A Monte Carlo simulation algorithm for finding MTBF

Prediction of mean time between failures (MTBF) is an important aspect of the initial stage of system development. It is often difficult to predict system MTBF during a given time since the component failure processes are extremely complex. The authors present a Monte Carlo simulation algorithm to calculate the MTBF during a given time of a binary coherent system. The algorithm requires the lifetime distributions of the components and the minimal path sets of the system. The MTBF for a specific time interval, e.g. a month or a year, can be estimated. If the component lifetime distributions are unknown, then a lower bound of system MTBF can be estimated by using known constant failure rates for each component     

Steady-State Reliability of Systems of Mutually Independent Subsystems

Predicting the reliability of a redundant system with repair is considerably simplified when the system can be subdivided into mutually independent subsystems. Results can be obtained without knowing the failure of repair time distributions of the subsystems. In this paper formulae are developed for the ``steady-state' availability and MTBF of a complex system in terms of the availabilities and MTBF's of its constituent subsystems. The basic concepts required are introduced and discussed in a review of a simplex system. These concepts are then applied to a complex system to obtain the main results of the paper. Finally, two examples are given to illustrate the application of these results.     

FPGA-based Monte Carlo simulation for fault tree analysis

The reliability analysis of critical systems is often performed using fault-tree analysis. Fault trees are analyzed using analytic approaches or Monte Carlo simulation. The usage of the analytic approaches is limited in few models and certain kinds of distributions. In contrast to the analytic approaches, Monte Carlo simulation can be broadly used. However, Monte Carlo simulation is time-consuming because of the intensive computations. This is because an extremely large number of simulated samples may be needed to estimate the reliability parameters at a high level of confidence.In this paper, a tree model, called Time-to-Failure tree, has been presented, which can be used to accelerate the Monte Carlo simulation of fault trees. The time-to-failure tree of a system shows the relationship between the time to failure of the system and the times to failures of its components. Static and dynamic fault trees can be easily transformed into time-to-failure trees. Each time-to-failure tree can be implemented as a pipelined digital circuit, which can be synthesized to a field programmable gate array (FPGA). In this way, Monte Carlo simulation can be significantly accelerated. The performance analysis of the method shows that the speed-up grows with the size of the fault trees. Experimental results for some benchmark fault trees show that this method can be about 471 times faster than software-based Monte Carlo simulation.     

A rapid smart approach for reliability and failure mode analysis of memories and large systems

This paper presents a novel system simulation methodology based on the known Monte Carlo technique, used for reliability and failure mode analysis of complex and large systems. The presented approach, called “state-merging and assorted random-testing” (SMART), is particularly applicable to systems involving different types of clusters of identical components, and is ideally suited for simulation of huge memories and similar systems. Simulators based on this approach are insensitive to the number of system components, system reliability or the number of associated spares or standby units, and thus they afford an extremely small simulation time compared to the accelerated Monte Carlo simulation time.     

Availability analysis of steam and power generation systems in the thermal power plant

The paper discusses the availability analysis of a steam generation system consisting of three subsystems A, B and D and a power generation system consisting of four subsystems E, F, G and H arranged in series, with three states viz., good, reduced and failed. Taking constant failure and repair rates for each working unit, the mathematical formulation is done using the Birth-Death process. Expressions for steady state availability and the MTBF (mean time between failure) are derived. The graphs are given, depicting the effect of failure and repair rates on the system availability. The results are supplied to the plant personnel, to plan the policies for failure free running of the systems for a long duration.     

Comparison of Monte Carlo Techniques for Obtaining System-Reliability Confidence Limits

Digital computer techniques are developed using a) asymptotic distributions of maximum likelihood estimators, and b) a Monte Carlo technique, to obtain approximate system reliability s-confidence limits from component test data. 2-Parameter Weibull, gamma, and logistic distributions are used to model the component failures. The components can be arranged in any system configuration: series, parallel, bridge, etc., as long as one can write the equation for system reliability in terms of component reliability. Hypothetical networks of 3, 5, and 25 components are analyzed as examples. Univariate and bivariate asymptotic techniques are compared with a double Monte Carlo method. The bivariate asymptotic technique is shown to be fast and accurate. It can guide decisions during the research and development cycle prior to complete system testing and can be used to supplement system failure data.     

Bounds on MTBF of Systems Subjected to Periodic Maintenance

Mean time between failures (MTBF) is a common reliability measure used to assess the failure behavior of repairable systems. In order to increase MTBF, in most systems, it is a common practice to perform preventive maintenance activities at periodic intervals. In this paper: We first discuss the validity of a commonly used equation for computing MTBF of systems subjected to periodic maintenance. For complex systems where this equation is valid, we propose a simple and better approximation than the exponential approximation proposed in a recent paper. In addition, we prove that for systems with increasing failure rate on average (IFRA) distributions, the exponential approximation proposed in a recent paper always underestimates the MTBF; hence, it is a lower bound at best. The proposed approximation and bounds are applicable for a wide range of systems because systems which contain components with exponential or any increasing failure rate (IFR) distribution (viz., Weibull with$beta≫1$, gamma, Gumbel,$s$-normal, and uniform) follow an IFRA distribution. As a special case, the proposed bounds & approximations provide better results for systems that contain only exponential failure distributions.     

