Warm Standby Research Articles

Optimizing Costs in a Reliability System under Markovian Arrival of Failures and Reposition by K-Policy Inspection

This paper presents an N warm standby system under shocks and inspections governed by Markovian arrival processes. The inspections detect the number of down units, and their replacement is carried out if there are a minimum K of failed units. This is a policy of the type (K,N) used in inventory theory. The study is performed via the up and down periods of the system (cycle); the distribution of these random times and the expected costs for each period comprising the cycle are determined on the basis of individual costs due to maintenance actions (per inspection and replacement of every unit) and others due to operation or inactivity of the system, per time unit. Intermediate addressed calculus are the distributions of the number of inspections by cycle and the expected cost involving every inspection, depending on the number of replaced units. The system is studied in transient and stationary regimes, and some reliability measures of interest and the cost rate are calculated. An optimization of these quantities is performed in terms of the number K in a numerical example. This general model extends to many others in the literature, and, by using the matrix-analytic method, compact and algorithmic expressions are achieved, facilitating its potential application.

Availability and Reliability Analysis of a k-Out-of-n Warm Standby System with Common-Cause Failure and Fuzzy Failure and Repair Rates

In the real life, there exists limited information or uncertainty in knowledge about failure and repair rates which follow one of the standard distributions as exponential distribution and Weibull distribution with some parameters. We suppose that these parameters are fuzzy which allow one to specify a system design for a “worst-case scenario.” In this paper, the fuzzy availability and the fuzzy reliability of a redundant repairable parallel k-out-of-n warm standby system with common-cause failure are evaluated. We assume that the failure time of each operating unit or warm standby unit follows Weibull distribution with two fuzzy parameters and the repair time of any failed unit follows exponential distribution with one fuzzy parameter. Each fuzzy parameter is represented by triangular membership function estimated from statistical data taken from random samples of each unit. Also, we give a numerical example for a fuzzy repairable parallel 3-out-of-5 warm standby system with two active and three warm standby units to get analytically and represent graphically the fuzzy availability and reliability function of this fuzzy system.

Exploiting Performance Analysis of Redundant System (KM+1S)

The present investigation seeks the steady state availability, reliability and mean time to failure of the 1-out-of (k + 1): G redundant system. A system having k active units (kM) and one unit (1S) as a warm standby redundancy have considered. The effects of various parameters on reliability measures have been analyzed by deriving two models. Model I is designed as a reliability model and Model II for steady state availability. The assumptions have been made that the detected faults in the redundant system is covered imperfectly. The Markov process, supplementary variable technique, Laplace transformation are adopted to determine the transient behavior of the system. Presented results based on numerical data to demonstrate the practical utilization of the developed models. This study is very helpful for the engineers to design a highly reliable redundant system with high profit in the industry.

Optimal periodic switching strategy for a two‐unit warm standby degradation system

AbstractIn the traditional switching policy of a standby system, the standby unit is switched to the normal operation state only after the active unit fails. In contrast, in satellite engineering, a new periodic switching strategy is used by technicians in the satellite gyroscope standby system. Due to the performance degradation of the gyroscope in the long‐term operation and standby process, satellites may fail on orbit. For this problem, an operation optimization model is established for a two‐unit warm standby degradation system considering the periodic switching strategy. First, the degradation process of the units is described by a multiphase Wiener process. Second, based on the first‐hitting time theory, the analytic expressions of reliability and mean time to failure (MTTF) of the degradation system are derived. Third, the optimal periodic switching interval is determined to maximize the system MTTF by using the particle swarm optimization algorithm (PSO). Finally, a numerical example of a gyroscope warm standby subsystem is provided to validate the proposed model.

Architecture Design and Reliability Evaluation of a Novel Software-Defined Train Control System

Communication-based train control (CBTC) has been the prevailing technology of the urban transit signaling system. However, CBTC also faces a few issues to extend and maintain because of its complicated structure. This paper presents a novel urban transit signaling system architecture, software-defined train control (SDTC), which is based on cloud and high-speed wireless communication technology. The core functions of the proposed SDTC, including the onboard controller, are implemented in the cloud platform, with only sensors and input–output (IO) units remaining on the trackside and the train. Because of the scalable framework, the system function can be expanded according to the user’s demand, making signaling as a service possible. With warm standby server redundancy, SDTC has better reliability. Compared with the traditional CBTC architecture, the mean time between failures is improved by 39% by calculating typical project parameters by the Markov model based on some assumptions.

