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.     

Confidence Limits for Redundant-System Availability

s-Confidence limits are established for the Availability of a standby redundant system (1-out-of-N:G system) for both hot and cold spares consisting of several identical units and repair facilities. The failure and repair rates of the units are s-independent, constant, and estimated from test data.     

System-Reliability Evaluation Techniques for Complex/Large Systems?A Review

This paper is a review of literature related to system reliability evaluation techniques for small to large complex systems. The literature is classified according to system models and evaluation techniques. The technique(s) we recommend for each system model are indicated.     

Finding the Better of Two Similar Designs by Monte Carlo Techniques

During the iterative design of a system (or circuit) the designer is often faced with the problem of ranking two designs according to some criterion. If the system elements have uncertain values, each system manifestation can be evaluated as to whether or not it meets some performance criterion. The fraction which meets or exceeds the criterion is called the yield. Monte Carlo techniques can be used to simulate the population of systems and thus to estimate the ranking of two designs. The first result presented in the paper is a derivation of the probability that one design is better than another, along with confidence limits for that probability. If the two designs are topologically the same, i.e., they differ only in the nominal values and actual distributions of true parameter values, then the same set of random numbers can be used for one simulation of each design. Due to the similarity there may be a positive correlation between the 2 results which can then be used to narrow the confidence limits from the crude method mentioned above. The second result is a derivation of these narrow confidence limits.     

Approximate Tolerance Limits and Confidence Limits on Reliability for the Gamma Distribution

No exact method is known for determining tolerance limits or s-confidence limits for reliability for the gamma distribution when both parameters are unknown. Perhaps the simplest approximate method is to determine a tolerance limit assuming the shape parameter known and then replace the shape parameter with its ML estimate to obtain approximate limits. Simulated values of the true probability levels, achieved by this method, indicate that this method is not suitable, contrary to what has been anticipated. A second approach is to consider the corresponding tolerance limits assuming the distribution mean known and the shape parameter unknown, and then replace the distribution mean by the sample mean. This approach gives useful results for many practical cases. Simulated values of the true probability levels achieved are presented for some typical cases and limiting values are provided. This method appears satisfactory for all values of the shape parameter, for the common s-confidence levels, and moderate sample sizes.     

Confidence Limits for Weibull Regression With Censored Data

The response variable in an experiment follows a 2-parameter Weibull distribution having a scale parameter that varies inversely with a power of a deterministic, externally controlled, variable generically termed a stress. The shape parameter is invariant with stress. A numerical scheme is given for solving a pair of nonlinear simultaneous equations for the maximum likelihood (ML) estimates of the common shape parameter and the stress-life exponent. Interval and median unbiased point estimates for the shape parameter, stress-life exponent and a specified percentile at any stress, are expressed in terms of percentage points of the sampling distributions of pivotal functions of the ML estimates. A numerical example is given.     

Ellipse sampling for Monte Carlo applications

A novel ellipse sampling technique is presented. The technique is efficient, stratified, low distortion and works for both polar and concentric maps between a square and an ellipse. The technique preserves adjacency and fractional area, does not require any numerical computation and has proven to be feasible in Monte Carlo applications.     

Confidence Limits for System Reliability: A Sequential Method

A sequential method is given for obtaining confidence limits for system reliability when ``pass-fail' test data have been obtained on components. Costs of testing are examined and a rule is derived for determining the order in which to test the components so that the average cost of testing is minimized. The method is presented first for series systems, but in Section IV the extension to parallel systems is considered and in Section V the procedure is applied to a series-parallel configuration. Comparisons are given with fixed sample-size testing and it is shown that the sequential method is statistically efficient and that many of the difficulties encountered when using fixed sample sizes are eliminated by testing sequentially.     

A Comparison of Four Monte Carlo Methods for Estimating the Probability of s-t Connectedness

This paper describes and compares the performance of four alternative Monte Carlo sampling plans for estimating the probability that two nodes, s and t, are connected in an undirected network whose arcs fail randomly and independently. Models of this type are commonly used when computing the reliability of a system of randomly failing components. The first method, dagger sampling, relies for its advantage on inducing negative correlation between the outcomes of the replications in the sample. The second method, sequential destruction/construction exploits permutation properties of arc failures and successes. The third method uses easily determined bounds on the reliability probability to gain an advantage. The fourth approach enumerates all failure sets of the network to achieve its appeal. An example based on a 30-arc 20-node network illustrates the variance reducing features and the time and space needs of each sampling plan. Dagger sampling and sequential construction offer limited benefits when compared to the bounds and failure-sets methods. The failure-sets method performs best on the example for small failure probabilities. However, in general it offers no guarantee of a smaller variance than crude Monte Carlo and requires substantially more memory than the other methods. Moreover, this memory requirement can grow rapidly as the size of the network increases. By contrast, the bounds method guarantees a smaller variance than for crude Monte Carlo sampling and has modest memory requirements.     

Bayesian Confidence Limits for the Reliability of Cascade Exponential Subsystems

The problem treated here is that of deriving exact Bayesian confidence intervals for the reliability of a cascade system consisting of N independent subsystems each having an exponential distribution of life with a failure rate which is estimated from life test data. The posterior probability density function of the system reliability is derived in closed form, using the method of the Mellin integral transform. The posterior distribution function is obtained, yielding Bayesian confidence limits on the total system reliability. These results, which are believed to be new for N > 3, have an immediate application to problems of reliability evaluation and test planning.     

