Burr Type Research Articles

Spectrum peak detection algorithm based on trend accumulation without base deduction

谱峰的检测分析在色谱技术研究中具有十分重要的作用,但在色谱数据采集、传输的过程中,不同程度的噪声干扰给谱峰检测带来了极大的困难。目前传统的谱峰检测算法普遍通过基底扣除的方式对谱峰的形态进行预定义,将谱峰分为单峰、重叠峰等多个种类。针对不同种类的谱峰采用不同的检测方法,这就导致了传统的谱峰检测算法具有高复杂度、低自动化程度以及容易失真等缺点。因此,该文从另一个角度出发提出了一种新型的谱峰检测算法。该算法取消基底扣除以及谱峰分类这一步骤,直接在源数据曲线的基础上进行谱峰检测,主要分为离散差分、趋势累积以及遍历寻峰3个步骤。首先通过信号量表征数据升降趋势;然后进行数据趋势累积,根据累积总和定位谱峰,采用三点定位的方式,即峰起点、极值点和峰终点描述一个谱峰的位置;最后根据遍历排序的方式进行谱峰的筛选。此外,通过谱峰扣除的方式得到曲线基底部分。采用C语言设计编写了算法程序,并对多个动态比表面积分析仪测定的色谱图进行了检测分析,结果显示使用该算法可以精准区分谱峰部分与基底部分,受数据曲线毛刺、震荡等噪声干扰很小,谱峰的三点定位十分准确,且不受其复杂形态的影响,具有很强的普适性。与其他算法相比,该算法定位准确,结构清晰,具有较好的稳定性以及可靠性。该文报道了无基底扣除以及趋势累积等新型谱峰检测思想在吸脱附色谱曲线中的应用,证明了其在吸脱附色谱峰检测中的有效性和良好的应用前景。

A stochastic simulation scheme for the long-term persistence, heavy-tailed and double periodic behavior of observational and reanalysis wind time-series

Lacking coastal and offshore wind speed time series of sufficient length, reanalysis data and wind speed models serve as the primary sources of valuable information for wind power management. In this study, long-length observational records and modelled data from Uncertainties in Ensembles of Regional Re-Analyses system are collected, analyzed and modelled. The first stage refers to the statistical analysis of the time series marginal structure in terms of the fitting accuracy, the distributions’ tails behavior, extremes response and the power output errors, using Weibull distribution and three parameter Weibull-related distributions (Burr Type III and XII, Generalized Gamma). In the second stage, the co-located samples in time and space are compared in order to investigate the reanalysis data performance. In the last stage, the stochastic generation mathematical framework is applied based on a Generalized Hurst-Kolmogorov process embedded in a Symmetric-Moving-Average scheme, which is used for the simulation of a wind process while preserving explicitly the marginal moments, wind’s intermittency and long-term persistence. Results indicate that Burr and Generalized Gamma distribution could be successfully used for wind resource assessment, although, the latter emerged enhanced performance in most of the statistical tests. Moreover, the credibility of the reanalysis data is questionable due to increased bias and root mean squared errors, however, high-order statistics along with the long-term persistence are thoroughly preserved. Eventually, the simplicity and the flexibility of the stochastic generation scheme to reproduce the seasonal and diurnal wind characteristics by preserving the long-term dependence structure are highlighted.

Parameter Estimation for Composite Dynamical Systems Based on Sequential Order Statistics from Burr Type XII Mixture Distribution

Considering the impact of the heterogeneous conditions of the mixture baseline distribution on the parameter estimation of a composite dynamical system (CDS), we propose an approach to infer the model parameters and baseline survival function of CDS using the maximum likelihood estimation and Bayesian estimation methods. The power-trend hazard rate function and Burr type XII mixture distribution as the baseline distribution are used to characterize the changes of the residual lifetime distribution of surviving components. The Markov chain Monte Carlo approach via using a new Metropolis–Hastings within the Gibbs sampling algorithm is proposed to overcome the computation complexity when obtaining the Bayes estimates of model parameters. A numerical example is generated from the proposed CDS to analyze the proposed procedure. Monte Carlo simulations are conducted to investigate the performance of the proposed methods, and results show that the proposed Bayesian estimation method outperforms the maximum likelihood estimation method to obtain reliable estimates of the model parameters and baseline survival function in terms of the bias and mean square error.

