An alternative inverse Gaussian distribution

An alternative inverse Gaussian distribution expressed in terms of the Bessel function is introduced. Both theoretical and empirical motivation is provided. Various particular cases and expressions for moments are derived. Estimation procedures by the method of moments and the method of maximum likelihood as well as the associated Fisher information matrix are derived. A simulation study is performed to investigate the asymptotic distribution of an associated boundary crossing variable. Finally, an application is illustrated to show that the proposed distribution can be a better model for reliability data than one based on the standard inverse Gaussian distribution.     

Extended maximum generally weighted moving average control chart for monitoring process mean and variability

In this paper, we propose an extended control chart, called the maximum generally weighted moving average (MaxGWMA) control chart, to simultaneously detect both increases and decreases in the mean and/or variability of a process. Simulations are performed to evaluate the average run length, standard deviation of the run length, and diagnostic abilities of the MaxGWMA and maximum exponentially weighted moving average (MaxEWMA) charts. An extensive comparison reveals that the MaxGWMA control chart is more sensitive than the MaxEWMA control chart.     

Cumulative quantity control chart for the mixture of inverse Rayleigh process

The engineering processes are made up of a number of the phenomenons working together that may lead to defects with multiple causes. In order to model such types of multiple cause defect systems we may not rely on simple probability models and hence, the need arises for mixture models. The commonly used control charts are based on simple models with the assumption that the process is working under the single cause defect system. This study proposes a control chart for the two component mixture of inverse Rayleigh distribution. The proposed chart namely IRMQC chart is based on mixture cumulative quantity using the quantity of product inspected until specified numbers of defects are observed. The single cause chart is also discussed as a special case of the proposed mixture cumulative quantity chart. The control structure of the proposed chart is designed, and its performance is evaluated in terms of some useful measures, including average run length (ARL), expected quality loss (EQL) and relative ARL (RARL). An illustrative example along a case study, is also given to highlight the practical aspects of the proposal.     

Knowledge-based target detection in compound Gaussian clutter with inverse Gaussian texture

This paper addresses the problem of adaptive detection of radar targets embedded in heterogeneous compound-Gaussian clutter environments. Based on the Bayesian theory, a priori knowledge of clutter is utilized to improve detection performance. The clutter texture is modeled by the inverse Gaussian distribution to describe the heavy-tailed clutter. Furthermore, clutter's heterogeneity results in insufficient secondary data, and the inverse complex Wishart distribution is exploited to model the speckle covariance matrix. Based on a priori distributions of clutter, a novel detector without using secondary data is derived via the generalized likelihood ratio test (GLRT). Monte Carlo experiments are performed to evaluate the detection performance of the proposed detector. Experimental results illustrate that the proposed detector outperforms its competitors in scenarios with limited secondary data.     

Modified non-Gaussian multivariate statistical process monitoring based on the Gaussian distribution transformation

Independent component analysis (ICA) has been applied for non-Gaussian multivariate statistical process monitoring (MSPM) for several years. As the independent components do not satisfy the multivariate Gaussian distribution, a missed alarm occurs when monitoring with traditional statistics. In this paper, we propose a Gaussian distribution transformation (GDT)-based monitoring method. Independent components are first transformed into approximate Gaussian distributions through the proposed nonlinear mapping. Then, we propose new statistics and their control limits to reduce missed alarms. The proposed method is particularly suitable for slight magnitude fault and early-stage fault detection. The ratio part of the area above the curve (RPAAC) is developed to evaluate the performance in fault detection. The experimental results from a synthetic example show the effectiveness of our proposed method. We also apply our method to monitor an electrical fused magnesia furnace (EFMF), and eruption and furnace wall melt faults can be detected in time.     

A sum of squares double exponentially weighted moving average chart

The sum of squares double exponentially weighted moving average (SS-DEWMA) chart is proposed to improve the performance of the single SS-EWMA chart, in the detection of initial out-of-control signals. The SS-DEWMA chart uses the sum of squares statistic and it simultaneously monitors the process mean and variance in a single chart. A simulation study is conducted to show that the optimal SS-DEWMA chart provides better zero state average run length (ARL) and standard deviation of the run length (SDRL) performances than the optimal SS-EWMA chart. In addition, as suggested by one of the reviewers, the cyclical steady state ARLs and SDRLs of the SS-DEWMA and SS-EWMA charts are compared, where it is found that the former did not perform as well as the latter. Note that to the best of the authors’ knowledge, a study on DEWMA type charts’ steady state ARL and SDRL performances has yet to be made in the literature. A situation in which the SS-DEWMA chart could be more useful than the SS-EWMA chart is explained in Sections 4 and 6.     

Synthetic double sampling np control chart for attributes

The quality of a product, based on the number of non-conforming items can be controlled using the np chart. This paper proposes a synthetic double sampling (DS) np chart which comprises two sub-charts, i.e. the DS np and conforming run length (CRL) sub-charts. For the zero-state case, the synthetic DS np chart surpasses its standard counterpart, i.e. the synthetic np and the basic DS np chart, and other np type charts like the standard np, combined synthetic and np (Syn-np), variable sample size (VSS) np, exponentially weighted moving average (EWMA) np and cumulative sum (CUSUM) np charts, for detecting increases in the fraction of non-conforming items p, for most shift sizes. The synthetic DS np chart also performs reasonably well in the steady-state case in comparison with other charts mentioned above. Thus, among the competing charts, the synthetic DS np chart stands out as one of the best charts.     

