Burr Type Research Articles

Modeling and Prediction of Exchange Rates Using Topp-Leone Burr Type X, Machine Learning and Deep Learning Models

Modeling and Prediction of Exchange Rates Using Topp-Leone Burr Type X, Machine Learning and Deep Learning Models

A review on metallic drilling burrs: geometry, formation and effect on the mechanical strength of metallic assemblies

Abstract Machining processes produce unwanted remainders of material on the free edges which are called burrs. In particular, the drilling process generates an entry burr, and a typically larger exit burr. When drilling stacks of several workpieces, exit and entry burrs are produced simultaneously at the interfaces. The presence of burrs can degrade the static and fatigue strength of the parts and assemblies containing them. An example concerns the burrs formed at the interface during the drilling of multi-stacks in One-Way-Assembly processes, where deburring is not systematically applied. The effect on fatigue can be significant. Reductions of up to 70 % in fatigue life have been reported, even though the explanatory rationale is not clear. This paper reviews existing works on burrs, focusing on drilling burrs. A description of the morphology of different types of burrs and of measurement technologies is given. Burr formation mechanisms and its modelling are reviewed. Burr control strategies and the main deburring technologies are examined. The limited literature on the effects of burrs on the static and fatigue strength of mechanical assemblies is also explored.

Some Properties of the Cosine Lomax Distribution with Applications

This paper introduces a new trigonometric distribution, named the Cosine Lomax (CLM) distribution. This distribution is a combination of the Lomax distribution and the Cosine-G family of distributions. Among the many mathematical moments, moment-generating function, incomplete moments, and the quantile function. We try to determine the model parameters using the maximum likelihood estimation method. Simulation studies evaluate the effectiveness of maximum likelihood estimators using bias and root mean square error. We applied the CLM distribution to two real-world datasets and tested for consistency using the Akaike information criterion, the consistent AIC, the Hannan-Quinn information criterion, the Bayesian information criterion, the Kolmogorov-Smirnov p-value, Cramer Von-Mises, and Andersen-Darling. The CLM model fared better when compared to the following distributions: Lomax, Inverse Lomax, Inverse Weibull, Burr Type X, Rayleigh, and Exponential, as well as measures of data set fit.

Estimation and Some Statistical Properties of the hybrid Weibull Inverse Burr Type X Distribution with Application to Cancer Patient Data

In this paper, the Burr type X distribution is represented as a mixture with the hybrid Weibull family, called hybrid hybrid Hybrid Weibull Inverse Burr Type X (HWIBX) distribution in order to justify its usefulness in modeling statistical regularities in extreme values recorded in non-stationary streams of media events, the basic new distribution functions are presented in addition to several statistical and mathematical properties of the hybrid distribution as well as estimating the model parameters by three methods, namely maximum likelihood, least squares, and weighted least squares with Conduct Monte Carlo simulations for the three methods. Finally, these results are illustrated through an example of matching the hybrid distribution with data representing the values Bladder cancer and survival times (given in years) of a group comprising 46 patients treated with chemotherapy alone and knowing the results of the improvement of this expansion through comparison with some other distributions using some Statistical metrics.

0,1]Truncated Exponentiated Exponential Burr type X Distributionwith Applications

We introduce a new flexible distribution four-parameter which is called [0,1]Truncated Exponentiated Exponential Burr type X distribution ([0,1] TEE-BX). Using binomial series expansion and exponential expansion, the new distribution is expanded by four parameters. We derive moments, moment generating function, quantile function, order statistics and the Rényi entropy. The maximum likelihood estimation method is used to estimate the parameters of the proposed TEE-BX model [0,1]. Finally, using two real-world data sets, the performance of the [0,1] TEE-BX distribution is explored. Based on the certain goodness of fit criteria, we conclude that the [0,1] TEE-BX distribution has a better fit than the other distributions.

Distributions of walking access to public transport in Melbourne, Australia – Evidence on acceptable and tolerable walking distances

The international literature indicates a wide interest in the distances public transport users walk to access their services. Urban and transport planners seek information on acceptable walking distances (AWD) in the provision of minimum levels of service coverage. This study uses a large database from Melbourne, Australia, to analyze trip length frequency distributions (TLFD) of walking access and egress to consider AWD in a multimodal public transportation system and to examine tolerable walking distances (TWD). AWD provides a guide to planners about stop/station locations for desirable minimum service coverage. TWD is a representative maximum walking distance for assessing the effectiveness of that service provision and can be used in conjunction with AWD. A statistical distribution function for walking distances can facilitate the use of regional values for AWD and TWD in transit service planning. The Burr Type XII distribution is shown to provide a good fit to the observed data. This provides a valuable tool for the analysis of percentile walking distances and suggests a general framework for the study of AWD and TWD in any city or region.