Conditional Availability of Intermittently-Used Systems in Non-Markov Environment

This paper discusses the steady-state conditional availability of intermittently-used systems during the periods of demand. All the distributions governing system and demand status are arbitrary. The history dependence of the system and demand behavior is tackled by introducing history and cumulative-history functions. The system is assumed to fail only in use. Two processing disciplines regarding an interrupted demand (due to a system failure) are treated: fail-resume and failrepeat. The steady-state conditional availability under the fail-resume discipline is MTBF/(MTBF + MTTR), but not under the fail-repeat discipline. Therefore, care must be exercised not to misuse the formula.     

A Monte Carlo Technique for Obtaining System Reliability Confidence Limits from Component Test Data

A digital computer technique is developed, using a Monte Carlo simulation based on common probability models, with which component test data may be translated into approximate system reliability limits at any confidence level. The probability distributions from which the component failures are assumed to come are the exponential, Weibull (shape parameter K known), gamma (shape parameter ? known), normal, and lognormal. The components can be arranged in any system configuration, series, parallel, or both. Since reliability prediction is meaningful only when expressed with an associated confidence leve, this method provides a valuable and economical tool for the reliability analyst.     

Availability analysis under multiple link failures in WDM networks with shared-link connections

In optical Wavelength Division Multiplexing (WDM) networks, different protection schemes have been proposed in the literature, namely, dedicated protection and shared protection. Shared protection techniques significantly reduce the required spare capacity by providing the same level of availability as dedicated protection. However, current mission critical applications (which heavily depend on the availability of communication resources) require connection availability in the order of 99.999% or higher, which corresponds to a downtime of almost 5 min a year on the average. Therefore, in order to satisfy a connection serviceavailability requirement defined by the users Service Level Agreement in a cost-effective and resource-efficient way, network operators need a systematic mechanism to evaluate the network availability under multiple failure scenario to ensure that current network configuration can meet the required availability degree; otherwise, a network upgrade is required. Unfortunately, under multiple failure scenario, traditional availability analysis techniques based on reliability block diagrams are not suitable for survivable networks with shared spare capacity. Therefore, a new concept is proposed to facilitate the calculations of network availability. In this paper, we propose an analytical model for evaluating the availability of a WDM network with shared-link connections under multiple link failures. The analytical model is also verified using Monte Carlo simulation. The proposed model significantly contributes to the related areas by providing network operators with a quantitative tool to evaluate the system availability and, thus, the expected survivability degree of WDM optical networks with shared connections under multiple link failures.     

Efficient Evaluation of System Reliability by Monte Carlo Method

This paper presents a new Monte Carlo method to estimate the reliability of a large complex system represented by a reliability block diagram or by a fault tree. Two binary functions are introduced; one dominates the system structure function and the other is dominated by the structure function. These functions can be constructed easily by using part of path sets and cut sets of the system. Through the use of these binary functions, two variance-reducing techniques (control variate and importance sampling) are applied to the Monte Carlo evaluation of the system reliability. We prove that the new Monte Carlo method gives a reliability estimate with a smaller variance than that of the crude Monte Carlo method.     

A recursive variance-reduction algorithm for estimatingcommunication-network reliability

In evaluating the capacity of a communication network architecture to resist possible faults of some of its components, several reliability metrics are used. This paper considers the 𝒦-terminal unreliability measure. The exact evaluation of this parameter is, in general, very costly since it is in the NP-hard family. An alternative to exact evaluation is to estimate it using Monte Carlo simulation. For highly reliable networks, the crude Monte Carlo technique is prohibitively expensive; thus variance reduction techniques must be used. We propose a recursive variance-reduction Monte-Carlo scheme (RVR-MC) specifically designed for this problem, RVR-MC is recursive, changing the original problem into the unreliability evaluation problem for smaller networks. When all resulting systems are either up or down independently of components state, the process terminates. Simulation results are given for a well-known test topology. The speedups obtained by RVR-MC with respect to crude Monte Carlo are calculated for various values of component unreliability. These results are compared to previously published results for five other methods (bounds, sequential construction, dagger sampling, failure sets, and merge process) showing the value of RVR-MC     

Reliability Assessment of Microgrid Using Sequential Monte Carlo Simulation

Sequential Monte Carlo simulation method is introduced to the reliability assessment of microgrid,and a Weibuil distribution wind speed model is built to simulate the hourly wind speed of a specific site.Wind turbine generator model combined with a two-state reliability model is applied to Monte Carlo simulation method,and results show that the wind turbine reliability model works well with sequential Monte Carlo simulation.A two-state reliability model of micro gas turbine and a load model from IEEE reliability test system(IEEE RTS)are also introduced to the reliability evaluation of microgrid.Case studies show that Monte Carlo simulation method is flexible and efficient dealing with microgrid consisting of renewable resources with fluctuation characteristics.     