The Burr Type Xii Distribution with Some Statistical Properties

The Burr Type Xii Distribution with Some Statistical Properties

Ratio and Inverse Moments of Marshall-Olkin Extended Burr Type Xii Distribution Based on Lower Generalized Order Statistics

Ratio and Inverse Moments of Marshall-Olkin Extended Burr Type Xii Distribution Based on Lower Generalized Order Statistics

Beta-Burr Type X Distribution with Application to Luteinizing Hormone Data

Beta-Burr Type X distribution is a three parameter distribution and can model right skewed, left skewed, and symmetric data. Beta-Burr Type X distribution is the result of composition distribution functions of beta distribution and Burr Type X distribution. In this study, the characteristics such as probability density function (PDF), cumulative distribution function (CDF), the r-th moment, mean, and variance are presented. The maximum likelihood method is used to estimate the parameters of Beta-Burr Type X distribution, and the solution is obtained using a numerical method. As an illustration, Beta-Burr Type X distribution is used to model the data of luteinizing hormone in female blood samples.

Droplet and bone dust contamination from high-speed drilling during mastoidectomy.

The aim of this study was to examine contamination from otolaryngologic procedures involving high-speed drilling, specifically mastoid surgery, and to assess the adequacy of PPE in such procedures. Mastoid surgery was simulated in a dry laboratory using a plastic temporal bone, microscope and handheld drill with irrigation and suction. Comparisons of distance of droplet and bone dust contamination and surgeon contamination were made under differing conditions. Irrigation speed, use of microscope and drill burr size and type were compared. Measurement of the distance of field contamination while performing simulated mastoidectomy and location of surgeon contamination. There was a greater distance field contamination and surgeon contamination without the use of the microscope. Contamination was reduced by using a smaller drill burr and by using a diamond burr when compared to a cutting burr. The use of goggles and a face mask provided good protection for the surgeon. However, the microscope alone may provide sufficient protection to negate the need for goggles. While the risks of performing mastoid surgery during the coronavirus pandemic cannot be completely removed, they can be mitigated. Such factors include using the microscope for all drilling, using smaller size drill burrs and creating a safe zone around the operating table.

Efficient Removal of Milling Burrs by Abrasive Flow

Various types of burrs are formed during machining, press forming, and laser cutting. Deburring tools with cutting edges as well as wire brushes are widely used for deburring when the burr edges are accessible. When the burr edges are difficult to reach, abrasive flow machining is a good candidate. In this work, the removal of milling burrs is attempted using several types of flow guides. The effects of process parameters, such as the shapes of the flow guides and viscosity of the abrasive fluid, are investigated by conducting orthogonal array experiments. An index representing the suitability of the flow field for deburring is suggested based on the flow velocity and shear stress in the vicinity of the burr edge. The index values obtained for each of the experiments from the CFD simulations seem to match the deburring performances of the flow guides.

Bayesian Estimation of Entropy for Burr Type XII Distribution under Progressive Type-II Censored Data

With the rapid development of statistics, information entropy is proposed as an important indicator used to quantify information uncertainty. In this paper, maximum likelihood and Bayesian methods are used to obtain the estimators of the entropy for a two-parameter Burr type XII distribution under progressive type-II censored data. In the part of maximum likelihood estimation, the asymptotic confidence intervals of entropy are calculated. In Bayesian estimation, we consider non-informative and informative priors respectively, and asymmetric and symmetric loss functions are both adopted. Meanwhile, the posterior risk is also calculated to evaluate the performances of the entropy estimators against different loss functions. In a numerical simulation, the Lindley approximation and the Markov chain Monte Carlo method were used to obtain the Bayesian estimates. In turn, the highest posterior density credible intervals of the entropy were derived. Finally, average absolute bias and mean square error were used to evaluate the estimators under different methods, and a real dataset was selected to illustrate the feasibility of the above estimation model.

Competing Hazards Regression Parameter Estimation Under Different Informative Priors

In the analysis of survival data, cause specific quantities of competing risks get considerable attention as compared to latent failure time approach. This article focuses on parametric regression analysis of survival data using cause specific hazard function with Burr type XII distribution as a baseline model. We obtained maximum likelihood and Bayes estimates of cumulative cause specific hazard functions under competing risk setup. For Bayesian point of view we proposed a class of informative priors for parameters to observe the comprehensive compatibility and their effectiveness under two different loss functions. The appropriateness of model is measured by the simulation study. Finally, we illustrate the proposed methodologies using bone marrow transplant data from the Princess Margaret Hospital Ontario, Canada.

