一般Ⅱ型逐次截尾数据下Integrated beta分布参数的极大似然估计

在可靠性理论研究中,常常需要估计寿命分布的参数.本文讨论了在一般Ⅱ型逐次截尾样本下Integrated beta分布参数的极大似然估计.在Integrated beta分布模型下,利用牛顿-拟牛顿最大化方法得到了参数的极大似然估计,并通过数值模拟和一个实例评价了得到的极大似然估计.

Reliability Estimation for Component-Based Software Using General Masking Grouped Data

Masked data are the system failure data when exact component causing system failure might be unknown.In this paper,the mathematical description of general masked data was presented in software reliability engineering.Furthermore,a general maskedbased additive non-homogeneous Poisson process(NHPP) model was considered to analyze component reliability.However,the problem of masked-based additive model lies in the difficulty of estimating parameters.The maximum likelihood estimation procedure was derived to estimate parameters.Finally,a numerical example was given to illustrate the applicability of proposed model,and the immune particle swarm optimization(IPSO) algorithm was used in maximize log-likelihood function.

Singularity of Some Software Reliability Models and Parameter Estimation Method

According to the principle, “The failure data is the basis of software reliability analysis”, we built a software reliability expert system (SRES) by adopting the artificial intelligence technology. By reasoning out the conclusion from the fitting results of failure data of a software project, the SRES can recommend users “the most suitable model” as a software reliability measurement model. We believe that the SRES can overcome the inconsistency in applications of software reliability models well. We report investigation results of singularity and parameter estimation methods of experimental models in SRES.

A Censored Nonparametric Software Reliability Model

This paper analyses the effect of censoring on the estimation of failure rate, and presents a framework of a censored nonparametric software reliability model. The model is based on nonparametric testing of failure rate monotonically decreasing and weighted kernel failure rate estimation under the constraint of failure rate monotonically decreasing. Not only does the model have the advantages of little assumptions and weak constraints, but also the residual defects number of the software system can be estimated. The numerical experiment and real data analysis show that the model performs wdl with censored data.

Singularity of Software Reliability Models LVLM and LVQM

According to the principle, “The failure data is the basis of software reliabilityanalysis”, we built a software reliability expert system (SRES) by adopting the artificialtechnology. By reasoning out the conclusion from the fitting results of failure data of asoftware project, the SRES can recommend users “the most suitable model” as a softwarereliability measurement model. We believe that the SRES can overcome the inconsistency inapplications of software reliability models well. We report investigation results of singularity and parameter estimation methods of models, LVLM and LVQM.

Robust and Efficient Reliability Estimation for Exponential Distribution

In modeling reliability data,the exponential distribution is commonly used due to its simplicity.For estimating the parameter of the exponential distribution,classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient.However,the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers.In this study,a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic.To examine the robustness of this new estimator,asymptotic variance,breakdown point,and gross error sensitivity were derived.This new estimator offers reasonable protection against outliers besides being simple to compute.Furthermore,a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator,weighted likelihood estimator,and M-scale estimator in the presence of outliers.Finally,a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.

Reliability analysis of extended generalized inverted exponential distribution with applications

A general version of the inverted exponential distribution is introduced, studied and analyzed. This generalization depends on the method of Marshall-Olkin to extend a family of distributions. Some statistical and reliability properties of this family are studied. In addition, numerical estimation of the maximum likelihood estimate（MLE） parameters are discussed in details. As an application, some real data sets are analyzed and it is observed that the presented family provides a better fit than some other known distributions.

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.

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.

Progress in Theoretical Research on Reliability for China's Space Engineering

With the support of the Fundamental Reliability Theoretical Research (FRTR) Foundation of the Quality Control Bureau of Ministry of Astronautics (MOA), PRC, 9 Chinese institutes and universities have worked for years on reliability statistics problems pending to be solved in space research and development. This paper gives a brief review of our main research results, including (1) Results on Normal Distributions; (2) Results on Weibull Distributions; (3) Results on the Synthesisof System Reliability-Theoretical Method; (4) Results on the Synthesis of System Reliability-Approximation Method: Binomial Distribution, Exponential Distribution, Weibull Distribution, Parallel System, General Cases; (5) Structual Reliability; (6) Zero-Failure Reliability Estimation; (7) Storage Life and Others. All these results can be acquired from the Quality Control Bureau of the Ministry of Aero-Space Industry (MAS).