Operation optimization model for warm standby system based on nonperiodic and imperfect multiple active switching policy

Traditional standby system models predominantly assume that a standby unit is activated only after an active unit fails. However, a periodic active switching policy is adopted for some critical subsystems of on-orbit satellites. For this problem, an operation optimization model for warm standby systems under multiple active switching is studied. First, the multiple active switching processes of the warm standby system are described, and virtual age theory is introduced to analyse the lifetime distributions of the unit in different states. Next, since switching does not always occur perfectly, analytical expressions of the system reliability and mean time-to-failure (MTTF) are derived for the warm standby system under nonperiodic, imperfect multiple active switching, which can be applied to units or systems with arbitrary time-to-failure distributions. Furthermore, by maximizing the MTTF of the warm standby system, the corresponding nonperiodic or periodic switching intervals can be determined by the genetic algorithm (GA). Finally, a numerical example of a gyroscope warm standby system following the Weibull distribution is provided to verify the model applicability, and sensitivity analyses of related parameters are performed to identify useful conclusions.

Optimal sequencing of elements activation in 1-out-of-n warm standby system with storage

Despite the rich body of research on reliability analysis and optimization of warm standby systems, the existing works have mostly failed to consider the practical storage component of such systems. This paper advances the state of the art by modeling and optimizing the reliability of a 1-out-of-n warm standby system with product storage, characterized by a maximum capacity, and specific uploading and downloading paces constraints. The storage may accumulate surplus product when the performance of the operating element exceeds the demand and compensate product deficiency otherwise. A numerical algorithm based on the probabilistic model is first proposed to evaluate the reliability or success probability of the system mission (MSP) that must satisfy a pre-specified demand during a required mission time. As a further contribution, the optimal element activation sequence problem is formulated and solved to maximize the mission success probability. Influences of several model parameters (storage capacity, demand, mission time, element reliability, and storage uploading/downloading pace constraints) on the MSP and optimization solutions are investigated through an example of a power system.

Performance of batch service queue model with second optional service, repairable breakdown and standby server

In this paper, we investigate the performance of batch service queue model with second optional service, repairable breakdown and warm standby server. Both primary operating and warm standby servers provide First Essential Service (FES) and Second Optional Service (SOS) to customers, wherein FES is all arriving customers and only some of them may further request the SOS. The service times, failure times and repair times of both primary operating and warm standby server are assumed to follow exponential distributions. We use Runge-Kutta method to obtain the transient state probabilities and matrix-decomposition method to obtain the steady-state probabilities of the model. Also, a cost model is presented to determine the optimal service rates so that the expected cost is minimised. Finally, the effect of the model parameters on the system behaviour is demonstrated through numerical results and discussions.

Minimum cost replacement and maintenance scheduling in dual-dissimilar-unit standby systems

Recent studies have shown that reusing standby elements during the mission may improve the mission success probability significantly. However, such a benefit cannot be effectively achieved without a careful design of the replacement and maintenance schedule (RMS), which determines work period durations of operating elements and types of maintenance performed for idle elements. This paper makes contributions by modeling and optimizing the RMS for a heterogeneous dual-unit warm standby system with the aim to minimize the total expected mission cost, covering operation, standby and maintenance costs as well as mission failure penalty cost. The two system elements are dissimilar, characterized by different performance, failure time distribution and cost parameters. For a successful mission, a specified amount of work must be accomplished before both elements become failed or unavailable. We propose a new probabilistic model-based methodology for assessing the mission success probability and expected mission cost (EMC) of the considered system. An optimization problem is further formulated and solved to find the optimal RMS minimizing the EMC. A case study of a two-pump oil transfer system is conducted to demonstrate the proposed model and effects of different cost parameters on the optimal RMS solution and corresponding mission success probability and EMC.

