无失效数据情形失效率的综合E-Bayes估计

给出了无失效数据情形失效率的E-Bayes估计和引进失效信息后的E-Bayes估计,并在此基础上给出了失效率和可靠度的综合E-Bayes估计。最后,结合实际问题进行了计算,对估计结果进行了分析,并将它们与未假定先验信息时的非Bayes置信限进行比较,结果表明该方法是合理的。     

Real-time failure detection: A nonlinear optimization problem that yields a two-ellipsoid overlap test

Real-time failure detection for systems having linear stochastic dynamical truth models is posed in terms of two confidence region sheaths. One confidence region sheath is about the expected no-failure trajectory; the other is about the Kalman estimate. If these two confidence regions of ellipsoidal cross section are disjoint at any time instant, a failure is declared.A test for two-ellipsoid overlap is developed which involves finding a single pointx* whose presence in both ellipsoids is necessary and sufficient for overlap. Thus, the overlap test is contorted into a search forx*, shown to be the solution of a nonlinear optimization problem that is easily solved once an associated scalar Lagrange multiplier is known. A successive approximations iteration equation for is obtained and is shown to converge as a contraction mapping. The method was developed to detect failures in an inertial navigation system that appear as uncompensated gyroscopic drift rate. For simulated gyroscopic failures, the iterations converged very quickly, easily allowing real-time failure detection.This work was supported by the Department of the Navy, Strategic Systems Project Office, SP-24.This paper is based on an earlier paper (Ref. 1) which was presented at the IEEE Conference on Decision and Control, Phoenix, Arizona, 1974. A stronger convergence proof is presented in the present paper.     

Sample size for the Z test and its confidence interval

The statistical power of a significance test is closely related to the length of the confidence interval (i.e. estimate precision). In the case of a Z test, the length of the confidence interval can be expressed as a function of the statistical power.     

Approximated Bayes and empirical Bayes confidence intervals—The known variance case

In this paper hierarchical Bayes and empirical Bayes results are used to obtain confidence intervals of the population means in the case of real problems. This is achieved by approximating the posterior distribution with a Pearson distribution. In the first example hierarchical Bayes confidence intervals for the Efron and Morris (1975, J. Amer. Statist. Assoc., 70, 311–319) baseball data are obtained. The same methods are used in the second example to obtain confidence intervals of treatment effects as well as the difference between treatment effects in an analysis of variance experiment. In the third example hierarchical Bayes intervals of treatment effects are obtained and compared with normal approximations in the unequal variance case.Financially supported by the CSIR and the University of the Orange Free State, Central Research Fund.     

Confidence limits for the mean of exponential distribution in any time-sequential samples

We present the general results determining confidence limits for the mean of exponential distribution in any time-sequential samples,which are obtained in any sequen- tial life tests with replacement or without replacement.Especially,we give the best lower confidence limits in the case of no failure data.     

第二讲:成败型情形和指数分布情形的可靠性评定

对于成败型情形,基于成功次数给出了成功率的优良置信限和置信区间;对于产品寿命服从指数分布的情形,针对不同类型的数据(定数截尾、定时截尾、定总时与定数混合截尾、工型区间删失等)分别给出了可靠性参数(平均无故障时间(MTBF),可靠度,可靠寿命)的点估计和置信限。     

关于无失效数据情形下的置信限

在本文中，我们对一些常见的可靠性参数了在没有失效数据情形下的置信限，不仅给出了计算最优置信下限的普遍公式，而且对指数分布，Ｗｅｉｂｕｌｌ分布和对数正态分布分别导出了具体结果。     

Reliability analysis of repairable systems from in–service failure count data

Point maximum likelihood estimators for parameters, mean number of failures, and failure rate in a non–homogeneous Poisson process are derived, when only count data from k identical processes are available. Approximate confidence intervals based on the parametric bootstrap technique are considered. The performances of both the point and interval estimation procedures are assessed via Monte Carlo simulation.     

On bounded maximum width sequential confidence ellipsoids based on generalized U-statistics

For a vector of (estimable) functionals of several independent distributions, sequential confidence ellipsoids (of bounded maximum width) based on a class of generalized U-statistics are studied. A stopping rule along with a procedure for choosing the component sample sizes at each stage is developed, so that the proposed confidence ellipsoid has a confidence coefficient asymptotically (as the prescribed maximum width shrinks to zero) equal to a preassigned 1 - α (0 < α < 1), and the expected total sample size is minimized for the procedure. Asymptotic efficiency of the procedure is also studied. The case of von Mises' functionals is treated briefly at the end.     

On the Brown–Proschan model when repair effects are unknown

A device is repaired after failure. The Brown–Proschan (BP) model assumes that the repair is perfect with probability p and minimal with probability (1−p). Theoretical results usually suppose that each repair effect (perfect or minimal repair) is known. However, this is not generally the case in practice. In this paper, we study the behavior of the BP model when repair effects are unknown. In this context, the main features of the failure process are derived: distribution functions of times between failures, failure intensity, likelihood function, etc. We propose to estimate the repair efficiency parameter p and the parameters of the first time to failure distribution with the likelihood function or equivalently the EM algorithm. We also propose to combine a moment estimation of the scale parameter and a maximum likelihood estimation of other parameters. Copyright © 2010 John Wiley & Sons, Ltd.