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.     

Weighted ensemble Monte Carlo

A new approach to the Monte Carlo method for the solution of electron transport problems in semiconductors is presented and applied to some special cases of interest. The method is based on an iterative expansion of the Boltzmann equation in Chambers form and yields a simulative algorithm where the scattering events are chosen with arbitrary probabilities. In this way it is possible to analyse in great details regions of real and/or momentum space that would rarely be visited in a standard simulation. Applications are shown to the problems of high energy tails, of the surmounting of a high energy barrier, and of the low-field contact region.     

Lower Confidence Limits for Availability Assuming Lognormally Distributed Repair Times

Exact lower confidence limits are established for the availability ratio A where A = ?y/(?y + ?x) and ?y is the mean time between failures and ?x is the mean time to repair. It is assumed that the time between failures has an exponential distribution while the time to repair is log-normally distributed, with known variance. A test of the hypothesis A = Ao is also developed and power curves are included. Some results on the comparison of confidence intervals when the time to repair is assumed to be exponentially distributed are given.     

A Monte Carlo approach for power estimation

The authors investigate a power estimation technique for VLSI that combines the accuracy of simulation-based techniques with the speed of the probabilistic techniques. The resulting method is statistical in nature; it consists of applying randomly generated input patterns to the circuit and monitoring, with a simulator, the resulting power value. This is continued until a value of power is obtained with a desired accuracy, at a specified confidence level. The authors present the algorithm and experimental results, and discuss the superiority of the approach     

Monte Carlo simulations for tilted-channel electron multipliers

Microchannel electron multipliers with tilted structures are simulated using the Monte Carlo method. Gains of secondary electrons are calculated for different structures of the electron multiplier. For a short tilted cylindrical channel of the electron multiplier, a maximum gain is achieved greater than 10⁴ at a tilt angle near 25°. The maximum gain is about 10³ times larger than that of the nontilted channel. An explanation for the improvement of gain in tilted channel is suggested     

Monte Carlo FEXT cancellers for DSL channels

Crosstalk coupling is a severe impairment to transmission on twisted-pair copper cables such as digital subscriber telephone loops (DSLs). In this paper, we investigate the problem of far-end crosstalk (FEXT) cancellation for DSL. We propose a new soft interference canceller for coordinated self-FEXT cancellation across multiple twisted-pairs. The proposed receiver treats the FEXT-impaired channel as a multiple-input multiple-output (MIMO) channel; it uses the sequential Monte Carlo (SMC) technique to exploit the sequential structure inherent in iterative cancellation techniques for MIMO decoding. On telephone loops with strong FEXT, the proposed algorithm shows 0.5-dB coding gain with respect to previously proposed techniques. Furthermore, being soft-input-soft-output in nature, the proposed SMC receiver can iteratively exchange extrinsic information with a MAP decoder to successively cancel FEXT, leading to a turbo FEXT canceller.     

Monte Carlo Procedure for Theory Problems Potential

A Monte Carlo Procedure is presented which can be used to solve electrostatic and TEM-mode transmission-line problems. A modification of the known Monte Carlo procedures is given, which makes it possible for the method to be used when the dielectric is inhomogenous. Two sources of error are investigated; a partial correction is given for one, and it is shown how the probability confidence limits for the other can be computed.     

Bayesian Confidence Limits For The Availability of Systems

This paper presents a numerical procedure for computing Bayes confidence intervals for the availability of a series or parallel system consisting of several statistically independent 2-state subsystems each having exponential distributions of life and repair time. The present results 1) provide a useful generalization of a previous result in which test data were limited to ``snap-shot' observations on the subsystems operating states; 2) allow conventional life-test data for estimating the exponential parameters. The methods are suited to numerical evaluation using electronic computers as shown by particular examples.     

Lower Confidence Limits and a Test of Hypotheses for System Availability

Any estimate of system availability calculated from time-to-failure and time-to-repair test data will be subject to some degree of uncertainty due to the uncertainty associated with the sample estimates of MTTF and MTTR. Although decisions about the true availability of the system should take this uncertainty into account, a point estimate of availability is usually the only statistic calculated. This paper derives techniques for placing a lower confidence limit on system availability and for deciding if the true system availability differs significantly from a specified value when MTTF and MTTR are estimated from test data. These techniques could be used to analyze existing test data or to design a test program for demonstrating system availability and/or detecting significant deviations from specified values of system availability. To facilitate utilization of these techniques, curves of the lower 0.90 and 0.95 confidence limits and power curves for the test of hypotheses at the 0.05 and 0.10 levels of significance are presented. Examples illustrating the use of the curves are given.     

Monte Carlo微粒模拟法研究GaAs的NDM

本文用Monte Carlo 微粒模拟法(Particle Simulation)研究了GaAs中导带电子的负微分迁移率NDM(Negative Differential Mobility).电子的起始状态假设按照麦克斯韦律分布在Γ带中.电子作漂移运动时考虑了极性光学波和声学波的谷内、谷间散射.散射后假设定向速度消失,简化了计算.结果表明和实验值符合良好.也和前人计算结果进行了比较.