System Steady-state Availability Research Articles

Measuring in-service traction elevator reliability based on orthogonal defect classification and Markov analysis

To solve the challenge of accurate in-service traction elevator failure prediction, maintenance cycle and steady availability, a novel reliability model is proposed which combines orthogonal defect classification (ODC) and Markov analysis (MA). The elevator failure data are classified by the ODC method. Then, the failure rate and maintenance rate of the elevator parts are obtained based on triangular fuzzy theory. By analyzing the maintenance function of each part, the optimum maintenance cycle of the elevator is determined. Finally, the transient state and steady state equations are established by MA to determine the steady availability of elevators. A case study on elevator accidents and failure data is used to validate the effectiveness of the proposed method. The results show that the system steady state availability of elevators in the study was 0.9002.

Reliability analysis of a two-unit‏ ‏standby system under Marshall–Olkin dependency

PurposeOne of the common approaches to improve systems reliability is using standby redundancy. Although many works are available in the literature on the applications of standby redundancy, the system components are assumed to be independent of each other. But, in reality, the system components can be dependent on one another, causing the failure of each component to affect the failure rate of the remaining active components. In this paper, a standby two-unit system is considered, assuming a dependency between the switch and its associated active component.Design/methodology/approachThis paper assumes that the failures between the switch and its associated active component follow the Marshall–Olkin exponential bivariate exponential distribution. Then, the reliability analysis of the system is done using the continuous-time Markov chain method.FindingsThe derived equations application to determine the system steady-state availability, system reliability and sensitivity analysis on the mean time to failure is demonstrated using a numerical illustration.Originality/valueAll previous models assumed independency between the switch and the associated active unit in the standby redundancy approach. In this paper, the switch and its associated component are assumed to be dependent on each other.

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.

Availability modelling for periodically inspected systems under mixed maintenance policies

The availability of a periodic inspection system under mixed maintenance policies is studied in this paper. To accommodate the characteristic of multiple failure modes for complex systems, the system failures can be divided into two failure modes: hard failure and soft failure. When hard failure occurs, the corresponding corrective maintenance will be performed, taking a random time under the perfect maintenance policy; in contrast, if the soft failure is found, the corresponding preventive maintenance will be performed, taking a random time under the imperfect maintenance policy. The dynamic age setback model is adopted for imperfect maintenance, which can accurately reflect the fault characteristics of the degraded system. Then an analytical model for system steady state availability and instantaneous availability are derived. Moreover, the optimal method to maximize the system steady-state availability through adjusting the inspection interval is researched. According to the above research, the optimization of system unit time cost, preventive maintenance intervals and availability is researched. Finally, the developed approach is demonstrated by a numerical example.

Availability Analysis of Software Systems with Rejuvenation and Checkpointing

In software reliability engineering, software-rejuvenation and -checkpointing techniques are widely used for enhancing system reliability and strengthening data protection. In this paper, a stochastic framework composed of a composite stochastic Petri reward net and its resulting non-Markovian availability model is presented to capture the dynamic behavior of an operational software system in which time-based software rejuvenation and checkpointing are both aperiodically conducted. In particular, apart from the software-aging problem that may cause the system to fail, human-error factors (i.e., a system operator’s misoperations) during checkpointing are also considered. To solve the stationary solution of the non-Markovian availability model, which is derived on the basis of the reachability graph of stochastic Petri reward nets and is actually not one of the trivial stochastic models such as the semi-Markov process and the Markov regenerative process, the phase-expansion approach is considered. In numerical experiments, we illustrate steady-state system availability and find optimal software-rejuvenation policies that maximize steady-state system availability. The effects of human-error factors on both steady-state system availability and the optimal software-rejuvenation trigger timing are also evaluated. Numerical results showed that human errors during checkpointing both decreased system availability and brought a significant effect on the optimal rejuvenation-trigger timing, so that it should not be overlooked during system modeling.

Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility

We study a K-out-of-M+W+C: G mixed standby system with an unreliable repair facility, in which there are M primary operating components, W warm standby components and C cold standby components. The life times of primary components and warm components are assumed to be exponentially distributed random variables. The repair facility is performed preventive maintenance (PM) when it is idle, and it is subject to breakdowns when it repairs a failed component (called as active breakdowns). Upon arrival, a failed component is repaired immediately if the repair facility is found free, and the failed component enters a retrial orbit for seeking repair service after some time later if the repair facility is found busy, under PM, or under repair. By adopting a Markov process approach and solving equations of statistical equilibrium in matrix form, we obtain the system steady-state availability of the machine system, the steady-state availability and the expected busy cycle of the repair facility. Furthermore, we obtain the reliability function and the mean time to the failure (MTTF) of the system by using Laplace transform method. Numerical examples are presented to show the effects of system parameters on the reliability function, steady-state availability and MTTF and to analyze the optimization problem of the cost-effectiveness ratio.