Bayesian analysis of an inverse Gaussian correlated frailty model

In survival analysis frailty is often used to model heterogeneity between individuals or correlation within clusters. Typically frailty is taken to be a continuous random effect, yielding a continuous mixture distribution for survival times. A Bayesian analysis of a correlated frailty model is discussed in the context of inverse Gaussian frailty. An MCMC approach is adopted and the deviance information criterion is used to compare models. As an illustration of the approach a bivariate data set of corneal graft survival times is analysed.     

A new monitoring design for uni-variate statistical quality control charts

In this research, an iterative approach is employed to analyze and classify the states of uni-variate quality control systems. To do this, a measure (called the belief that process is in-control) is first defined and then an equation is developed to update the belief recursively by taking new observations on the quality characteristic under consideration. Finally, the upper and the lower control limits on the belief are derived such that when the updated belief falls outside the control limits an out-of-control alarm is received. In order to understand the proposed methodology and to evaluate its performance, some numerical examples are provided by means of simulation. In these examples, the in and out-of-control average run lengths (ARL) of the proposed method are compared to the corresponding ARL’s of the optimal EWMA, Shewhart EWMA, GEWMA, GLR, and CUSUM[11] methods within different scenarios of the process mean shifts. The simulation results show that the proposed methodology performs better than other charts for all of the examined shift scenarios. In addition, for an autocorrelated AR(1) process, the performance of the proposed control chart compared to the other existing residual-based control charts turns out to be promising.     

Approximate Bayes estimators applied to the inverse Gaussian lifetime model

In this paper, Bayesian estimation of the two (unknown) parameters and reliability function of the Inverse Gaussian distribution are obtained by using the approximation forms of Lindley [1] and Tierney and Kadane [2]. Based on a Monte Carlo simulation, the Bayes estimates using Tierney and Kadane's approximation form is the best one, as compared with Lindley's form or maximum likelihood method.     

New EWMA control charts for monitoring process dispersion

There exist two EWMA-type dispersion charts for monitoring dispersion increases in the literature. One resets the EWMA statistic to zero whenever it is below zero. The other one truncates negative normalized observations to zero in the EWMA statistic. This paper proposes two one-sided EWMA charts for detecting dispersion increases and decreases, respectively, and one two-sided EWMA chart for monitoring dispersion increases or decreases simultaneously. Simulation studies show that the proposed upper-sided EWMA chart performs better than the two existing counterparts for detecting increases in dispersion, and that the proposed lower-sided EWMA chart significantly outperforms the two lower-sided EWMA charts developed similar to their two existing upper-sided EWMA charts for detecting decreases in dispersion. Moreover, the proposed two-sided EWMA chart provides much better sensitivity than the two two-sided EWMA charts generalized from the two existing upper-sided EWMA charts for detecting overall changes in dispersion.     

Adaptive detection of range-spread targets in compound Gaussian clutter with the square root of inverse Gaussian texture

The compound Gaussian clutter with the square root of inverse Gaussian texture component has been successfully used for modeling the heavy-tailed non-Gaussian clutter measured by high-resolution radars. In high-resolution radars, the targets may extend along multiple consecutive range cells, which are called range-spread targets. In this paper, we consider the range-spread target detection problem in the compound Gaussian clutter with the square root of inverse Gaussian texture. Three adaptive detectors are proposed based on Bayesian one-step generalized likelihood ratio test, maximum a posteriori generalized likelihood ratio test and Bayesian two-step generalized likelihood ratio test, respectively. Finally, the detection performances of the proposed detectors are evaluated by the Monte Carlo simulation. The simulation results show that the proposed detectors have better detection performance of range-spread target than the conventional generalized likelihood ratio test detector.     

Self-oriented control charts for efficient monitoring of mean vectors

This work presents a procedure for monitoring the centre of multivariate processes by optimising the noncentrality parameter with respect to the maximum separability between the in- and out-of-control states. Similarly to the Principal Component Analysis, this procedure is a linear transformation but using a different criterion which maximises the trace of two scatter matrices. The proposed linear statistic is self-oriented in the sense that no prior information is given, then it is monitored by two types of control charts aiming to identify small and intermediate shifts. As the control charts performances depend only on the noncentrality parameter, comparisons are made with traditional quadratic approaches, such as the Multivariate Cumulative Sum (MCUSUM), the Multivariate Exponentially Weighted Moving Average (MEWMA) and Hotelling’s T² control chart. The results show that the proposed statistic is a solution for the problem of finding directions to be monitored without the need of selecting eigenvectors, maximising efficiency with respect to the average run length.     

