Approximate inference for location and scale parameters withapplication to failure-time data

A new method (SP/CI) for obtaining approximate confidence intervals for the location, scale, and quantiles based on sample data parameters is presented. The basis of SP/CI is a saddlepoint expansion; the requirements are the maximum likelihood estimate (MLE), a few cross derivatives of the log-likelihood evaluated at the MLE, and quantiles of the log(F) distribution. SP/CI is illustrated numerically on several type-II censored reliability data sets using the extreme value and log-normal models. The accuracy is investigated by numerical comparison with the exact results, with best linear invariant estimator (BLIE), as well as with the results from other approximate methods discussed in the literature, including the asymptotic normality of the MLE, the likelihood ratio (LR) statistic, and corrections to the LR statistic recently developed     

Attribute data reliability decay models

The problem of estimating the reliability of a decaying system is considered. Several models are developed for providing reliability estimates when attribute (success, failure) sampling data over m stages indicates decreasing system reliability. An ordered maximum likelihood estimate model (MLE) is developed which provides decaying system reliability estimates under reliability order restrictions. A second classical model is an adaptation of the standard cumulative maximum likelihood estimate (mle) model. The model uses a weighting factor such that more current test information is weighted more heavily than is earlier data.Computer simulation trials were then conducted to compare the performance of the models with the standard cumulative MLE and binomial MLE models. The ordered MLE model is shown to yield the best results, performing even better than the binomial MLE model. The ordered MLE model produces generally conservative estimates of system reliability. The ordered MLE model also produces less error in its estimates than the binomial MLE model, both in terms of root mean squared error and standard deviation. Larger sample sizes are shown to yield the best results for both the binomial and ordered MLE models. While the ordered MLE model outperforms the binomial MLE model at every stage for sample sizes of 20 and 40, it is shown that the ordered MLE model offers significant improvement over the binomial MLE model for sample sizes of twenty.     

An exact forward-backward maximum likelihood autoregressiveparameter estimation method

A method for obtaining an exact maximum likelihood estimate (MLE) of the autoregressive (AR) parameters is proposed. The method is called the forward-backward maximum likelihood algorithm. Based on a new form of the log likelihood function for a Gaussian AR process, an iterative maximization is used to obtain an MLE of the inverse covariance matrix. The AR parameters are then determined via the normal equations. Experimental results comparing the new method with other popular AR spectrum estimation methods indicate the new method achieves low bias and low variance AR parameter estimates comparable with the existing methods     

Low complexity estimation of carrier and sampling frequency offsets in burst‐mode OFDM systems

We study communications under slowly varying channels, and consider three cases of knowledge of the channel impulse response (CIR): full knowledge, no knowledge, and partial knowledge of the CIR. By partial knowledge, we refer to knowing only either the CIR magnitudes or the CIR phases. It is known that obtaining the exact joint maximum‐likelihood estimate (MLE) of the CFO and the SFO requires a two‐dimensional search. Here, we present a new estimation method which uses the Taylor expansion of the MLE cost function, combined with the best linear unbiased estimator, to obtain a method which does not require such a search. The computational complexity of the new method is evaluated. Numerical simulations demonstrate that the new method approaches the corresponding Cramér‐Rao bound for a wide range of signal‐to‐noise ratios, and has superior performance compared to all other existing methods for approximating the solution for the joint MLE, while maintaining a low computational complexity. Copyright © 2015 John Wiley & Sons, Ltd.     