Reliability evaluation of demand-based warm standby systems with capacity storage

Warm standby is an energy-saving redundancy technique that consumes less energy than a conventional hot standby method. It can be naturally integrated with an energy storage technique to enhance system reliability. However, the integration approach of both techniques and the advantage it affords to system reliability have not been reported in literature. This study resolves this limitation by formulating a novel reliability model for demand-based warm standby systems with capacity storage. In this model, the chronological characteristics of warm standby components are explicitly explored before and after their activation. Moreover, different utilization sequences of warm standby components and storage components are embedded to analyze the effects of these sequences on system reliability. A multi-valued decision diagram is developed to evaluate system reliability considering successful activation probabilities of warm standby components. This diagram is applicable to arbitrary component lifetime distributions and warm standby systems. Numerical examples are presented to verify the application of the proposed methodology.

Influence of storage on mission success probability of m-out-of-n standby systems with reusable elements

Recent studies have shown that elements reusing through preventive replacements is beneficial in enhancing the mission success probability (MSP) of standby systems. While storage is often an essential unit for system functions, none of the existing works on standby systems with reusable elements have considered this unit in the system modeling and analysis. We make contributions by modeling and optimizing a m-out-of-n standby system with reusable elements and an imperfect storage unit. The system performs a mission task that must satisfy a pre-specified demand during the mission time. Surplus product produced by operating elements is stored; in the case of not meeting the demand, the storage unit, if available, supplies the saved product to compensate the deficiency. All the system elements, during their idle time, may undergo different types of actions including staying in the warm standby mode, being protected, undergoing imperfect or perfect maintenance. A probabilistic modeling approach is first proposed for assessing the MSP of the considered system. The optimal operation and maintenance schedule (OMS) problem is then formulated and solved, which determines the OMS maximizing the MSP. A case study on a standby power generation system is provided to demonstrate influences of several storage parameters (storage capacity, storage reliability, and storage activation procedure reliability) on the MSP and optimized OMS solutions.

Optimal multiple replacement and maintenance scheduling in two-unit systems

This paper models and optimizes the replacement and maintenance schedule (RMS) for a heterogeneous two-unit standby system. The system must accomplish a specified amount of work for a successful mission. When one unit executes the specified mission task, the other unit undergoes a certain type of maintenance based on the RMS, followed by staying in a warm standby mode if its next activation time is not up. The mission fails if both units fail before the task completion, or if one unit fails while the other one undergoes maintenance and thus is not ready to be activated and take over the task timely. A probabilistic model-based method is proposed to evaluate the mission success probability (MSP) of the considered system that may undergo multiple preventive replacements and different types of maintenance actions during the mission. The optimal RMS problem is then formulated and solved, which determines durations of operation periods of the activated unit and types of maintenance actions performed by the inactivated unit during its idle time for maximizing the MSP. A detailed case study on an oil transfer system with two heterogeneous pumps is provided to illustrate the proposed methodology and influences of multiple model parameters on the optimal RMS and corresponding MSP.

Operation strategy optimization for on-orbit satellite subsystems considering multiple active switching

To improve the reliability of satellites, there are many standby configurations in the key subsystems. Concerning the on-orbit operation of standby systems, the standby units usually switch to the operating state after the active units fail. However, a periodic switching strategy differing from this common strategy is employed for the gyroscope warm standby system of satellite in engineering. For this problem, a multiple active switching policy for standby units is considered, and the on-orbit operation strategy optimization problem is studied. First, the multiple active switching process of the gyroscope warm standby system and the virtual age theory are described. Second, under the imperfect and non-periodic multiple active switching strategy, the reliability function and mean time to failure (MTTF) of the warm standby system are derived based on the binary decision diagram (BDD) with units following arbitrary lifetime distributions. Furthermore, an operation optimization model is proposed by maximizing the MTTF of the warm standby system to obtain the optimal switching numbers and corresponding time points. Finally, a numerical example of the gyroscope warm standby system under the Weibull distribution is presented to show the application of the model, and a sensitivity analysis is carried out to identify the useful conclusions.

