Warm Standby Research Articles

Consecutive-type Reliability Structures Under Warm Standby Redundancy: Some Advances

In the present article, we investigate two different reliability structures, which belong to the class of consecutive-type systems under redundancy policy. The resulting structures consist of n independent components, but they also dispose warm standby ones. The distribution of the number of working warm components at the time of system’s failure is studied in some detail. Among others, explicit expressions for determining the corresponding probability mass function are established. A short discussion for future work is also developed.

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.

Bayesian inference for reliability of K-out-of-N: G repairable retrial systems with mixed standbys, switching failure and reboot delay

Existing reliability studies on K-out-of-N: G repairable retrial systems with mixed standbys mainly consider the case where the standby switching is completely reliable and the repair time follows an exponential distribution, and most of them directly analyze the system reliability indices based on probability theory. Given the existence of such phenomenon as standby switching failure in engineering, this paper proposes a novel reliability model of K-out-of-N: G repairable retrial system with switching failure, and performs statistical inference on the reliability to realize the modeling and evaluation of the system. The considered system consists of mixed standbys and a repairer with vacation. When an operating component fails, the warm standby one is switched to the operating one immediately, and the probability of switching failure during the switchover process is p. In the case where the repair time of failed components follows a general distribution, based on the supplementary variable method and recursive algorithm, the steps for calculating the system steady-state availability are presented. In the case of unknown parameters for repair time and retrial time, the Bayesian estimator of the steady-state availability under the squared error loss function and highest posterior density (HPD) confidence interval are obtained. In numerical simulation, the system reliability inference is realized by using the Monte Carlo (MC) method, and the validity of the inference method is analyzed.

Availability Evaluation of Warm Standby System with Fault Detection Delay and General Repair Times

This study analyzed the availability of a warm standby system that works with fault detection delay and general repair times. The time-to-detection delay is also considered as exponentially distributed. The detection state is used to detect the faults in the failed unit. The steady state availability of the system is obtained by using supplementary variable technique. Three types of repair time distributions are compared to find the best one.

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.

Vacation Policy for k-out-of-n Redundant System with Reboot Delay

Redundancy is a well-known concept for system resilience; k-out-of-n redundancy stipulates that a minimum number of functional components must be present for the system to function. Introducing a reboot delay acknowledges the temporal complexities of system recovery after a failure. A dynamic component is added by the vacation policy, which introduces strategic downtime for system components. This work predicts the performance measures of a multi-state system consisting of two subsystems A and B. Subsystem A follows the k-out-of-n: F policy and subsystem B has m working units and s warm standby units. The system is under the consideration of a single unreliable repairman who may go allow for vacation. There are two possibilities for a repairman’s vacation: if the system failed and the repairman is on vacation, in that case, if the repairman immediately returns from vacation, he/ she repairs the system but if the repairman does not return immediately from vacation, then the system takes a reboot action and when the repairman available, he/ she repairs the system. Failure and repair time of the units are expected to pursue an exponential distribution. In addition, the vacation time and reboot time regarding the failure of the units also pursue an exponential distribution. The concept of reboot and repairman’s vacation are incorporated to make the model more practical and versatile. The expressions for several performance measures such as availability, reliability, and MTTF are obtained with the help of the Markov process. Likewise, sensitivity analysis is done to study the impact of various parameters on system performance measures. The results are explained by taking numerical illustrations.

A Condition-Based Maintenance Policy Considering Batch Sizes for Warm Standby Systems With Priority to Repair

A Condition-Based Maintenance Policy Considering Batch Sizes for Warm Standby Systems With Priority to Repair

Sensitivity analysis of Non-Markovian repairable systems with warm standby system

Sensitivity analysis of Non-Markovian repairable systems with warm standby system

Redundancy Optimization for a System Comprising One Operative Unit and N Warm Standby Units with Switching Time

Redundancy Optimization for a System Comprising One Operative Unit and N Warm Standby Units with Switching Time

Optimizing dynamic performance of phased-mission systems with a common bus and warm standby elements

Optimizing dynamic performance of phased-mission systems with a common bus and warm standby elements

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.