A phase expansion for non-Markovian availability models with time-based aperiodic rejuvenation and checkpointing

This paper presents a stochastic framework, consisting of stochastic reward net (SRN) for capturing the transient behaviors of the system and its related non-Markovian state transition diagram, to model an operational software system that undergoes aperiodic time-based rejuvenation and checkpointing schemes, and further to investigate whether there exists the optimal rejuvenation schedule that maximizes the system steady-state availability. A phase expansion approach is adopted to solve the non-Markovian availability models, which are actually neither the semi-Markov processes nor the Markov regenerative processes. Our numerical results show an appropriate rejuvenation trigger timing range, resulting in the positive improvement effect on the system availability of a database system, and that there exists the optimal rejuvenation trigger timing maximizing the system availability.

A computational method for finding the availability of opportunistically maintained multi-state systems with non-exponential distributions

Availability is one of the most important performance measures of a repairable system. Among various mathematical methods, the method of supplementary variables is an effective way of modeling the steady-state availability of systems governed by non-exponential distributions. However, when all the underlying probability distributions are non-exponential (e.g., Weibull), the corresponding state equations are difficult to solve. To overcome this challenge, a new method is proposed in this article to determine the steady-state availability of a multi-state repairable system, where all the state sojourn times, as well as the maintenance times, are generally distributed. As an indispensable step, the well-posedness and stability of the system’s state equations are illustrated and proved using C0 operator semigroup theory. Afterwards, based on the generalized Integral Mean Value Theorem, the expression for system steady-state availability is derived as a function of state probabilities. Then, the original problem is transformed into a system of linear equations that can be easily solved. A simulation study and an instance studied in the literature are used to demonstrate the applications of the proposed method in practice. These numerical examples illustrate that the proposed method provides a new computational tool for effectively evaluating the availability of a repairable system without relying on simulation.

Enhanced Markov-based model for the availability analysis of distributed software and hardware systems

Markov model for a simple two-host system used in determining the system availability of homogeneously distributed software and hardware systems is based on the concept of containing only hardware and software in each host. This system is found to be quite slow and tedious resulting to delays in computing system availability at a given time. Present research aim at stochastically analysing the availability of heterogeneously distributed software and hardware systems with software redundancy in standby, using an enhanced model to address the problem of low availability. The low availability is achieved through identifying the components responsible for mitigating the availability and define actions that can improve the availability of the systems. Markov method is used to develop expressions for system steady-state probabilities and system availability respectively. The model is implemented using Java programming language. To make the computation and analysis of systems availability more efficient, numerical examples are presented in order to illustrate the performance of the model.

A New Analytic Method of Multistate Single-component System Reliability Model

For the reliability modeling of multistate single-component system, single maintenance bench provides the preventive maintenance and alternative maintenance services on the basis of system performance level following the stochastic detection strategy. Phase-type distribution is employed in place of exponential distribution and other typical distributions to describe the stochastic time variable in the reliability modeling process in a unified manner. Through matrix analysis, the analytic expressions for reliability indicators including system steady-state availability, mean time between failures (MTBF) and failure rate of system are obtained. A numerical application is presented to verify the applicability of the model and demonstrate the influence of preventive maintenance threshold and preventive maintenance rate on system reliability.

