Interval Estimation for the Stress-Strength Reliability with Bivariate Normal Variables

We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.

Interval Estimation in a Two Parameter Weibull Distribution Based on Type-2 Censored Data

In this paper, we consider the construction of the approximate profile- likelihood confidence intervals for parameters of the 2-parameter Weibull distribution based on small type-2 censored samples. In previous research works, the traditional Wald method has been used to construct approximate confidence intervals for the 2-parameter Weibull distribution under type-2 censoring scheme. However, the Wald technique is based on normality assumption and thus may not produce accurate interval estimates for small samples. The profile-likelihood and Wald confidence intervals are constructed for the shape and scale parameters of the 2-parameter Weibull distribution based on simulated and real type-2 censored data, and are hence compared using confidence length and coverage probability.

Heating load interval forecasting approach based on support vector regression and error estimation

As the existing heating load forecasting methods are almostly point forecasting,an interval forecasting approach based on Support Vector Regression (SVR) and interval estimation of relative error is proposed in this paper.The forecasting output can be defined as energy saving control setting value of heating supply substation;meanwhile,it can also provide a practical basis for heating dispatching and peak load regulating operation.By means of the proposed approach,SVR model is used to point forecasting and the error interval can be gained by using nonparametric kernel estimation to the forecast error,which avoid the distributional assumptions.Combining the point forecasting results and error interval,the forecast confidence interval is obtained.Finally,the proposed model is performed through simulations by applying it to the data from a heating supply network in Harbin,and the results show that the method can meet the demands of energy saving control and heating dispatching.

Parameter Estimations for Generalized RayleighDistribution under Progressively Type-I IntervalCensored Data

In this paper, inference on parameter estimation of the generalized Rayleigh distribution are investigated for progressively type-I interval censored samples. The estimators of distribution parameters via maximum likelihood, moment method and probability plot are derived, and their performance are compared based on simulation results in terms of the mean squared error and bias. A case application of plasma cell myeloma data is used for illustrating the proposed estimation methods.

Parameter Interval Estimation for Yule-Simon Distribution

Yule-Simon distribution has a wide range of practical applications, such as in networkscience, biology and humanities. A lot of work focuses on the study of how well the empirical datafits Yule-Simon distribution or how to estimate the parameter. There are still some open problems,such as the error analysis of parameter estimation, the theoretical proof of the convergence of theiterative algorithm for maximum likelihood estimation of parameters. The Yule-Simon distributionis a heavy-tailed distribution and the parameter is usually less than 2, so the variance does notexist. This makes it difficult to give an interval estimation of the parameter. Using the compressiontransformation, this paper proposes a method of interval estimation based on the centrallimit theorem. This method can be applied to many heavy-tailed distributions. The other twoasymptotic confidence intervals of the parameter are obtained based on the maximum likelihoodand the mode method. These estimation methods are compared in simulations and applications toempirical data.

The Data Generating Model in Toxicity Test and Estimation for the Toxicity Indicators

This paper gives the mathematical reason that the probit analysis method of toxicity measurement is reasonable, and proposes a new approach to compute the interval estimation of median lethal dose and 95% lethal dose. Based on the dose-response function of pesticides, this study firstly establishes a model of the data generating progress in toxicity test and proves that when the linear models of the logarithm of probability value and dose have been estimated, the weighted linear regression should be used, it is the reason why there is the heteroscedasticity of random disturbance term in the regression model, and the weight is right the reciprocal of the variance for random disturbance term. Secondly, based on the numerical simulation method, this paper gives a new approach for the interval estimation of median lethal dose and 95% lethal dose.