Improving Energy and Power Efficiency Using NComputing and Approaches for Predicting Reliability of Complex Computing Systems

Opting to follow the computing-design philosophy that the best way to reduce power consumption and increase energy efficiency is to reduce waste, we propose an architecture with a very simple ready-implementation by using an NComputing device that can allow multi-users but only one computer is needed. This intuitively can save energy, space as well as cost. In this paper, we propose a simple and realistic NComputing architecture to study the energy and power-efficient consumption of desktop computer systems by using the NComputing device. We also propose new approaches to estimate the reliability of k-out-of-n systems based on the delta method. The k-out-of-n system consisting of n subsystems works if and only if at least k-of-the-n subsystems work. More specificly, we develop approaches to obtain the reliability estimation for the k-out-of-n systems which is composed of n independent and identically distributed subsystems where each subsystem （or energy-efficient usage application） can be assumed to follow a two-parameter exponential lifetime distribution function. The detailed derivations of reliability estimation of k-out-of-n systems based on the biased-corrected estimator, known as delta method, the uniformly minimum variance unbiased estimate （UMVUE） and maximum likelihood estimate （MLE） are discussed. An energy-management NComputing application is discussed to illustrate the reliability results in terms of the energy consumption usages of a computer system with qua（t-core, 8 GB of RAM, and a GeForce 9800GX-2 graphics card to perform various complex applications. The estimated reliability values of systems based on the UMVUE and the delta method differ only slightly. Often the UMVUE of reliability for a complex system is a lot more difficult to obtain, if not impossible. The delta method seems to be a simple and better approach to obtain the reliability estimation of complex systems. The results of this study also show that, in practice, the NComputing architecture improves both energy cost saving and energy efficient living spaces.

Modeling Reliability Engineering Data Using Scale-Invariant Quasi-Inverse Lindley Model

An important property that any lifetime model should satisfy is scale invariance.In this paper,a new scale-invariant quasi-inverse Lindley(QIL)model is presented and studied.Its basic properties,including moments,quantiles,skewness,kurtosis,and Lorenz curve,have been investigated.In addition,the well-known dynamic reliability measures,such as failure rate(FR),reversed failure rate(RFR),mean residual life(MRL),mean inactivity time(MIT),quantile residual life(QRL),and quantile inactivity time(QIT)are discussed.The FR function considers the decreasing or upside-down bathtub-shaped,and the MRL and median residual lifetime may have a bathtub-shaped form.The parameters of the model are estimated by applying the maximum likelihood method and the expectation-maximization(EM)algorithm.The EM algorithm is an iterative method suitable for models with a latent variable,for example,when we have mixture or competing risk models.A simulation study is then conducted to examine the consistency and efficiency of the estimators and compare them.The simulation study shows that the EM approach provides a better estimation of the parameters.Finally,the proposed model is fitted to a reliability engineering data set along with some alternatives.The Akaike information criterion(AIC),Kolmogorov-Smirnov(K-S),Cramer-von Mises(CVM),and Anderson Darling(AD)statistics are used to compare the considered models.

SOFTWARE TOOLS FOR ANALYZING NBTI-INDUCED DIGITAL CIRCUIT DEGRADATION

As semiconductor manufacturing migrates to more advanced technology nodes, accelerated aging effect for nanoscale devices poses as a key challenge for designers to find countermeasures that effectively mitigate the degradation and prolong system's lifetime. Negative Bias Temperature Instability (NBTI) is emerging as one of the major reliability concerns. Two software tools for NBTI analyzing are proposed in this paper, one for transistor-level, and the other for gate-level. The transistor-level can be used to estimate the delay degradation due to NBTI effect very accurately, while the gate-level can be used for repeat analysis in circuit optimization because of its fast computing speed.