Effect of Tool Coating and Cutting Parameters on Surface Roughness and Burr Formation during Micromilling of Inconel 718

Surface roughness and burr formation are among the most important surface quality metrics which determine the quality of the fabricated parts. High precision machined microparts with complex features require micromachining process to achieve the desired yet stringent surface finish and dimensional accuracy. In this research, the effect of cutting speed (m/min), feed rate (µm/tooth), depth of cut (µm) and three types of tool coating (AlTiN, nACo and TiSiN) were analyzed to study their effect on surface roughness and burr formation during the micromachining of Inconel 718. The analysis was carried out using an optical profilometer, scanning electron microscope and statistical technique. Machining tests were performed at low speed with a feed rate (µm/tooth) below the cutting-edge radius for 10 mm cutting length using a carbide tool of 0.5 mm diameter on a CNC milling machine. From this research, it was determined that the depth of cut was the main factor affecting burr formation, while cutting velocity was the main factor affecting the surface roughness. In addition, cutting tool coating did not significantly affect either surface roughness or burr formation due to the difference in coefficient of friction. The types of burr formed during micromilling of Inconel 718 were mainly influenced by the depth of cut and feed rate (µm/tooth) and were not affected by the cutting velocity. It was also concluded that the results for the surface finish at low-speed machining are comparable to that of transition and high-speed machining, while the burr width found during confirmation experiments at low-speed machining was also within an acceptable range.

E-Bayesian estimation of Burr Type XII model based on adaptive Type-Ⅱ progressive hybrid censored data

In this paper, we obtain the E-Bayesian estimation of the parameter and the reliability function of the Burr type-XII distribution under adaptive progressive Type-Ⅱ censoring scheme. The E-Bayesian estimation is investigated using three different prior distributions based on squared error and LINEX loss functions. The properties of the E-Bayesian estimation and the E-posterior risk under squared error and LINEX loss functions are also discussed. An extensive simulation study is conducted to compare the behaviour of the E-Bayesian estimation with the corresponding Bayes and maximum likelihood estimators. We analyze one real data set to show the applicability of the different estimators in practice.

Properties of Burr distribution and its application to heavy-tailed survival time data

Burr distribution is Burr Type XII distribution which is one among the twelve types of the continuous distributions in Burr system. It has two positive shape parameters, namely k and c. It is implied from the probability density function which can be either decreasing or unimodal, and the hazard rate function which can be either decreasing or upside-down bathtub-shaped. The other distributional properties and the moment properties of Burr distribution will be discussed in more detail. By considering these properties, we will study its tail behaviour. To estimate the parameters k and c, the maximum likelihood method will be considered. Based on the properties of the data representing the remission time of bladder cancer patients, we infer that Burr distribution is suitable to model the data. The goodness-of-fit using the Kolmogorov–Smirnov test shows that Burr distribution fits well to the data.

A New Bimodal Distribution for Modeling Asymmetric Bimodal Heavy-Tail Real Lifetime Data

We introduced and studied a new generalization of the Burr type X distribution. Some of its properties were derived and numerically analyzed. The new density can be “right-skewed” and symmetric with “unimodal” and many “bimodal” shapes. The new failure rate can be “increasing,” “bathtub,” “J-shape,” “decreasing,” “increasing-constant-increasing,” “reversed J-shape,” and “upside-down (reversed U-shape).” The usefulness and flexibility of the new distribution were illustrated by means of four asymmetric bimodal right- and left-heavy tail real lifetime data.

Effect of Spindle Speed, Feed Rate and Cooling Medium on the Burr Structure of Aluminium through Milling

The burr is formed during milling, when the tool exits the work piece in any machining operation. The burr formation on a milling machine with the use of end mill cutter with different speed and different cooling mediums like air, water, and cutting fluid are discusses. The tool used for the machining operation is an end mill cutter tool. This work is taken up to examine the effect of different speeds and different cooling mediums on burr formation in the milling operation of aluminium in a dry and wet atmosphere. Results are found on the exit edge of the work piece, found during the milling operation. This paper manages with the aspects that influence the formation of burr and type of burr formed while doing experiment. The parameters considered are, the maximum length of stroke, drive speed (step cone pulley), range of speed arrangement groove and the selection of a cooling medium. The drive speed of the milling machine was measuring by Tachometer in all drive stages. The pictures of produced burrs were taken with the support of a digital microscope and digital camera.