Estimation of the amount of erosion at unconformities in the last stage of the Eocene Sanduo period in the Subei Basin,China

Strata erosion is a widespread phenomenon in sedimentary basins. The generation, migration, and accumulation of hydrocarbon is influenced by the scale of erosion, so estimating the amount of erosion is essential in the analysis of oil and gas bearing basins. According to the geological features in the Subei Basin and the actual data, using the integrated method, we estimated the level of erosion at the unconformities caused by the Sanduo event. By using the mudstone interval transit time method and the vitrinite reflectance method on data from typical wells, it can be concluded that the Gaoyou, Jinhu, and Hongze depressions suffered strong strata erosion from the late Eocene to Oligocene, and the total strata erosion thickness was 300–1,100 m. Different tectonic units in the same depression have extremely uneven erosion intensity: the low convex regions have the maximum erosion thickness, amounting to 800–1,100 m; the slope regions have an erosion thickness of generally 600–800 m; the erosion thickness of the slope-hollow transition zone is 300–500 m. For the whole basin, we used the strata thickness trend analysis method combined with the interval transit time and vitrinite reflectance methods to estimate the erosion thickness in the Sanduo period. The results show that the most severe erosion of the Sanduo event in the Subei Basin is between 1,000 m to 1,200 m, mainly located in depressions around the Jianhu Uplift; the deep hollow area has the least erosion, generally about 300–600 m, and the erosion in the slope area is about 600–900 m. Compared with the northern part, the southern part has relatively little erosion. It is also proved that the Sanduo movement has heterogeneous intensity, and the western region has greater intensity than the eastern region.

Combination of structural reliability and interval analysis

In engineering applications, probabilistic reliability theory appears to be presently the most important method, however, in many cases precise probabilistic reliability theory cannot be considered as adequate and credible model of the real state of actual affairs. In this paper, we developed a hybrid of probabilistic and non-probabilistic reliability theory, which describes the structural uncertain parameters as interval variables when statistical data are found insufficient. By using the interval analysis, a new method for calculating the interval of the structural reliability as well as the reliability index is introduced in this paper, and the traditional probabilistic theory is incorporated with the interval analysis. Moreover, the new method preserves the useful part of the traditional probabilistic reliability theory, but removes the restriction of its strict requirement on data acquisition. Example is presented to demonstrate the feasibility and validity of the proposed theory.

Estimation of the Unknown Parameters for the Compound Rayleigh Distribution Based on Progressive First-Failure-Censored Sampling

This article considers estimation of the unknown parameters for the compound Rayleigh distribution (CRD) based on a new life test plan called a progressive first failure-censored plan introduced by Wu and Kus (2009). We consider the maximum likelihood and Bayesian inference of the unknown parameters of the model, as well as the reliability and hazard rate functions. This was done using the conjugate prior for the shape parameter, and discrete prior for the scale parameter. The Bayes estimators hav been obtained relative to both symmetric (squared error) and asymmetric (LINEX and general entropy (GE)) loss functions. It has been seen that the symmetric and asymmetric Bayes estimators are obtained in closed forms. Also, based on this new censoring scheme, approximate confidence intervals for the parameters of CRD are developed. A practical example using real data set was used for illustration. Finally, to assess the performance of the proposed estimators, some numerical results using Monte Carlo simulation study were reported.

Numerical Robust Stability Estimation in Milling Process

The conventional prediction of milling stability has been extensively studied based on the assumptions that the milling process dynamics is time invariant. However, nominal cutting parameters cannot guarantee the stability of milling process at the shop floor level since there exists many uncertain factors in a practical manufacturing environment. This paper proposes a novel numerical method to estimate the upper and lower bounds of Lobe diagram, which is used to predict the milling stability in a robust way by taking into account the uncertain parameters of milling system. Time finite element method, a milling stability theory is adopted as the conventional deterministic model. The uncertain dynamics parameters are dealt with by the non-probabilistic model in which the parameters with uncertainties are assumed to be bounded and there is no need for probabilistic distribution densities functions. By doing so, interval instead of deterministic stability Lobe is obtained, which guarantees the stability of milling process in an uncertain milling environment, In the simulations, the upper and lower bounds of Lobe diagram obtained by the changes of modal parameters of spindle-tool system and cutting coefficients are given, respectively. The simulation results show that the proposed method is effective and can obtain satisfying bounds of Lobe diagrams. The proposed method is helpful for researchers at shop floor to making decision on machining parameters selection.

