Mixed Redundancy 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.

A novel importance measure considering multi-constraints for RAP optimization of 1-out-of-n subsystems with mixed redundancy strategy

Intelligent optimization algorithms are the mainstream approach to solving redundancy allocation problems (RAP) with challenging features. Since importance measures (IM) can identify critical components, the combination of IM-based local optimization and intelligent algorithms has wide applications in various optimization problems; however, it is less studied in RAP. Existing IMs also failed to address both the objective function and multiple constraints like cost and weight; this may result in an imprecise identification of critical subsystems for RAP optimization. This paper considers a RAP with a mixed strategy, i.e., active and standby strategies can be applied to a subsystem simultaneously. Two novel IMs are proposed based on a Lagrangian function: cost-centric RAP-based importance (CRI) and weight-centric RAP-based importance (WRI). CRI (WRI) reveals the comprehensive effect of cost (weight) consumption on the system reliability and other resources. A local optimization algorithm guided alternately by CRI and WRI is presented to adjust the redundancy level of subsystems; then, this algorithm is introduced into a genetic algorithm (GA) to determine the component types and redundancy level of all subsystems. Compared with other algorithms and previous studies, the superiority of the proposed hybrid GA is demonstrated via numerical experiments and a well-known benchmark example.

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.

Lifetime Distribution for a Mixed Redundant System with Imperfect Switch and Components Having Phase–Type Time-to-Failure Distribution

Recently, a mixed redundancy was introduced among the redundant design strategies to achieve a more reliable system within the equivalent resources. This study deals with a lifetime distribution for a mixed redundant system with an imperfect fault detector/switch. The lifetime distribution model was formulated using a structured continuous Markov chain (CTMC) and considers the time-to-failure (TTF) distribution of a component as a phase-type distribution (PHD). The model’s versatility and practicality are enhanced because the PHD can represent diverse degradation patterns of the components exposed to varied operating environments. The model provides accurate reliability for a mixed redundant system by advancing the approximate reliability function suggested in previous studies. Furthermore, the model would be useful in system design and management because it provides information such as the nth moment of the system’s lifetime distribution. In numerical experiments on some examples, the mixed redundancy was confirmed to devise a more reliable system than the existing active and standby redundancies, and the improvement effect increased as the number of redundant components decreased. The optimal structure for maximizing the expected lifetime of the system changes depends on the reliability of the components and fault detector/switch.

Reliability analysis and optimization of multi-phased spaceflight with backup missions and mixed redundancy strategy

Reliability analysis and optimization of multi-phased spaceflight with backup missions and mixed redundancy strategy

A Q-learning guided search for developing a hybrid of mixed redundancy strategies to improve system reliability

A Q-learning guided search for developing a hybrid of mixed redundancy strategies to improve system reliability

Redundancy allocation under state‐dependent distributional uncertainty of component lifetimes

In this paper, we consider a redundancy allocation problem in a series‐parallel system with uncertain component lifetimes of multiple states, which involves multitype components and mixed redundancy strategy. We develop a distributionally robust redundancy allocation model using state‐dependent ambiguity set, which describes the mean, expected cross‐deviation, and the support conditional on each state of the component lifetime distribution. Our structural analysis of the worst‐case system reliability function identifies a concave equivalent for the conditional worst‐case reliability function in each state and achieves an averaged finite piece‐wise affine representation for the overall worst‐case system reliability function, which enjoys valuable operational insights for reliability evaluation and scalable optimization of the redundancy designs. Furthermore, we analyze the reliability guarantees for the worst‐case reliability in optimality under possible misspecification of ambiguity‐set parameters, which admit the structure of “Reliability Target + Target Surplus + Estimated Elasticity,” and insightfully imply that the auxiliary dual variables obtained via solving the design problem can be regarded as the scale of elasticity. Computationally, the redundancy design problem can be linearized and reformulated as a mixed 0–1 second‐order cone program. Exploiting the above finite piece‐wise affine structure of the worst‐case reliability function, the design problem also admits a practical iterative decomposition scheme with finite convergence, which is more scalable especially for the possible situations of large number of states in practice. Finally, numerical experiments including a case with real‐life data of braking system components well justify the value of state information incorporated by our model in producing favorable cost‐effective redundancy designs for reliability operations.