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.

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.

Sensitivity Analysis for a Redundant System with Random Inspection and R Repairmen Under Repair Pressure

This study examines a repairable K -out-of- N + W : G system with warm standby components and R repairmen, where common cause failure (CCF), random inspection, and a repair pressure coefficient are involved. Due to the typical non-self-announcement of the standby component’s failure, performing a random inspection on warm standby components is necessary to find whether there are failed standby components. When the number of failed components is larger than R (heavy loading occurs), all the repairmen increase their repair rates under a repair pressure coefficient to reduce the waiting queue and enhance the reliability and availability of the system. By adopting a matrix-analytic method and Markov renewal theory, this study provides the steady-state distribution and some reliability indices mean time to first failure time (MTTFF) and reliability function from the arbitrary initial state. By some numerical experiments, sensitivity analysis is finally given to show the effect of the system parameters on some performance measures.

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>

Reliability analysis of N-policy vacation based FTC system subject to standby switching failures

The paper is aimed to investigate the reliability metrics of a multi-unit fault-tolerant control (FTC) system wherein the units are subject to failure and those are repairable by two heterogeneous servers. Server 1 remains permanently available for essential service of failed units, whereas server 2 goes on vacation and renders service based on the N-policy threshold, which may also provide optional and essential services. Server 1 may break down at a steady rate during its servicing period but immediately gets repaired and resume servicing the failed units. When the working unit fails, the available warm standby unit holds responsibility for the smooth operation of the system. The transition of standby units to operational mode may be unsuccessful with switching failure probability. We develop a Markovian model to obtain the steady-state probabilities. We explore computational and sensitivity analysis of different performance measures for various variability of the parameters

Reliability analysis of redundant retrial machining system subject to standby switching failure

ABSTRACT With the rapid development of the Internet and hardware, cloud computing has been widely applied in various industries. Supporting services using high-quality and reliable communications equipment with an effective repair system is essential. A potential application of a cloud computing system for online data analysis services with multiple virtual machines is presented herein. The primary and standby virtual machines are both assumed to be unreliable. In this study, we analyze a retrial machine repair system with warm standbys and switching failure. When the repair facility is inaccessible, the failed machine joins a retrial pool and tries to access the repair service after a random period. The Laplace transform technique and matrix-analytical method are employed to derive the system performance measures of the reliability and mean time to failure. Moreover, numerical results are provided to investigate the effects of system parameters on system performances.

Availability and cost-benefit evaluation for a repairable retrial system with warm standbys and priority

This paper investigates a warm standby repairable retrial system with two types of components and a single repairman, where type 1 components have priority over type 2 in use. Failure and repair times for each type of component are assumed to be exponential distributions. The retrial feature is considered and the retrial time of each failed component is exponentially distributed. By using Markov process theory and matrix-analytic method, the system steady-state probabilities are derived, and the system steady-state availability and some steady-state performance indices are obtained. Using the Bayesian approach, the system parameters can be estimated. The cost-benefit ratio function of the system is constructed based on the failed components and repairman's states. Numerical experiments are given to evaluate the effect of each parameter on the system steady-state availability and optimize the system cost-benefit ratio with repair rate as a decision variable.

Reliability and Sensitivity Analyses of an Unreliable Retrial Machine Repair System with Warm Standby Switching Failure

In this study, an unreliable machine repair system with warm standby switching failure and retrial behavior is examined. An application of the Ceph storage cluster system is described to illustrate the applicability of the proposed model and establish its results. To analyze the reliability of the application system, two-state-transition rate diagrams and their associated differential-difference equations are provided. Laplace transforms and the matrix-analytical method are employed to obtain the steady-state probabilities. Explicit expressions for the reliability function, mean time to failure, and steady-state availability of the examined system are then derived. With these system performance measures, we perform a sensitivity analysis of the system parameters to identify critical variables. Furthermore, the numerical results for various parameter settings are tabulated and presented graphically. Finally, managerial insights and constructive results are provided as a guide for managers in determining an effective strategy for performance enhancement.