Maximum likelihood analysis of component reliability using maskedsystem life-test data

Life data from multicomponent systems are often analyzed to estimate the reliability of each system component. Due to the cost and diagnostic constraints, however, the exact cause of system failure might be unknown. Referring to such situations as being masked, the authors use a likelihood approach to exploit all the available information. They focus on a series system of three components, each with a constant failure rate, and propose a single numerical procedure for obtaining maximum-likelihood estimations (MLEs) in the general case. It is shown that, under certain assumptions, closed-form solutions for the MLEs can be obtained. The authors consider that the cause of system failure can be isolated to some subset of components, which allows them to consider the full range of possible information on the cause of system failure. The likelihood, while presented for complete data, can be extended to censoring. The general likelihood expressions can be used with various component life distributions, e.g., Weibull, lognormal. However, closed-form MLEs would most certainly be intractable and numerical methods would be required     

Uniqueness of maximum likelihood estimators of the 2-parameterWeibull distribution

We present a simple statistic, calculated from either complete failure data or from right-censored data of type-I or -II. It is useful for understanding the behavior of the parameter maximum likelihood estimates (MLE) of a 2-parameter Weibull distribution. The statistic is based on the logarithms of the failure data and can be interpreted as a measure of variation in the data. This statistic provides: (a) simple lower bounds on the parameter MLE, and (b) a quick approximation for parameter estimates that can serve as starting points for iterative MLE routines; it can be used to show that the MLE for the 2-parameter Weibull distribution are unique     

Statistical analysis of maximum likelihood estimator images of human brain FDG PET studies

The work presented evaluates the statistical characteristics of regional bias and expected error in reconstructions of real positron emission tomography (PET) data of human brain fluoro-deoxiglucose (FDG) studies carried out by the maximum likelihood estimator (MLE) method with a robust stopping rule, and compares them with the results of filtered backprojection (FBP) reconstructions and with the method of sieves. The task of evaluating radioisotope uptake in regions-of-interest (ROIs) is investigated. An assessment of bias and variance in uptake measurements is carried out with simulated data. Then, by using three different transition matrices with different degrees of accuracy and a components of variance model for statistical analysis, it is shown that the characteristics obtained from real human FDG brain data are consistent with the results of the simulation studies.     

半导体器件并联系统可靠性评估的经验Bayes方法

为了提高机载开关电源中半导体器件并联系统可靠性评估的准确性,运用经验 Bayes 法和经典的统计方法,研究了该系统的可靠性评估问题。分别给出了系统可靠性指标的经验 Bayes 估计,极大似然估计。利用 Monte-Carlo方法,对两种估计结果进行了比较,结果表明,经验 Bayes 估计的最大绝对误差为 0.07,它小于极大似然估计的最大绝对误差 0.368。     

Confidence interval for the mean of the exponential distribution,based on grouped data

When the available data from an exponential distribution are grouped, the maximum likelihood estimator (MLE) for the mean and several modified MLE have been discussed in literature. However, little work has been done on interval estimators based on such grouped data. This paper derives the asymptotic property of a statistic which is used to construct an approximate confidence interval for the mean. The width of this approximate confidence interval, based on grouped data, is compared with those based on complete samples, and samples with type-I and type-II censoring. The limits of the ratios of these widths are derived when the sample size approaches infinity. The approximate confidence interval from grouped data is wider than those from complete and censored samples. However, Monte Carlo simulation indicates that the proposed method based on grouped data is adequate, considering the restricted information in this case     

Weibull component reliability-prediction in the presence of maskeddata

Analysts are often interested in obtaining component reliabilities by analyzing system-life data. This is generally done by making a series-system assumption and applying a competing-risks model. These estimates are useful because they reflect component reliabilities after assembly into an operational system under true operating conditions. The fact that most new systems under development contain a large proportion of old technology also supports the approach. In practice, however, this type of analysis is often confounded by the problem of masking (the exact cause of system failure is unknown). This paper derives a likelihood function for the masked-data case and presents an iterative procedure (IMLEP) for finding maximum likelihood estimates and confidence intervals of Weibull component life-distribution parameters. The approach is illustrated with a simple numerical example     