Classical and Bayesian Inference for the Burr Type XII Distribution Under Generalized Progressive Type I Hybrid Censored Sample

This paper describes the classical and Bayesian estimation for the parameters of the Burr Type XII distribution based on generalized progressive Type I hybrid censored sample. We first discuss the maximum likelihood estimators of unknown parameters using the expectation-maximization (EM) algorithm and associated interval estimates using Fisher information matrix. We then derive the Bayes estimators with respect to different symmetric and asymmetric loss functions. In this regard, we use Lindley’s approximation and importance sampling methods. Highest posterior density (HPD) intervals of unknown parameters are constructed as well. The results of simulation studies and real data analysis are conducted to compare the performance of the proposed point and interval estimators.

Minimum Lq‐distance estimators for non‐normalized parametric models

AbstractWe propose and investigate a new estimation method for the parameters of models consisting of smooth density functions on the positive half axis. The procedure is based on a recently introduced characterization result for the respective probability distributions, and is to be classified as a minimum distance estimator, incorporating as a distance function the Lq‐norm. Throughout, we deal rigorously with issues of existence and measurability of these implicitly defined estimators. Moreover, we provide consistency results in a common asymptotic setting, and compare our new method with classical estimators for the exponential, the Rayleigh and the Burr Type XII distribution in Monte Carlo simulation studies. We also assess the performance of different estimators for non‐normalized models in the context of an exponential‐polynomial family.

A Generator of Bivariate Distributions: Properties, Estimation, and Applications

In 2020, El-Morshedy et al. introduced a bivariate extension of the Burr type X generator (BBX-G) of distributions, and Muhammed presented a bivariate generalized inverted Kumaraswamy (BGIK) distribution. In this paper, we propose a more flexible generator of bivariate distributions based on the maximization process from an arbitrary three-dimensional baseline distribution vector, which is of interest for maintenance and stress models, and expands the BBX-G and BGIK distributions, among others. This proposed generator allows one to generate new bivariate distributions by combining non-identically distributed baseline components. The bivariate distributions belonging to the proposed family have a singular part due to the latent component which makes them suitable for modeling two-dimensional data sets with ties. Several distributional and stochastic properties are studied for such bivariate models, as well as for its marginals, conditional distributions, and order statistics. Furthermore, we analyze its copula representation and some related association measures. The EM algorithm is proposed to compute the maximum likelihood estimations of the unknown parameters, which is illustrated by using two particular distributions of this bivariate family for modeling two real data sets.

Statistical Inference for Burr Type X Distribution using Geometric Process in Accelerated Life Testing Design for Time censored data

In accelerated life testing researcher generally use a life stress relationship between life characteristic and stress to estimate the parameters of failure time distributions at use condition which is just a re-parameterization of original parameters but from statistical point of view it is easy and reasonable to deal with original parameters of the distribution directly instead of developing inference for the parameters of the life stress relationship. So, an attempt is made here to estimate the parameters of Burr Type X life distribution directly in accelerated life testing by assuming that the lifetimes at increasing stress levels forms a geometric process. A mathematical model for the analysis of constant stress accelerated life testing for type-I censored data is developed and the estimates of parameters are obtained by using the maximum likelihood method. Also a Fisher information matrix is constructed in order to get the asymptotic variance and interval estimates of the parameters. Lastly, a simulation study is performed to illustrate the statistical properties of the parameters and the confidence intervals.

On adaptive progressive hybrid censored Burr type III distribution: application to the nano droplet dispersion data

ABSTRACT In the current paper, the maximum likelihood and Bayes estimators for the two shape parameters of the Burr Type III distribution are investigated based on adaptive Type II progressive hybrid censored data. The maximum likelihood estimators are provided for estimating the unknown parameters. The existence and uniqueness of the maximum likelihood estimation are shown using the graphical method. The Bayes estimates are obtained under two loss functions using the Lindley’s method and Metropolis-Hastings sampling procedure. Further, approximate and Bayesian intervals are constructed. Monte Carlo simulation study is performed to check the accuracy of the estimates and compare the performance of the proposed confidence intervals. Also, the nano droplet data is analyzed to illustrate the application and development of the inference methods.