are investigated to compare the proposed model with the previous ones. The obtained results show that the proposed RRAP can improve the reliability of the system in different cases by 10 % to 63 % in terms of the maximum possible improvement index.

Reliability analysis of multi-state balanced systems with standby components switching mechanism

An increasing attention has been paid to the reliability analysis of balanced system. In previous studies, there were three rebalancing strategies for balanced systems: forcing down the unbalanced pair of subsystems, restarting components that have been shut down, and dynamically adjusting the state of the working components. In this paper, a new rebalancing strategy is proposed by switching the standby components for a multi-state balanced system. The system consists of m subsystems, each with one working component and n-1 standby components. The system is balanced when the working components do not fail and the system's balanced degree doesn't exceed a threshold. Two cases of system balance conditions are considered: one is based on component states and the other is based on symmetric component states. If the system is imbalanced or fails, the system needs to adjust the state of the working component by switching switches to let the system operate normally. The switching rules for each case are given separately. In this paper, the finite Markov chain imbedding approach (FMCIA) is used to derive the system reliability. Finally, numerical examples and sensitivity analysis are given.

A novel condition‐based maintenance policy considering imperfect switching for warm standby systems

AbstractThis paper proposes a novel condition‐based maintenance model for a two‐component warm standby system considering an imperfect switching policy. Unlike the conventional models, joint optimization of preventive and failure switching strategies is investigated. The standby component can be switched preventively when the component reaches the preventive maintenance (PM) threshold before the online one fails. The failure switching is triggered when the online component reaches the corrective maintenance (CM) threshold. In addition, the switching mechanism between the two components is related to the order fulfillment rate. The optimal PM threshold and order fulfillment rate can be derived by minimizing the long‐term average cost rate. A numerical example is provided to demonstrate the robustness of the decision model under different scenarios through sensitivity analysis. Ultimately, the effectiveness of the proposed model in this article was verified by comparing the models.

Effect of test-caused degradation on the unavailability of standby safety components

This paper proposes a safety-critical standby component unavailability model that contains aging effects caused by the elapsed time from installation, component degradation due to surveillance tests, and imperfect maintenance actions. An application of the model to a Motor-Operated Valve and a Motor-Driven Pump involved in the HPIS of a VVER/1000-V446 nuclear power plant is demonstrated and compared with other existing models at component and system levels. In addition, the effects of different unavailability models are reflected in the NPP's risk criterion, i.e., core damage frequency, over five maintenance periods. The results show that, compared with other models that do not simultaneously consider the full effects of degradation and maintenance impacts, the proposed model realistically evaluates the unavailabilities of the safety-related components and the involved systems as a plant age function. Therefore, it can effectively reflect the age-dependent CDF impact of a given testing and maintenance policy in a specified time horizon.

A study on utilization of a cold standby component to enhance the mean residual life function of a coherent system

In this article, we consider a particular type of coherent systems, in which, when the coherent system fails, either no active component remains or the remaining active components are connected in parallel. This work studies two coherent systems of such type with two components, four coherent systems with three components, and seven coherent systems with four components as examples. Lifetime as well as system signature of each of these coherent systems is given. We investigate the restart of such a coherent system using a single cold standby component. The reliability of a system is studied through the (reliability) characteristics such as reliability function, mean time to failure, mean residual life functions of the system. We compute signature-based exact expression for the reliability function of the considered coherent system, which is equipped with a cold standby component. Also, we obtain three different mean residual life functions of the system. So far, no attempt has been made to study such coherent systems in cold standby sparing; therefore, we have provided some new results. We illustrate the theoretical results by considering three particular coherent systems as examples.

