最大熵法可靠度理论在工程中的应用

基于信息论中最大熵的概念，探讨了最大熵法的可靠度理论在工程中的应用。讨论了样本的均值、标准差对收敛性的影响，以及样本数量与最大熵法阶数对概率密度函数、超越概率、可靠指标精度的影响。提出了结构分析中应采用四阶矩法，并给出应用该方法时精度控制的若干建议。     

A Comparison of Two Optimal Inspection Procedures in the Presence of Errors

It is well known that the Bayes procedure minimizes the expected loss when the a priori probabilities of the states of nature are known, but it is not clear that the procedure continues to have this property in the presence of unknown errors which occur if these probabilities must be estimated. Furthermore, it is possible that the expected loss for another procedure does not increase as fast as that for the Bayes procedure. A procedure which might behave this way is the procedure for a group of N items, designated the N-procedure, because the expected loss for this procedure does not depend explicitly on the a priori probabilities. It is found, however, that the Bayes procedure consistently yields lower expected costs than the N-procedure. The results obtained suggest that the Bayes procedure will give smaller expected losses than other procedures in the presence of unknown errors in the a priori probabilities. Somewhat surprisingly, the superiority of the Bayes procedure increases with the size of the errors of the estimated a priori probabilities, regardless of whether the estimated probabilities lie above or below the correct values.     

Maximum Likelihood and Restricted Likelihood Solutions in Multiple-Method Studies

A formulation of the problem of combining data from several sources is discussed in terms of random effects models. The unknown measurement precision is assumed not to be the same for all methods. We investigate maximum likelihood solutions in this model. By representing the likelihood equations as simultaneous polynomial equations, the exact form of the Groebner basis for their stationary points is derived when there are two methods. A parametrization of these solutions which allows their comparison is suggested. A numerical method for solving likelihood equations is outlined, and an alternative to the maximum likelihood method, the restricted maximum likelihood, is studied. In the situation when methods variances are considered to be known an upper bound on the between-method variance is obtained. The relationship between likelihood equations and moment-type equations is also discussed.     

Estimating Errors in the Inspection of Complex Products

It has been experimentally determined that human inspectors visually examining a complex product for defects may be expected to miss 15 percent of the defects present. Under the conditions of this experiment (30 percent lot fraction defective), this level of performance would result in a type II error of 10 percent and a type I error of 3 percent. A combination of iconic and Monte Carlo simulation was used in performing the experiment.     

The Absolute Maximum of the Likelihood Function of the Rice Distribution: Existence and Uniqueness

The Rice probability density function has received considerable attention for its various important technical and scientific applications. One of the more attractive techniques for extracting the distribution parameters, and possibly the most frequently applied, relies on the maximization of the likelihood function for a given set of experimentally determined samples, and many applications are documented in the literature. This paper offers a mathematical analysis which demonstrates that, subject to conditions universally verified in physical systems, an absolute maximum exists, and it is the unique point internal to the domain of existence which zeroes the gradient of the likelihood function. In all previous results, the presence of additional maxima, which are possibly larger than the one that had numerically been found, could not be excluded. We can incidentally state that this paper demonstrates that all previous results based on numerically finding a maximum indeed corresponded to absolute maxima. The mathematical derivations offered here are also suggestive of actions capable of improving the insight into the maximum-likelihood technique and its numerical implementation.     

The Folded Normal Distribution: Accuracy of Estimation By Maximum Likelihood

This paper is a sequel to two previous papers on the subject of the Folded Normal Distribution appearing in Technometrics, S, pp. 543–550 and 551–562, (1961). In these earlier papers methods for estimating the parameters of the Folded Normal Distribution were proposed. Thii paper gives approximations for the standard errors for the maximum liklihood estimates of these parameters.     

Tables for Maximum Likelihood Estimates: Singly Truncated and Singly Censored Samples

In a previous paper in Technometrics, Vol. 1, 1959, the author derived the maximum liklihood estimates of the mean and variance for simply truncated or simply censored samples drawn from a Normal distribution. This paper extends considerably the tables originally published, and contains a further worked example.     

Modeling Errors in Sampling Inspection: Effect of Degraded Performance

Studies have shown that inspection is not error-free and is systematically influenced by such factors as time available, the payoffs, complexity of the task, the decision goal, defect rate, and so on. This study shows how models of decision-making can be used to obtain better designs of sampling plans in the presence of human inspection error. This study also outlines a methodology to develop sampling plans under different levels of degraded human performance. Results revealed that sampling plans are sensitive to decision goals and the level of degradation.     

Maximum Likelihood Estimation of the Parameters of the Gamma Distribution and Their Bias

The numerical technique of the maximum likelihood method to estimate the parameters of Gamma distribution is examined. A convenient table is obtained to facilitate the maximum likelihood estimation of the parameters and the estimates of the variance-covariance matrix. The bias of the estimates is investigated numerically. The empirical result indicates that the bias of both parameter estimates produced by the maximum likelihood method is positive.     

Entropy generation during flow boiling of pure refrigerant and refrigerant-oil mixture

Optimization of evaporators in refrigeration systems, for instance, can be conducted using entropy generation as a criterion. The latter can be used for choosing a technology (smooth tubes, enhanced tubes, tube diameter, etc) or selecting a fluid. Once this optimization is performed, the refrigerant charge can be evaluated. In this paper, different entropy generation expressions are presented for a diabatic two-phase flow of a pure refrigerant and a refrigerant-oil mixture. These expressions are developed based on the separated flow model. Depending on the boundary conditions, the equations are different and the conclusions differ from one to the other. It is shown that for a heat flux condition at the tube wall, the use of enhanced tubes is recommended at low mass velocities whereas, the use of smooth tubes is better at higher mass velocities. On the contrary, for a constant wall temperature, the use of enhanced tubes is always better than smooth tubes. The role of oil is also emphasized. The higher the oil concentration in the refrigerant, the higher the entropy generation.     