网络可靠性仿真

讨论了在链路以及节点均可能失效情况下,把节点的失效等效为与之相连链路的失效,运用蒙特卡洛法对网络可靠性进行仿真。并给出了仿真次数对仿真结果的误差的影响。     

Approximated reliability of r-out-of-n(F) system with common cause failure and maintenance

In modern industries very high reliability system are needed. To improve the reliability of system, the component redundancy and maintenance of component or system play an impotant role and must be studied. This paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or CCF(Common Cause Failure). Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By using the analyzed MTBF, we compute MTBF of r-out-of-n(F) system. The MTBF with CCF is saturable even if repair rate is large.Approximated reliability of the r-out-of-n(F) system with maintenance and Common Cause Failure O.SummaryThe paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or Common Cause Failure. Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By analyzing this mean visiting time equations, we compute MTBF and shows computational example. The MTBF with CCF is saturable even if repair rate is large. In general the maintenance overcomes MTBF bounds, But the repair method not overcome the MTBF saturation when the system has Common Cause Failure.     

MTBF of a complex binary coherent system

It is noted that there has yet been no detailed study of the relationships between the MTBF (mean time between failures) of a system and the sequences of component failures, except for the case of a series system where every component failure causes a system failure. The author defines MTBF anew and derives relationships between the properties of the MTBF of a binary coherent system and the properties of the sequences of component failures, assuming that the lifetime distributions of the components are either new-better-than-used (NBU) exponential or increasing failure rate (IFR). Lower bounds of MTBF that can be used to predict the MTBF and to decide whether the system would satisfy the MTBF requirement are derived     

Reliability Analysis of Hierarchical Systems Using Statistical Moments

In many practical engineering circumstances, systems reliability analysis is complicated by the fact that the failure time distributions of the constituent subsystems cannot be accurately modeled by standard distributions. In this paper, we present a low-cost, compositional approach based on the use of the first four statistical moments to characterize the failure time distributions of the constituent components, subsystems, and top-level system. The approach is based on the use of Pearson distributions as an intermediate analytical vehicle, in terms of which the constituent failure time distributions are approximated. The analysis technique is presented for -out-of- systems with identical subsystems, series systems with different subsystems, and systems exploiting standby redundancy. The moment-in-moment-out approach allows for the analysis of systems with arbitrary hierarchy, and arbitrary (unimodal) failure time distributions, provided the subsystems are independent such that the resulting failure time can be expressed in terms of sums or order statistics. The technique consistently exhibits very good accuracy (on average, much less than 1 percent error) at very modest computing cost.     

A Comparison of Three Methods for Calculating Lower Confidence Limits on System Reliability Using Binomial Component Data

The Maximus, bootstrap, and Bayes methods can be useful in calculating lower s-confidence limits on system reliability using binomial component test data. The bootstrap and Bayes methods use Monte Carlo simulation, while the Maximus method is closed-form. The Bayes method is based on noninformative component prior distributions. The three methods are compared by means of Monte Carlo simulation using 20 simple through moderately complex examples. The simulation was generally restricted to the region of high reliability components. Sample coverages and average interval lengths are both used as performance measures. In addition to insights regarding the adequacy and desirability of each method, the comparison reveals the following regions of superior performance: 1. The Maximus method is generally superior for: a) moderate to large series systems of reliable components with small quantities of test data per component, and b) small series systems of repeated components. 2. The bootstrap method is generally superior for highly reliable and redundant systems. 3. The Bayes method is generally superior for: a) moderate to large series systems of reliable components with moderate to large numbers of component tests, and b) small series systems of reliable non-repeated components.     

Sequential Destruction Method for Monte Carlo Evaluation of System Reliability

Circumstances favoring the use of Monte Carlo methods for evaluating the reliability of large systems are discussed. A new method, that of Sequential Destruction (SD) is introduced. The SD method requires no preparatory topological analysis of the system, and remains viable when element failure probabilities are small. It applies to a variety of reliability measures and does not require element failures to be s-independent. The method can be used to improve the performance of selective sampling techniques. Substantial variance reductions, as well as computational savings, are demonstrated using a sample system with more than 100 elements.     

可靠性工程分配法在雷达设计中的应用

在工程设计中经常要评估产品可靠性方面的指标，如失效率、平均无故障时间、平均维修时间等数值的测算和分配。总结了双基地多普勒气象雷达可靠性设计方面的一些具体工作，以及可靠性原理在其中的应用。