Availability and reliability analysis of a retrial system with warm standbys and second optional repair service

This article deals with availability and reliability characteristics for a repairable fault-tolerant system with warm standbys and second optional repair service. The failure times of primary components and warm standby ones are assumed to be exponentially distributed, and the failed components can be repaired by a repairman. For each failed component, the repairman provides two phases of repair service. All the failed components need the first essential repair, whereas only part of them demand the second optional repair. By using Markov theory and solving Matrix equation satisfied by the steady-state probabilities of the system, we present the steady-state availability of the system. By using Laplace transform method, we obtain the reliability function and the mean time to first failure of the system. Numerical examples are given to make research of the effect of the system parameters on the reliability function, steady-state availability and MTTF.

Joint optimization of mission abort and component switching policies for multistate warm standby systems

Safety-critical systems have been widely applied in various practical engineering fields to perform specific missions. Failures of such systems will lead to significant damage, thus, mission abort polices can be implemented to enhance system survivability. Warm standby is one of the most commonly used techniques in mission-critical and safety-critical systems to reduce failure risk during mission execution. Switching between working component and standby component is a feasible way to balance component degradation and extend system lifetime. Motivated by these results, we propose a joint optimization model that captures both component switching and mission abort policies for multistate warm standby systems. The optimal component switching and mission abort policies based on component condition are obtained to balance the trade-off between mission success probability and system survivability and to minimize the long-run expected total economic loss. A numerical study of virtual machine system is conducted to demonstrate the proposed model and obtained results.

Availability and Comparison of Four Retrial Systems with Imperfect Coverage and General Repair Times

In various industries, system availability assessment has been extensively investigated. Particularly, a stable power supply system is essential and critical in many service systems such as communication networks, mass transit systems, data storage centers and product manufacturing processes, etc. When an unreliable power supply unit fails, the repair services may be unavailable and a random period of (retrial) time for contact and confirmation is needed. Thus, this paper compares four retrial power supply systems with general repair time, warm standby units, and imperfect coverage possibility. That is, the power generation equipment is assumed unreliable and may fail anytime. The steady-state probabilities and the associated availabilities of four retrial systems are derived explicitly. A comparative analysis of the availability and the cost-benefit ratio among four retrial systems is presented. The efficiencies of four considered retrial systems are sorted and the optimal retrial system is provided. Based on the calculated numerical results, the management insights for practical applications are also proposed for decision making.

Reliability analysis and state transfer scheduling optimization of degrading load-sharing system equipped with warm standby components

Standby redundancy can meet system safety requirements in industries with high reliability standards. To evaluate reliability of standby systems, failure dependency among components has to be considered especially when systems have load-sharing characteristics. In this paper, a reliability analysis and state transfer scheduling optimization framework is proposed for the load-sharing 1-out-of- N: G system equipped with M warm standby components and subject to continuous degradation process. First, the system reliability function considering multiple dependent components is derived in a recursive way. Then, a Monte Carlo method is developed and the closed Newton-Cotes quadrature rule is invoked for the system reliability quantification. Besides, likelihood functions are constructed based on the measurement information to estimate the model parameters of both active and standby components, whose degradation paths are modeled by the step-wise drifted Wiener processes. Finally, the system state transfer scheduling is optimized by the genetic algorithm to maximize the system reliability at mission time. The proposed methodology and its effectiveness are illustrated through a case study referring to a simplified aircraft hydraulic system.

Sensitivity Analysis of Data Center Electrical Infrastructures Considering Aspects of Dependability and Cost

In the last years, the demand and use of data center have increased greatly due to the services offered by them. There must be a concern with data centers to allow the infrastructure to be available most of the time. Considering this need, this work has the objective of conducting a sensitivity analysis in the electrical infrastructure of the data center, thus finding the most sensitive equipment, taking into account the availability, reliability and cost. After obtaining the most sensitive equipment, it applies warm standby and hot standby replication techniques. The present work makes use of a hybrid modeling approach that considers the advantages of Stochastic Petri Nets (SPN) and Reliability Block Diagrams (RBD) to evaluate the dependability and cost of equipment acquisition.

Reliability Optimization of a k-out-of-n Series-Parallel System with Warm Standby Components

Reliability Optimization of a k-out-of-n Series-Parallel System with Warm Standby Components

Cost analysis of a repairable warm standby k-out-of-n: G and 2-out-of-4: G systems in series configuration under catastrophic failure using copula repair

Cost analysis of a repairable warm standby k-out-of-n: G and 2-out-of-4: G systems in series configuration under catastrophic failure using copula repair