A model of system limiting availability under imperfect maintenance

PurposeThe purpose of this paper is to explore the impact of the Kijima Type II imperfect repair model on the availability of repairable systems (RS). Since many individuals are interested in measuring the extent to which the system will be available after it has been run for a long time, the specific interest in this study is in the steady-state (limiting) availability behavior of such systems. Furthermore, the authors study the impact of age-based preventive maintenance (PM) on the RS performance.Design/methodology/approachBecause of the complexity of the underlying assumptions of the Kijima Type II model, the authors use simulation modeling to estimate the system availability. Based on preliminary simulation results, the availability function achieves a steady-state value greater than zero. The system steady-state availability is then estimated from the simulation output by computing the average of the availability estimates beyond the initial transient period. Next, the authors develop a meta-model to convert the system reliability and maintainability parameters into the coefficients of the limiting availability estimate without the simulation effort. Using a circumscribed central composite experimental design, the authors confirm the accuracy of the meta-model.FindingsThe results show that the meta-model is robust, and provides good estimates of the system limiting availability. Also, the authors find that when using a Kijima Type II model for a system repair process, age-based PM can improve the steady-state availability value. Therefore, an optimal age-based PM policy that maximizes the system’s steady-state availability can be identified.Originality/valueIn practice, it is important to study the system steady-state availability because many individuals, i.e. engineers, are more interested in measuring the extent to which the system will be available after it has been run for a long time. Therefore, this study represents a significant addition to the body of knowledge related to virtual age modeling, in that it incorporates a Kijima type II model and considers system steady-state availability.

Availability and maintenance modelling for systems subject to multiple failure modes

The availability and optimal maintenance policies of a competing-risk system undergoing periodic inspections are studied in this paper. Specifically, a repairable system with a working state and M failure modes is considered. Each failure mode has a random failure time. When the system fails from the ith(i=1,2,…,M) failure mode, corresponding corrective repair is performed which takes a random time Yi(i=1,2,…,M). Some analytical results on the instantaneous availability and the steady-state availability for the system are derived. The model is then utilized to obtain the optimal inspection interval that maximizes the system steady-state availability or minimizes the average long-run cost rate. A numerical example for Remote Power Feeding System is presented to demonstrate the application of the developed approach.

A New Approach for Solving Bi-Objective Redundancy Allocation Problem Using DOE, Simulation and <italic>ε</italic>-Constraint Method

The redundancy allocation problem (RAP) has been studied for many different system structures, objective functions, and distribution assumptions. In this paper, we present a problem formulation and a solution methodology to maximize the system steady-state availability and minimize the system cost for the repairable series-parallel system designs. In the proposed approach, the components’ time-to-failure (TTF) and time-to-repair (TTR) can follow any distribution such as the Gamma, Normal, Weibull, etc. We estimate an approximation of the steady-state availability of each subsystem in the series-parallel system with an individual meta-model. Design of experiment (DOE), simulation and the stepwise regression are used to build these meta-models. Face centred design, which is a type of central composite design is used to design experiments. According to a max–min approach, obtained meta-models are utilized for modelling the problem alongside the cost function of the system. We use the augmented ε-constraint method to reformulate the problem and solve the model. An illustrative example which uses the Gamma distribution for TTF and TTR is explained to represent the performance of the proposed approach. The results of the example show that the proposed approach has a good performance to obtain Pareto (near-Pareto) optimal solutions (system configurations).

Reliability analysis of a k-out-of-n:G system with general repair times and replaceable repair equipment

This paper studies a k-out-of-n:G repairable system with one replaceable repair equipment, where the lifetimes and repair times of components follow exponential distributions and arbitrary distributions, respectively. When one component breaks down, it is repaired by the repair equipment. Further, the repair equipment may fail during the repair period and then be replaced by a new one. The replacement time of the repair equipment is a generally distributed random variable. Employing the semi-Markov process theory and the Laplace (Laplace–Stieltjes) transform, the mean time to the first failure, the steady-state system availability, the rate of occurrence of failures of the system, the probability that the repair equipment is being replaced and the rate of occurrence of failures of the repair equipment are derived. Meanwhile, some numerical illustrations are reported to demonstrate how the various parameters of the model influence the behaviour of the system. Finally, a special case -out-of-n:G repairable system is discussed to validate the correctness of the theoretical results.

Availability evaluation of manufacturing systems using Semi-Markov model

Availability is a key measure of performance of systems in general and manufacturing systems are no exception. The elements of complex manufacturing systems such as Computer Integrated Manufacturing (CIM) follow variable, i.e., decreasing or increasing failure and repair rates. This creates difficulty in their availability evaluation. Conventional methods, which predict availability based on past experience, are inadequate for such systems. Existing analytical or simulation methods provide inaccurate availability estimate as these assume constant failure and repair rates, which follow exponential distribution. To address this concern, this paper suggests a methodology for availability evaluation of manufacturing systems using Semi-Markov model, which considers variable failure or repair rates. This is carried out by first understanding the system structure by identifying its elements; subsystem, assembly and component at its hierarchical levels and subsequently identifying their states; failed, operating, etc. Based on this, Semi-Markov models are developed for each element at various hierarchical levels of the system. The unique feature of this approach is that it does assume Weibull distribution for variable failure times and lognormal for variable repair times. The developed models are solved using an analytical solution method to obtain steady-state probabilities of their states and hence, the system steady-state availability. The methodology is illustrated by means of a case study conducted on a Vertical Machining Center (VMC) that is used in an automotive production plant.