Probability estimation based on grey system theory for simulation evaluation

In the evaluation of some simulation systems, only small samples data are gotten due to the limited conditions. In allusion to the evaluation problem of small sample data, an interval estimation approach with the improved grey confidence degree is proposed.On the basis of the definition of grey distance, three kinds of definition of the grey weight for every sample element in grey estimated value are put forward, and then the improved grey confidence degree is designed. In accordance with the new concept, the grey interval estimation for small sample data is deduced. Furthermore,the bootstrap method is applied for more accurate grey confidence interval. Through resampling of the bootstrap, numerous small samples with the corresponding confidence intervals can be obtained. Then the final confidence interval is calculated from the union of these grey confidence intervals. In the end, the simulation system evaluation using the proposed method is conducted. The simulation results show that the reasonable confidence interval is acquired, which demonstrates the feasibility and effectiveness of the proposed method.

A Dimension-Reduction Interval Analysis Method for Uncertain Problems

In this paper,an efficient interval analysis method called dimension-reduction interval analysis(DRIA)method is proposed to calculate the bounds of response functions with interval variables,which provides a kind of solution method for uncertainty analysis problems of complex structures and systems.First,multi-dimensional function is transformed into multiple one-dimensional functions by extending dimension reduction method to the interval analysis problem.Second,all the one-dimensional functions are transformed to standard quadratic form by second order Taylor expansion method.As a result,the multi-dimensional function is approximately represented by the functions that each interval variable occurs once,and interval power arithmetic can be used to efficiently calculate the bounds of response functions in restricted overestimation.Finally,three numerical examples and an engineering application are investigated to demonstrate the validity of the proposed method.

Micro-motion dynamics analysis of ballistic targets based on infrared detection

The dynamic characteristics related to micro-motions, such as mechanical vibration or rotation, play an essential role in classifying and recognizing ballistic targets in the midcourse, and recent researches explore ways of extracting the micro-motion features from radar signals of ballistic targets. In this paper, we focus on how to investigate the micro-motion dynamic characteristics of the ballistic targets from the signals based on infrared (IR) detection, which is mainly achieved by analyzing the periodic fluctuation characteristics of the target IR irradiance intensity signatures. Simulation experiments demonstrate that the periodic characteristics of IR signatures can be used to distinguish different micro motion types and estimate related parameters. Consequently, this is possible to determine the micro-motion dynamics of ballistic targets based on IR detection.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

Bayesian Estimation and Prediction for the Maxwell Failure Distribution Based on Type II Censored Data

We present Bayes estimators, highest posterior density (HPD) intervals, and maximum likelihood estimators (MLEs), for the Maxwell failure distribution based on Type II censored data, i.e. using the first r lifetimes from a group of n components under test. Reliability/Hazard function estimates, Bayes predictive distributions and highest posterior density prediction intervals for a future observation are also considered. Two data examples and a Monte Carlo simulation study are used to illustrate the results and to compare the performances of the different methods.

Robust Interval State Estimation for Distribution Systems Considering Pseudo-measurement Interval Prediction