Bayes estimation of component-reliability from masked system-lifedata

This paper estimates component reliability from masked series-system life data, viz, data where the exact component causing system failure might be unknown. It focuses on a Bayes approach which considers prior information on the component reliabilities. In most practical settings, prior engineering knowledge on component reliabilities is extensive. Engineers routinely use prior knowledge and judgment in a variety of ways. The Bayes methodology proposed here provides a formal, realistic means of incorporating such subjective knowledge into the estimation process. In the event that little prior knowledge is available, conservative or even noninformative priors, can be selected. The model is illustrated for a 2-component series system of exponential components. In particular it uses discrete-step priors because of their ease of development and interpretation. By taking advantage of the prior information, the Bayes point-estimates consistently perform well, i.e., are close to the MLE. While the approach is computationally intensive, the calculations can be easily computerized     

A maximum likelihood estimate for two-variable fractal surface

The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation method.     

Adaptive beamforming with conjugate symmetric weights

The Hermitian persymmetric maximum likelihood estimator (MLE) is better than the conventional MLE in estimating the covariance matrix of a symmetrically distributed antenna array. Though using the Hermitian persymmetric MLE improves the performance of adaptive beamforming, it increases the computational load due to the forward-backward averaging of array input sample data. By observing that the weight vector obtained from the Hermitian persymmetric MLE is conjugate symmetric if the phase origin is chosen at the array geometry center, methods are developed to reduce the computational load of the direct-form beamformer and the generalized sidelobe canceler (GSC). The weights of both beamformers can be adapted with real computations, with significant savings in computation time     

Maximum-likelihood bearing estimation with partly calibrated arraysin spatially correlated noise fields

The problem of using a partly calibrated array for maximum likelihood (ML) bearing estimation of possibly coherent signals buried in unknown correlated noise fields is shown to admit a neat solution under fairly general conditions. More exactly, this paper assumes that the array contains some calibrated sensors, whose number is only required to be larger than the number of signals impinging on the array, and also that the noise in the calibrated sensors is uncorrelated with the noise in the other sensors. These two noise vectors, however, may have arbitrary spatial autocovariance matrices. Under these assumptions the many nuisance parameters (viz., the elements of the signal and noise covariance matrices and the transfer and location characteristics of the uncalibrated sensors) can be eliminated from the likelihood function, leaving a significantly simplified concentrated likelihood whose maximum yields the ML bearing estimates. The ML estimator introduced in this paper, and referred to as MLE, is shown to be asymptotically equivalent to a recently proposed subspace-based bearing estimator called UNCLE and rederived herein by a much simpler approach than in the original work. A statistical analysis derives the asymptotic distribution of the MLE and UNCLE estimates, and proves that they are asymptotically equivalent and statistically efficient. In a simulation study, the MLE and UNCLE methods are found to possess very similar finite-sample properties as well. As UNCLE is computationally more efficient, it may be the preferred technique in a given application     

Estimation of the geometric survival distribution

This paper discusses both point and interval estimation of the survivor function S₀=Pr{X⩾x₀} for the geometric distribution. When the number of devices n⩾50, the performance of the maximum likelihood estimator (MLE) and uniformly minimum variance unbiased estimator (UMVUE) of S₀ are essentially equivalent with respect to the relative mean-square-error (RMSE) to S₀. However, when the failure probability per time unit p⩾0.50, and n⩽30, the UMVUE is preferable to the MLE with respect to the RMSE. For interval estimation of S₀ with no censoring, 4 asymptotic interval-estimators are derived from large-sample theory, and one from the exact distribution of the negative binomial. When p⩽0.2 and n⩾30, all 5 interval-estimators perform reasonably well with respect to coverage probability. Since using the interval estimator derived from the exact distribution can assure “coverage probability”⩾“desired confidence”, this estimator is probably preferable to the other asymptotic ones when p⩾0.50, and n⩽10. Finally, consider right-censoring, in which the failure-time that occurs after a fixed follow-up time period, is censored. We extend the interval estimator using the asymptotic properties of the MLE to account for right censoring. Monte Carlo simulation is used to evaluate the performance of this interval estimator; the censoring effect on efficiency is discussed for a variety of situations     