A new dynamic model to optimize the reliability of the series-parallel systems under warm standby components

<p style='text-indent:20px;'>Redundancy allocation problem (RAP) is a common technique for increasing the reliability of systems. In this paper, a new model for the RAP is introduced that takes into account the warm standby and mixed strategy, the model dynamics, and the type of the strategy in redundancy allocation problems. A recursive formula is first obtained for the reliability function in the dynamic warm standby and mixed redundancy strategies that leverages the success mode analysis and works for any arbitrary failure-time distribution. Failure rates for warm standby units change before and after their replacement with a damaged unit, and, therefore, the reliability function in warm standby varies with time (i.e., the model is dynamic). Although dynamic models are commonplace in practice, they are more challenging to assess than static models, which have been mainly considered in the literature. An optimization problem is then formulated to select the best redundancy strategy and redundancy levels. Genetic algorithm and particle swarm optimization are leveraged to solve the problem. Finally, the efficiency of the presented method is verified through a numerical example. The experimental results verify that the proposed model for RAP significantly improves the system reliability, which can be of vital importance for system designers.</p>

Assessing the sufficiency indicators of a set of spare parts, tools and accessories for uninterruptible power supplies of a data centre using data sheet specifications

Aim. To suggest a method of estimating the parameters of a set of spare parts, tools and accessories (SPTA) according to data sheet specifications for industrial uninterruptible powers supplies (UPS) of data centres using state-of-the-art techniques. Methods. The paper uses methods of the dependability theory, the Markov process theory and the optimisation method. Results. Using the suggested approach, the stages of parametric synthesis of an SPTA kit were defined for mainline modular UPS that feature redundancy with repair and limited SPTA. For each stage, the application of mathematical models required for calculating the dependability characteristics and parameters of power module components based on UPS dependability indicators is substantiated along with the mathematical models that associate the sufficiency indicators of an SPTA kit with its parameters. Those models allow calculating the failure and recovery rates of UPS power modules, as well as the mean time to failure and restoration based on the data sheet specifications of reliability, maintainability and availability. In turn, the obtained dependability characteristics are the input data for calculating the SPTA sufficiency values (average delay in meeting a request). Using the value of average delay in meeting a request with an SPTA kit as a criterion for the mean time to power module restoration allows suggesting that it is, in principle, possible to ensure the specified dependability indicators in the course of its operation, and, therefore, such UPS can be used. Should the latter be possible, then using the value of average delay in meeting a request as a restriction, while taking into account the restrictions on the initial SPTA inventory, will allow synthesising the SPTA kit (select a replenishment strategy and define its parameters (delivery time, etc.). Comparing the logistical capabilities and the resulting data for the selected replenishment strategy will allow making a final conclusion regarding the capability to maintain the specified UPS dependability characteristics throughout the operation period. Using the above method, the parameters were synthesised of a single kit of spare parts, tools and accessories, using the Protect 3.M UPS as an example. Conclusion. The approach suggested in the paper allows estimating both the general feasibility of ensuring the specified dependability, and the economic expediency of using industrial mainline modular UPS with redundancy and recovery. Additionally, if ensuring the UPS dependability is possible, but the operating costs of its maintenance are unacceptable, the possibility of reducing the number of repair teams (reducing the cost of their deployment) and/or using more efficient redundancy methods (mixed redundancy, mixed redundancy with rotation, etc.) should be evaluated. However, it should be taken into consideration that the proposed approach based on the use of mathematical models does not guarantee a 100% accuracy of SPTA parameter estimation, as the mathematical models that it uses, like any other models, have a limited accuracy and the results obtained with their help require experimental confirmation by means of testing or controlled operation.

A novel general model for RAP and RRAP optimization of k-out-of-n:G systems with mixed redundancy strategy

A novel general reliability model optimization model based on mixed redundancy strategy is proposed for k-out-of-n:G subsystems. In this model, the minimum required component for subsystem operation k is involved as a variable to adapt to general situations, and the redundancy strategy is considered to be a decision variable that any one of strategies (active, cold-standby or mixed) can be selected for each subsystem. To improve modeling accuracy and reduce complexity, the system reliability function is established by using continuous-time Markov chain. A pseudo-parallel genetic algorithm (PPGA) is designed for redundancy allocation problem (RAP) and reliability–redundancy allocation problem (RRAP) optimization. To verify the proposed model and the designed algorithm, numerical analysis for four typical benchmark test problems were performed. The comparisons of the proposed new model with the models under the choice of redundancy strategies based on lower bound formulation (LBF), as well as based on Markov method, for each benchmark problem show that the proposed model can provide higher reliability than previous models. The results of the algorithm performance comparison show that the designed PPGA can not only search for the optimal reliability for RAP and RRAP, but also has the advantage of fast convergence.

Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure

In this paper, a three components repairable system under K-mixed redundancy strategy with unreliable switching failure is proposed, in which the lifetimes of components, the repair time of failure components and the vacation time are distributed with different phase-type (PH) distributions. The multiple vacation policy of the repairman is adopted so that the human resources can be fully utilized. The proposed repairable system model is studied in both transient and stationary regimes with matrix-analytic method. Some reliability indexes are obtained by employing Kronecker operator theory and aggregated stochastic theory. Finally, a numerical example and a comparison analysis between K-mixed redundancy strategy model and mixed redundancy strategy model are implemented to illustrate the results obtained in the paper.

A Markovian analytical approach to a repairable system under the mixed redundancy strategy with a repairman

AbstractThe mixed redundancy strategy is one of the most powerful techniques for improving system performance. This novel strategy has, however, been mostly studied in non‐repairable redundant systems, while the present study aims to study, for the first time, its application to a repairable system with a repairman in availability and maintainability perspectives. In this system, a repairman is responsible for providing the repair services. The intended system simultaneously benefits from the repairman's vacation concept following different policies, namely: vacation interruption and multiple vacations. Moreover, the system consists of two types of repairs, specifically: regular and working vacation repair. Also, successive vacation times are governed by the Markovian arrival process. Accordingly, the system is analyzed by modeling a vector‐valued Markov process and several performance measures are derived in both transient and stationary regimes following the matrix‐analytic procedure. Finally, the performance of the proposed approach is verified using numerical examples that involve a system with three repairable non‐identical components under the mixed strategy as well as a micro‐grid system with three parallel subsystems as a real‐life case study.

A new model for the reliability-redundancy allocation problem with the mixed redundancy strategy

In this paper, the reliability-redundancy allocation problem with the mixed redundancy strategy is revisited to develop a new model that can be beneficially exploited to estimate exact reliability values. The model is capable of not only optimally calculating reliability values in a very short time but also choosing the best strategy for each subsystem from among active, standby, and mixed strategies. In previous studies, reliability calculation for the mixed strategy had been accomplished using a lower bound formulation that was sophisticated, time-consuming, and approximate. The proposed model is developed based on a continuous-time Markov chain model. It is applied to three famous benchmark tests that are subsequently solved using a powerful evolutionary algorithm called the water cycle algorithm. Computational results confirm the robustness and superiority of this new model over previous ones in calculating reliability. Besides, the proposed algorithm outperforms the previous ones in finding good results.

Condition-based optimization of non-identical inspection intervals for a k-out-of-n load sharing system with hybrid mixed redundancy strategy

This paper aims to minimize the expected daily inspection cost of a k-out-of-n load-sharing system with identical components. We consider a hybrid mixed-redundancy strategy for the components’ utilization at the beginning of each inspection interval when failed components are replaced by standbys using an imperfect switch. The number of active components at the beginning of inspection intervals as well as the duration of inspection intervals are varying, and depend on the number of available components. The components are assumed identical with a constant failure rate, which implies the components’ distribution function is exponential. We optimize both the number of active components at the beginning of each interval and the duration of the inspection intervals to minimize the system’s expected daily cost (SEDC). The SEDC has four components: the system’s inspection cost, the components’ repair cost, the system’s repair cost, and the system’s downtime cost. A new heuristic algorithm is used to optimize the model. Due to the model’s complexity, a genetic algorithm is suggested for large-size problems. The results show the model decreases the SEDC by a maximum of 64.89% compared to other existing strategies with fixed inspection intervals.

Optimal component sequence in heterogeneous 1-out-of-N mixed RRAPs

The present study revisits the reliability-redundancy allocation problem (RRAP), as the most important problem in the design phase of complex systems. It is investigated with heterogeneous components allowed, which makes it formidable to find the optimal component sequence in each subsystem. Furthermore, a mixed redundancy strategy is applied to subsystems whose reliability requires complicated and time-consuming calculations to determine. A Markov-based model is developed to address both these issues at a low computation cost. Finally, the proposed approach is implemented on two famous benchmark test problems. Results demonstrate that, compared to the previously reported solutions, the proposed approach yields much better structures with higher reliability values without increasing the cost or volume of the systems.