Eucalyptus-based private clouds: availability modeling and comparison to the cost of a public cloud

High availability in cloud computing services is essential for maintaining customer confidence and avoiding revenue losses due to SLA violation penalties. Since the software and hardware components of cloud infrastructures may have limited reliability, the use of redundant components and multiple clusters may be required to achieve the expected level of dependability while also increasing the computational capacity. A drawback of such improvements is the respective impact on the capital and increase in acquisition and operational costs. This paper presents availability models for private cloud architectures based on Eucalyptus platform, and presents a comparison of costs between these architectures and similar infrastructure rented from a public cloud provider. Metrics for capacity-oriented availability and system steady-state availability are used to compare architectures with distinct numbers of clusters. A heterogeneous hierarchical modeling approach is employed to represent the systems considering both hardware and software failures. The results highlight that improvements on the availability are not significant when increasing the system to more than two clusters. The analysis also shows that the average available capacity is close to the maximum possible capacity in all architectures, and that it takes 18 months, in average, for these private cloud architectures to pay off the cost equivalent to the computational capacity rented from a public cloud.

Toward high assurance software systems with adaptive fault management

In this paper, we develop an adaptive approach to estimate the optimal preventive rejuvenation schedule, which maximizes the steady-state system availability. We formulate the upper and lower bounds of the predictive system availability using the one-look ahead predictive survival function from system failure time data and derive the pessimistic and optimistic rejuvenation policies. Then, we derive adaptive rejuvenation policies from the original data together with a right-censored observation. In the simulation experiments, we show the usefulness of the adaptive nonparametric predictive inference approach proposed in this paper.

Reliability Comparison Between Redundant Repairable Network Flow Systems

The importance in promoting, sustaining industries, manufacturing systems and economy through reliability measurement has become an area of interest. Reliability is one of the most important factors in any successful industries and manufacturing settings. In this paper, we study the reliability of three different repairable redundant network flow systems. First order differential equations method is used to obtain the explicit expressions for mean time to system failure, steady-state availability, busy period of repairman and profit function. Some numerical experiments are conducted in order to illustrate the effects of failure and repair rates on reliability indices such as mean time to system failure, steady-state availability and profit function. Furthermore, we compare the configurations based on reliability indices and cost benefits for the three configurations and find that configuration II is more reliable than configuration I and III.

Steady-state availability analysis of repairable mechanical systems with opportunistic maintenance by using Semi-Markov process

In this paper, a methodology for analysis of steady-state availability of repairable mechanical systems with opportunistic maintenance is presented, which is based on Semi-Markov process (SMP). SMP models; combining corrective maintenance with the opportunistic maintenance are proposed. The opportunistic maintenance is based on the condition of the component. An analytical framework is suggested for the solution of the SMP models. System steady-state availability is evaluated and compared in three cases of corrective maintenance; perfect, minimal and imperfect repairs; with and without opportunistic maintenance. The benefits of opportunistic maintenance are quantified in terms of the increased system availability. The proposed methodology is useful for maintenance engineers in implementing appropriate maintenance policy. The methodology is also helpful to designers to target a desired value of the system availability for the type and level of repair. The proposed methodology is demonstrated for a system, consisting of a centrifugal pump and the transmission unit in a series configuration.

Availability Modeling and Analysis of a Single-Server Virtualized System with Rejuvenation

Availability of business-critical application servers is an issue of paramount importance that has received special attention from the industry and academia in the last decade. This paper presents two stochastic reward net based availability models for a single-server virtualized system. The similarity in both models is that software rejuvenation is applied at not only virtual machine monitor (VMM) level using a time-base policy but also at virtual machines (VMs) using a prediction-based policy. The key difference is that the passive software replication and the active software replication are respectively adopted at the VM level of both models. We compare these models in terms of steady-state system availability by numerical analysis. Results show steady-state system availability with the active replication style gets a bit better than that of the passive one. Further, we study the impact of two critical parameters, the VMM rejuvenation interval and the VM aging detection probability, on downtime and on the number of transaction lost by sensitivity analysis.