Analyzing the Impact of Repairable 1-out-of-3 Cold Standby Components on System Availability: A Capacity Analysis

Analyzing the Impact of Repairable 1-out-of-3 Cold Standby Components on System Availability: A Capacity Analysis

Joint optimization of mission abort and system structure considering dynamic tasks

Mission abort has recently attracted considerable attention to enhance the safety of critical systems during the primary mission (PM). Most of the existing research focuses on mission abort policies for systems performing a deterministic PM, i.e., operating for a fixed mission duration or completing a specified amount of work. However, in practice, systems are commonly required to perform dynamic tasks. This paper first makes advancements by jointly optimizing condition-based mission abort policies and system structure for the l-out-of-n: G warm standby system, where the dynamic arrival of tasks with a random amount of work is considered. In such systems, some components are initially in active mode, and the remaining warm standby components provide fault tolerance. Two types of mission success criteria are considered and corresponding mission abort policies are proposed based on different decision criteria. Mission reliability (MR) and system survivability (SS) are derived using recursive methods, considering the random switching of the active, idle, and warm standby modes under dynamic arrival of tasks. Mission abort policies and system structure are jointly optimized to balance MR and SS with the objective of minimizing the expected total cost. An example of a multiprocessor system is presented to illustrate the proposed model.

Integrated unavailability analysis including test degradation and efficiency, components ageing and common cause failures

The article proposes an integrated model for the unavailability of standby components and systems, considering the impacts of ageing, test degradation and test efficiency on independent and common cause failures (CCF) probabilities. The results showed a considerable impact of test efficiency on systems reliability and risk.The CCF model was expanded to incorporate the additional contribution derived from the repair time of identical and redundant components. Two application cases, of system unavailability and Probabilistic Safety Assessment (PSA), were evaluated for several combinations of test efficiency, degradation and ageing, using the traditional and the expanded CCF models. Ignoring the contribution to CCFs derived from the repair time leads to significant risk underestimations, even when ageing and test degradation are not included.Great uncertainties of the model parameters represent an important restriction for the introduction of adverse test effects in risk analysis, but they are important contributors that must be considered explicitly.

A Markov chain-based genetic algorithm for solving a redundancy allocation problem for a system with repairable warm standby components

Many studies have been conducted on designing systems based on the redundancy allocation problem (RAP). However, considering repairable warm-standby components (which are subject to failure even in an idle state) is somewhat neglected by researchers due to the complex mathematical models. One of the crucial aspects of these systems is considering the probability of failure when switching to a standby component or subsystem. This study tries to highlight these imperfect switching and switch selection strategies in the redundancy allocation designs. In this regard, this article is dedicated to developing two RAP models (a single objective and a bi-objective) with warm standby repairable components by proposing a solving approach based on the genetic algorithm (GA) and Markov chains. Since the model’s objective functions minimize the system’s mean time to failure (MTTF) and cost, we discussed how imperfect switches affect the total system’s cost and mean time to failure for the proposed RAPs. Finally, we adopted a GA and a non-dominated sorting genetic algorithm (NSGA-II) to solve the proposed models due to the models’ complexity. Solving these models clearly indicates the critical role of selecting an appropriate switching strategy on the system’s costs and reliability.

Reliability analysis and optimization for a redundant system with dependent failures and variable repair rates

This paper considers the reliability analysis and the bi-objective optimal problem for a redundant system with two dependent failures: common cause failure (CCF) and load-sharing failure, where the system contains N active components, W warm standbys and C cold standbys, a K-mixed redundancy strategy is considered. In the system, there is a repair team providing variable repair rates according to differential situations: when there are standby components available in the system, the repair team assigns a regular repairman to repair the failed components, with the known fact that regular repairman is not as skilled as an expert repairman in doing some complex repair; when all the spares are exhausted, the repair team assigns an expert repairman to attend failed components; when the system breaks down due to a CCF’s occurrence, the repair team provides a very special repair service to restore the system to normal working state. The steady-state distribution of the system is obtained by matrix-analytic method. The sets of equations satisfied by the reliability functions and transient availabilities from arbitrary initial state are respectively presented and solved by Markov renewal theory, Laplace–Stieltjes transform (LST) and Laplace transform (LT) technique. Based on the obtained results, sensitivity analysis is performed by some numerical experiments. From economic view point, the bi-objective optimization problem is constructed and solved by NSGA-II algorithm for the minimal expected total cost and maximal availability.