Maximum Likelihood Estimation in the Weibull Distribution Based On Complete and On Censored Samples

This paper is concerned with the two-parameter Weibull distribution which is widely employed as a model in life testing. Maximum likelihood equations are derived for estimating the distribution parameters from (i) complete samples, (ii) singly censored samples and (iii) progressively (multiple) censored samples. Asymptotic variance-covariance matrices are given for each of these sample types. An illustrative example is included.     

The role of the British Society for Strain Measurement and in particular the Product Quality and Reliability Testing Group in enhancement of the Nation's quality and reliability initiative*

This paper reviews the very important role of the BSSM in contributing to the wide understanding and application of experimental stress analysis in product design evaluation and testing. The paper presents the benefits of strain measurement techniques and a number of initiatives which have been taken by the BSSM in relation to quality and reliability which have included meetings held in conjunction with other organisations, the BSSM Certificate Scheme and involvement in standards for strain gauge measurements. The paper concludes with some facts and figures related to Quality Assurance, and costs of failure and fracture, from authoritative published sources in the UK and USA.     

Maximum Likelihood Estimators of Regression Coefficients for the Case of Autocorrelated Residuals

The classical linear regression model is extended to include the case in which the residuals are dependent with covariance matrix

where

A system of equations in the maximum likelihood estimators for the regression coefficients, a, and γ is derived and an iterative procedure for solving the system of equations is developed.     

计量抽样检查在射孔器材抽样检验方案的设计与应用

针对射孔器穿孔深度和穿孔孔径符合正态分布的理论特点,应用不合格品率的计量抽样检查方法设计了射孔器穿孔深度和穿孔孔径的检验方案.通过验证证明了该方法的科学合理性,并通过试验数据说明了该检验方案的实施对于提高产品稳定性方面的贡献和对提高油气井产能的意义.     

线搜索下带误差项的Dai-Yuan共轭梯度算法

本文在共轭梯度不能精确计算的情况下,采用Wolfe或Armijo步长规则研究了带误差项的Dai-Yuan(abbr．DY)共轭梯度法,我们的方法的一个很重要的特征就是步长不一定趋于零。这种特征使得我们的分析对许多实际问题很有用。我们在很一般的假设条件下证明了算法的全局收敛性。最后给出了数值算例。     

The Principle of Maximum Entropy Applied in the Evaluation of the Measurement Uncertainty

The maximum entropy approach is a flexible and powerful tool for assigning a probability distribution to a measurable quantity treated as a random variable subjected to known moment constraints. The aim of this paper is to describe how the principle of maximum entropy may be used to transform information about the value of a quantity into a probability density function (pdf) that reflects exactly that information and nothing else. This principle will be applied to common cases of metrological interest, where different kinds of information are available. The derivation of the pdf is given in each case, and two practical examples with numerical results are reported to demonstrate the efficiency of the maximum entropy method     

On the Performance of Shewhart median Chart in the Presence of Measurement Errors

In the literature, median control charts have been introduced under the assumption of no measurement error. However, measurement errors always exist in practice and may considerably affect the ability of control charts to detect out‐of‐control situations. In this paper, we investigate the performance of Shewhart median chart by using a linear covariate error model. Several figures and tables are presented and commented to show the statistical performance of Shewhart median control chart in the presence of measurement errors. We also investigate the positive effect of taking multiple measurements for each item in a subgroup on the performance of Shewhart median chart. An example illustrates the use of Shewhart median chart in the presence of measurement errors. Copyright © 2016 John Wiley & Sons, Ltd.     

The Efficiencies of Maximum Likelihood and Minimum Variance Unbiased Estimators of Fraction Defective in the Normal Case

This paper compares two point estimators of fraction defective of a normal distribution when both population parameters are unknown; the minimum variance unbiased estimator, (x), and the maximum likelihood estimator, (x). Using minimum mean squared error as a criterion, it is shown that the choice of estimator depends upon the true value of F(x), and the sample size. In the domain .0005 ≤ F(x) ≤ .50, the maximum likelihood estimator is generally superior even for small sample sizes, except for F(x) less than about 0.01, or greater than 0.25. Furthermore, the bias in the m.l.e. is slight over much of the domain where this estimator has smaller mean squared error.

As a practical solution to the estimation problem. it is suggested that the m.v.u.e. be calculated, and if this estimate is between 0.01 and 0.25, it should be replaced with the m.l.e. This combined estimator is shown to be nearly as efficient as the better of the m.v.u.e. and m.l.e. throughout the domain of F(x).     

Inspection Error Adjustment in the Design of Single Sampling Attributes Plan

This article presents an approach for the design of single sampling attributes plans of given strength when inspection errors are present. The design criterion considered is the specification of two points of the Operating Characteristic curve. The design approach also recommends repeated testing of sampled nonconforming units for conformance in order to reduce the adverse effect of the inspection errors. It is shown that realistic sampling plan parameters can be obtained if the inspection error probabilities are taken into account in the design of sampling plans.