Dynamic parameter inverse analysis of concrete dams based on Jaya algorithm with Gaussian processes surrogate model

A dynamic parameter inverse analysis process for concrete dams based on Gaussian process regression and Jaya algorithm is presented. Gaussian process regression is used to establish a response surface representing the relationship between dynamic elastic modulus and modal parameters (natural frequency and mode shape). The Jaya algorithm is applied for dynamic parameter identification by minimizing the objective function. To verify the performance of the proposed method, we consider a concrete single buttress dam and a hyperbolic concrete arch dam as numerical examples. Numerical results show that Gaussian process regression can significantly improve the parameter identification efficiency without compromising on accuracy. Furthermore, the Jaya algorithm is compared with particle swarm optimization algorithm and genetic algorithm; the results show that the Jaya algorithm is promising in parameter recognition.     

一种改进正态逆高斯分布模型的图像去噪算法*

针对传统去噪算法去除含噪声较大的图像时仍有部分噪声残留的问题,本文基于变换域提出一种改进正态逆高斯分布的图像去噪算法。该算法在非下采样剪切波变换域,利用最优线性插值阈值函数改进正态逆高斯模型作为系数分布模型,对高频子带分解系数进行统计建模,以贝叶斯最大后验概率理论实现图像去噪。实验结果表明对于添加不同标准差的高斯白噪声图像,该算法在有效保留图像细节和纹理信息的同时在峰值信噪比方面优于同类去噪算法。     

基于高斯分布建模的序列推荐算法

目前大多数序列推荐系统(SRS)都假设需要预测的下一项与用户的上一项输入有关,然而真实场景中,用户可能会在浏览过程中误点击与自身兴趣偏好不一致的项目(不可靠实例)。针对此问题,提出了一种基于高斯分布建模的序列推荐算法。该算法首先通过一个含有多头自注意力的不确定性感知图集合网络(uncertainty-aware graph ensemble network,UAN),通过降低输入项的不确定性来提取输入的序列模式;其次将提取的输入序列模式建模为一个高斯分布,得到序列信息中的动态用户偏好以及偏好的不确定性;再将传统的推荐目标函数拓展为一个采样损失函数和一个不确定性正则化器,赋予每个训练实例适当的不确定性;最后将高损失且低不确定性的不可靠实例去除,增强序列推荐的准确性。该算法在三个公开的数据集Book-Crossing、MovieLens-1M和Steam上进行实验测试,结果表明,该算法相对于效果较好的基线取得了5.3%左右的提升,得到了更优的序列推荐结果,并能通过有效降低输入序列信息的不确定性,从而提升推荐准确率。     

一种基于高斯分布的白平衡改进算法

针对白平衡算法中普遍存在的校正不足及算法复杂度过高等问题,结合灰度世界算法和完美反射算法的优点,提出了一种基于高斯分解的自动白平衡算法。该算法通过对图像灰度分布的高斯分解,得到图像的高斯分布模型,并以此计算增益曲线。实验结果表明,该算法能有效校正图像的偏色问题,适用于多种不同场景。     

Simple linear profiles monitoring in the presence of within profile autocorrelation

Quality of some processes or products can be characterized effectively by a function referred to as profile. Many studies have been done by researchers on the monitoring of simple linear profiles when the observations within each profile are uncorrelated. However, due to spatial autocorrelation or time collapse, this assumption is violated and leads to poor performance of the proposed control charts. In this paper, we consider a simple linear profile and assume that there is a first order autoregressive model between observations in each profile. Here, we specifically focus on phase II monitoring of simple linear regression. The effect of autocorrelation within the profiles is investigated on the estimate of regression parameters as well as the performance of control charts when the autocorrelation is overlooked. In addition, as a remedial measure, transformation of Y-values is used to eliminate the effect of autocorrelation. Four methods are discussed to monitor simple linear profiles and their performances are evaluated using average run length criterion. Finally, a case study in agriculture field is investigated.     

Unified eigen analysis on multivariate Gaussian based estimation of distribution algorithms

Multivariate Gaussian models are widely adopted in continuous estimation of distribution algorithms (EDAs), and covariance matrix plays the essential role in guiding the evolution. In this paper, we propose a new framework for multivariate Gaussian based EDAs (MGEDAs), named eigen decomposition EDA (ED-EDA). Unlike classical EDAs, ED-EDA focuses on eigen analysis of the covariance matrix, and it explicitly tunes the eigenvalues. All existing MGEDAs can be unified within our ED-EDA framework by applying three different eigenvalue tuning strategies. The effects of eigenvalue on influencing the evolution are investigated through combining maximum likelihood estimates of Gaussian model with each of the eigenvalue tuning strategies in ED-EDA. In our experiments, proper eigenvalue tunings show high efficiency in solving problems with small population sizes, which are difficult for classical MGEDA adopting maximum likelihood estimates alone. Previously developed covariance matrix repairing (CMR) methods focusing on repairing computational errors of covariance matrix can be seen as a special eigenvalue tuning strategy. By using the ED-EDA framework, the computational time of CMR methods can be reduced from cubic to linear. Two new efficient CMR methods are proposed. Through explicitly tuning eigenvalues, ED-EDA provides a new approach to develop more efficient Gaussian based EDAs.