Reliability of a Multicomponent Stress-strength Model Based on a Bivariate Kumaraswamy Distribution with Censored Data

In this paper,we consider a system which has k statistically independent and identically distributed strength components and each component is constructed by a pair of statistically dependent elements with doubly type-II censored scheme.These elements(X1,Y1),(X2,Y2),…,(Xk,Yk)follow a bivariate Kumaraswamy distribution and each element is exposed to a common random stress T which follows a Kumaraswamy distribution.The system is regarded as operating only if at least s out of k(1≤s≤k)strength variables exceed the random stress.The multicomponent reliability of the system is given by Rs,k=P(at least s of the(Z1,…,Zk)exceed T)where Zi=min(Xi,Yi),i=1,…,k.The Bayes estimates of Rs,k have been developed by using the Markov Chain Monte Carlo methods due to the lack of explicit forms.The uniformly minimum variance unbiased and exact Bayes estimates of Rs,k are obtained analytically when the common second shape parameter is known.The asymptotic confidence interval and the highest probability density credible interval are constructed for Rs,k.The reliability estimators are compared by using the estimated risks through Monte Carlo simulations.

An Imperfect-debugging Fault-detection Dependent-parameter Software

Software reliability growth models （SRGMs） incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such as the number of remaining faults and software reliability. However, the model parameters of both the fault content rate function and fault detection rate function of the SRGMs are often considered to be independent from each other. In practice, this assumption may not be the case and it is worth to investigate what if it is not. In this paper, we aim for such study and propose a software reliability model connecting the imperfect debugging and learning phenomenon by a common parameter among the two functions, called the imperfect-debugging fault-detection dependent-parameter model. Software testing data collected from real applications are utilized to illustrate the proposed model for both the descriptive and predictive power by determining the non-zero initial debugging process.

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.

Parameter Estimation of Mixed Weibull Distributions Using Cuckoo Search

The lifetime data of products with multiple failure modes which are collected from life testing are often fitted by the mixed Weibull distributions. Since the mixed Weibull distributions contain no less than five parameters,the parameter estimation is difficult and inaccurate. In order to enhance the accuracy,a new method of parameter estimation based on Cuckoo search( CS) is proposed. An optimization model for the mixed Weibull distribution is formulated by minimizing the residual sum of squares. The optimal parameters are searched via CS algorithm. In the case study,the lifetime data come from the life testing of diesel injectors and are fitted by the twocomponent Weibull mixture. Regarding the maximum absolute error and the accumulative absolute error between estimated and observed values as the accuracy index of parameter estimation,the results of four parameter estimation methods that the graphic estimation method,the nonlinear least square method,the optimization method based on particle swarm optimization( PSO) and the proposed method are compared. The result shows that the proposed method is more efficient and more accurate than the other three methods.

Inference and Properties of Mixture Two Extreme Lower Bound Distributions

In this paper, we discuss the mixture model of two extreme lower bound distributions. First, some properties we obtain of the model with hazard function are discussed. In addition, the estimates of the unknown parameters via the EM algorithm are obtained. The performance of the findings in the paper is showed by demonstrating some numerical illustrations through Monte Carlo simulation.

New Method for Determining Characteristic Parameters of Normal Distribution

By proportional differentiating cumulative distribution function of normal distribution,the spectroscopy characteristics are found.The characteristic parameters can be extracted directly from the height and position of the spectroscopy peaks.On this basis,a new method for determining these parameters of normal distribution is developed.This method can be applied to microelectronics reliability study.

The Exponential Flexible Weibull Extension Distribution

This paper is devoted to study a new generalization of the flexible Weibull with three parameters. This model is referred to as the exponential flexible Weibull extension (EFWE) distribution which exhibits bathtub-shaped hazard rate function. Some statistical properties such as the mode, median, the moment, quantile function, the moment generating function and order statistics are discussed. Moreover, the maximum likelihood method for estimating the model parameters and the Fisher’s information matrix is given. Finally, the advantage of the EFWE distribution is concluded by an application using real data.