A novel component mixing and mixed redundancy strategy for reliability optimization

A novel component mixing and mixed redundancy strategy for reliability optimization

An exact algorithm for the redundancy allocation problem with heterogeneous components under the mixed redundancy strategy

The redundancy allocation problem (RAP) is one of the most commonly used approaches for improving the reliability of systems. The present study investigates the most recent variant of RAP, namely, the RAP with heterogeneous components under the mixed redundancy strategy. An exact branch-and-price (BP) algorithm is proposed for the problem that solves in less than one CPU second all the benchmark instances reported in the literature. The algorithm is not only the first exact one proposed for the RAP with a mixed strategy but also the first application of the BP algorithm in the literature of reliability optimization problems. The proposed BP algorithm is also capable of solving other variants of RAP, including RAPs with either an active or a standby strategy, making it possible to investigate the advantages of the mixed strategy over the active and standby strategies. Finally, a new set of instances is generated to evaluate the performance of the proposed algorithm in dealing with more challenging instances.

Bi-objective sequence optimization in reliability problems with a matrix-analytic approach

The redundancy allocation problem (RAP) is an intriguing area in the field of reliability optimization to which a lot of research has been devoted in recent years. In this paper, a bi-objective model is developed for RAP with a heterogeneous backup scheme and a mixed redundancy strategy. Elimination of the lower bound estimation and the exact calculation of the reliability of the mixed strategy forms one of the most striking features of the proposed model. Investigating the optimal sequence of components in each subsystem, the study modifies a non-dominated sorting genetic algorithm (NSGA-II), as a powerful multi-objective evolutionary one, to solve the proposed bi-objective model. Two numerical examples will then be used to verify the efficiency of the model in achieving enhanced system reliability. Finally, the results of Pareto optimal set are used to demonstrate that the assumptions made enable the proposed model to improve system reliability by offering various structures while simultaneously considering system limitations.

Inspection interval optimization for a k-out-of-n load sharing system under a hybrid mixed redundancy strategy

In this paper, we optimize the periodic inspection interval for a k-out-of-n load sharing system with a mixed redundancy strategy in which the components are identical. The system is inspected at fixed intervals. If the system has any failed components, they will be detected at the end of the inspection interval. The components will be sent for repair at the beginning of the next inspection interval and will be available at the end of the interval. We assume the component's repair time is less than the inspection interval. Similarly, if the system fails to work during an inspection interval, it will be detected at the end of the interval. In the proposed hybrid mixed redundancy strategy, the system starts working with any number of components between k and n, depending on the number of the available components at the beginning of the inspection interval. We consider replacing the failed component with a new one from the standby queue using an imperfect discrete switch. Moreover, after a component's failure, its load will be shared among the remaining components, which causes an increase in their failure rates. The presented work aims to find the optimal total expected system cost per unit time by determining the number of working components at the beginning of each time interval and the inspection interval. The expected total system cost consists of the system's inspection cost, components' repair cost, system's downtime cost, and repair cost. The presented problem is solved with a full enumeration method and a new heuristic algorithm. The results show the superiority of the presented mixed redundancy strategy in comparison with the traditional strategies. Moreover, the proposed heuristic algorithm performs better in terms of computational time (up to one percent) compared to the full enumeration techniques.

Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies and heterogeneous components: Erlang time-to-failure distribution

The redundancy allocation problem (RAP) of non-repairable series-parallel systems considering cold standby components and imperfect switching mechanism has been traditionally formulated with the objective of maximizing a lower bound on system reliability instead of exact system reliability. This objective function has been considered due to the difficulty of determining a closed-form expression for the system reliability equation. But, the solution that maximizes the lower bound for system reliability does not necessarily maximize exact system reliability and thus, the obtained system reliability may be far from the optimal reliability. This article attempts to overcome the mentioned drawback. Under the assumption that component time-to-failure is distributed according to an Erlang distribution and switch time-to-failure is exponentially distributed, a closed-form expression for the subsystem cold standby reliability equation is derived by solving an integrodifference equation. A semi-analytical expression is also derived for the reliability equation of a subsystem with mixed redundancy strategy. The accuracy and the correctness of the derived equations are validated analytically. Using these equations, the RAP of non-repairable series-parallel systems with a choice of redundancy strategies is formulated. The proposed mathematical model maximizes exact system reliability at mission time given system design constraints. Unlike most of the previous formulations, the possibility of using heterogeneous components in each subsystem is provided so that the active components can be of one type and the standby ones of the other. The results of an illustrative example demonstrate the high performance of the proposed model in determining optimal design configuration and increasing system reliability.