Parameter estimation for partially observed queues

We consider parameter estimation for a FIFO queue with deterministic service times and two independent arrival streams of “observed” and “unobserved” packets. The arrivals of unobserved packets are Poisson with an unknown rate λ while the arrivals of observed packets are arbitrary. Maximum likelihood estimation of λ is formulated based on the arrival times and waiting times of k observed packets. The likelihood function is derived in terms of the transition probabilities of the unfinished work process which are calculated recursively. Sufficient conditions for consistency, asymptotic normality, and asymptotic efficiency are given. The mean and variance of the MLE are measured in simulation experiments. Numerical results indicate that the MLE is consistent and asymptotically normal     

A semi-hidden Fritchman Markov modeling of indoor CENELEC A narrowband power line noise based on signal level measurements

To achieve error-free communication on the narrowband power line communication (NB-PLC) channel, there is need for constant measurement campaign and modeling of burst errors resulting from noise, perturbation and disturbances on the channel. This work thus reports a signal level measurement and First-Order Semi-Hidden Fritchman Markov modeling of the three major NB-PLC noise types for a typical South African residential and laboratory indoor low voltage environment. Two distinguishable disturbance scenarios: mildly disturbed and heavily disturbed were considered and Baum–Welch maximum likelihood estimation (MLE) algorithm is used to obtain the most probable model parameters that statistically depict the experimentally measured noise error sequences.     

On nonexistence of the maximum likelihood estimate in blind multichannel identification

In this paper, a blind multichannel identification problem for which the maximum likelihood estimate (MLE) does not exist is considered. More specifically, the likelihood function associated with this problem turns out to have no maximum but only saddle points. This interesting instance of nonexistence of the MLE for a practically relevant problem was first presented in the statistical literature on errors-in-variables regression (M. Solari, 1969). New insights into this result are presented in this paper, along with a direct proof based on the indefiniteness of the Hessian matrix.     

采用人工免疫算法的加速寿命试验分析方法

极大似然估计是加速寿命试验统计分析中常用的分析方法,但似然函数的优化问题是该方法广泛运用的主要障碍,常用的似然函数优化算法对初值要求高,而且容易陷入局部最优解.为了有效地解决上述问题,在似然函数的优化中引入了人工免疫算法,提出了一种采用人工免疫算法的步降应力加速寿命试验分析方法.利用人工免疫算法在解决多维复杂函数优化问题时强大的全局寻优能力,有效地解决了似然函数的优化问题.最后通过实例验证表明,采用人工免疫算法的步降应力加速寿命试验分析方法是有效的,而且在统计分析中避免了查统计用表,能够很方便的实现计算机编程计算,有较大的工程应用价值.     

Maintenance-policy cost-analysis for a series system withhighly-censored data

This paper considers the problem of estimating the optimal age-replacement time for a series arrangement of functional subsystems when data are subject to high levels of random censoring on the right. The system does not have redundant components. Simulation is used to compare the performance of the Kaplan-Meier Estimator (KME), the Piecewise Exponential Estimator (PEXE) and the Maximum Likelihood Estimator (MLE) in estimating the optimal replacement time for the system, as well as for each component, under high levels of random censorship. Monte Carlo analysis is used to estimate `average optimal age replacement times' determined using total time on test (TTT) transforms based on the KME, PEXE, and MLE methods. The optimal replacement time is used to calculate a value which is used to compare the relative long-run cost per unit-time for each method. The differences between using system-level data vs. component-level data to construct a maintenance policy are examined. With respect to cost effectiveness, the results identify the crucial factor in determining whether to perform system-level maintenance or component-level maintenance; that factor is the ratio of the `cost of performing preventive maintenance' and the `penalty cost of experiencing a system failure'. For the ratios used in this study (0.1 to 0.5) a `component-level maintenance policy' is more cost effective than a `system-level maintenance policy'. The results also show that for a correctly specified model and for large sample sizes, the age replacement times provided by the MLE are more accurate than those provided by the KME and PEXE, especially under high levels of censoring