Interval state estimation(ISE)can estimate state intervals of power systems according to confidence intervals of predicted pseudo-measurements,thereby analyzing the impact of uncertain pseudo-measurements on states.However,predicted pseudo-measurements have prediction errors,and their confidence intervals do not necessarily contain the truth values,leading to estimation biases of the ISE.To solve this problem,this paper proposes a pseudo-measurement interval prediction framework based on the Gaussian process regression(GPR)model,thereby improving the prediction accuracy of pseudo-measurement confidence intervals.Besides,a weight assignment strategy for improving the robustness of weighted least squares(WLS)ISE is proposed.This strategy quantifies the deviation between the pseudo-measurement intervals and their estimated intervals and assigns smaller weights to the pseudo-measurement intervals with larger deviations,thereby improving the estimation accuracy and robustness of the ISE.This paper adopts the data from the supervisory control and data acquisition(SCADA)system of the New York Independent System Operator(NYISO).It verifies the advantages of the GPR method for pseudo-measurement interval prediction by comparing it with the quantile regression and neural network methods.In addition,this paper demonstrates the effectiveness of the proposed weight assignment strategy through the IEEE 14-bus case.Finally,the differences in the estimation accuracy and the bad data identification between the robust interval state estimation and deterministic state estimation are discussed.

Immune Clone Maximum Likelihood Estimation of Improved Non-homogeneous Poisson Process Model Parameters

Aiming at the solving problem of improved nonhomogeneous Poisson process( NHPP) model in engineering application,the immune clone maximum likelihood estimation( MLE)method for solving model parameters was proposed. The minimum negative log-likelihood function was used as the objective function to optimize instead of using iterative method to solve complex system of equations,and the problem of parameter estimation of improved NHPP model was solved by immune clone algorithm. And the interval estimation of reliability indices was given by using fisher information matrix method and delta method. An example of failure truncated data from multiple numerical control( NC) machine tools was taken to prove the method. and the results show that the algorithm has a higher convergence rate and computational accuracy, which demonstrates the feasibility of the method.

Algorithms of Confidence Intervals of WG Distribution Based on Progressive Type-II Censoring Samples

The purpose of this article offers different algorithms of Weibull Geometric (WG) distribution estimation depending on the progressive Type II censoring samples plan, spatially the joint confidence intervals for the parameters. The approximate joint confidence intervals for the parameters, the approximate confidence regions and percentile bootstrap intervals of confidence are discussed, and several Markov chain Monte Carlo (MCMC) techniques are also presented. The parts of mean square error (MSEs) and credible intervals lengths, the estimators of Bayes depend on non-informative implement more effective than the maximum likelihood estimates (MLEs) and bootstrap. Comparing the models, the MSEs, average confidence interval lengths of the MLEs, and Bayes estimators for parameters are less significant for censored models.

A MICROCOMPUTER PROGRAM FOR CALCULATINGTHE CONFIDENCE INTERVALS OF SURVIVAL PROBABILITY IN MEDICAL FOLLOW－UP STUDIES

In cancer survival analysis, it is very frequently to estimate the confidence intervals for survival probabilities.But this calculation is not commonly involve in most popular computer packages, or only one methods of estimation in the packages. In the present Paper, we will describe a microcomputer Program for estimating the confidence intervals of survival probabilities, when the survival functions are estimated using Kaplan-Meier product-limit or life-table method. There are five methods of estimation in the program (SPCI), which are the classical(based on Greenwood's formula of variance of S(ti), Rothman-Wilson, arcsin transformation, log(-Iog) transformation, Iogit transformation methods. Two example analysis are given for testing the performances of the program running.

The Statistical Analysis of Interval-Censored Failure Time Data with Applications

The analysis of survival data is a major focus of statistics. Interval censored data reflect uncertainty as to the exact times the units failed within an interval. This type of data frequently comes from tests or situations where the objects of interest are not constantly monitored. Thus events are known only to have occurred between the two observation periods. Interval censoring has become increasingly common in the areas that produce failure time data. This paper explores the statistical analysis of interval-censored failure time data with applications. Three different data sets, namely Breast Cancer, Hemophilia, and AIDS data were used to illustrate the methods during this study. Both parametric and nonparametric methods of analysis are carried out in this study. Theory and methodology of fitted models for the interval-censored data are described. Fitting of parametric and non-parametric models to three real data sets are considered. Results derived from different methods are presented and also compared.