A Comparative Analysis of Flooding Methods on Random and Real Network Topologies

The Internet of Things (IoT) is revolutionizing industries by connecting everyday objects, known as smart devices, via the Internet. These devices, embedded with sensors and communication technologies, gather and share data. For the guaranteed gathering of information, the devices share global knowledge with each other, by using dissemination mechanisms in order to broadcast information. This study evaluates four flooding methods for broadcasting information across network nodes, namely: (i) blind flooding; (ii) probabilistic flooding; (iii) m-probabilistic flooding; and (iv) scoped probabilistic flooding, the latter to be introduced here. The evaluation considers random networks that are based on the Burr Type XII distribution and seven real networks. The evaluated flooding methods are studied on three different metrics: (i) coverage achieved; (ii) number of messages exchanged; and (iii) a metric that is based on binomial approximation. The latter is introduced to provide deeper insights into the particulars of the under-evaluation flooding methods. The results show that, under certain conditions, m-probabilistic flooding outperforms probabilistic flooding in terms of coverage, while requiring significantly fewer messages. Additionally, the study revealed that the scoped probabilistic flooding achieves coverage comparable to that of the probabilistic flooding while reducing the number of exchanged messages.

Which distribution to choose for deriving a species sensitivity distribution? Implications from analysis of acute and chronic ecotoxicity data

Species sensitivity distributions (SSDs) estimated by fitting a statistical distribution to ecotoxicity data are indispensable tools used to derive the hazardous concentration for 5 % of species (HC5) and thereby a predicted no-effect concentration in environmental risk assessment. Whereas various statistical distributions are available for SSD estimation, the fundamental question of which statistical distribution should be used has received limited systematic analysis. We aimed to address this knowledge gap by applying four frequently used statistical distributions (log-normal, log-logistic, Burr type III, and Weibull distributions) to acute and chronic SSD estimation using aquatic toxicity data for 191 and 31 chemicals, respectively. Based on the differences in the corrected Akaike’s information criterion (AICc) as well as visual inspection of the fitting of the lower tails of SSD curves, the log-normal SSD was generally better or equally good for the majority of chemicals examined. Together with the fact that the ratios of HC5 values of other alternative SSDs to those of log-normal SSDs generally fell within the range 0.1–10, our findings indicate that the log-normal distribution can be a reasonable first candidate for SSD derivation, which does not contest the existing widespread use of log-normal SSDs.

On Bayesian inference of reliability parameter in Burr-type XII model based on imprecise data: a survey on fuzzy modelling

There are always two major sources of uncertainty in measurements related to lifetime surveys: variation among the observations and imprecision of individual observation called fuzziness. The typical statistical analysis is based on variation among the observations and does not consider the imprecision due to individual observation. However, ignoring the imprecision of individual observations may cause losing information and getting misleading results. It is mandatory to analyse such data, to extend the real numbers classically and Bayesian estimation methods to fuzzy numbers. Inference on the Burr-type (BT) XII model, based on precise measurements, is carried out by researchers, yet the problem of estimating parameters, in the presence of fuzzy data, remains unresolved. We are estimating the BT XII distribution parameters and their corresponding reliability when the available data are in the fuzzy numbers. The maximum likelihood estimation (MLE), the Bayesian method and the method of moments are used for estimating parameters. Finally, these estimators are compared via a Monte-Carlo simulation study.

Risk of hearing loss in non-operated ear due to mastoid drilling

Background: The study purpose is to evaluate the effect of drill-generated high intensity noise on hearing sensitivity in contralateral ear. Methods: Sixty patients who underwent mastoidectomy were studied to see the effect of mastoid drilling on hearing sensitivity in normal ear using pure tone audiometry (PTA) and distortion product otoacoustic emission (OAE) values recorded preoperatively and postoperatively. Results: For PTA, there is no significant hearing loss for 0.25 kHz and 0.50 kHz for all PODs. For 1 kHz, 2 kHz and average PTA there is significant temporary hearing loss from POD 1 to POD 7 which normalizes around POD 30. However, there is significant temporary threshold shift for 4 kHz and 8 kHz from POD 1 to POD 5 and the hearing sensitivity improves to preoperative levels at POD 7. For OAE, 1 kHz, 4 kHz and average OAE there is significant temporary hearing loss from POD 1 to POD 7 which normalizes around POD 30. However, there is significant temporary threshold shift for 2 kHz and 6 kHz from POD 1 to POD 5 and hearing sensitivity improves to preoperative levels at POD 7. There is a significant correlation between drilling duration and PTA averages and OAE averages. Conclusions: Sensorineural hearing loss is more prevalent following modified radical and radical mastoidectomy as compared to canal wall up mastoidectomy. The factors influencing postoperative contralateral ear sensorineural hearing loss are type and size of burr and the duration of burr use.

Inference of reliability model with burr type XII distribution under two sample balanced progressive censored samples

Abstract The balanced joint progressive censoring scheme gives guidelines for researchers in reducing the expense and period of the experiment with modified efficiency. In this paper, the stress-strength reliability model are considered and investigated, in which two independent samples are generated from Burr Type XII distributions under balanced joint progressive censoring scheme. In the classical analysis, the maximum likelihood estimate of the reliability parameter is derived, then the relevant confidence interval is provided based on the Fisher matrix. Under the Bayesian framework, the Lindley’s technique and hybrid Gibbs within Metropolis-Hastings algorithm are applied to acquire the estimates of the parameters, and the corresponding highest posterior density credible interval of the reliability model is also constructed. The reliability inference is realized by numerical simulation, and the validity of the inference method is analyzed based on the splashing data of silicone oil droplets impact (SSODI) under two surfaces wettability conditions.

Statistical inference in Burr type XII lifetime model based on progressive randomly censored data

Censoring commonly occurs in real-world scenarios, either intentionally or unintentionally. Unintentional (or accidental) censoring usually happens randomly, i.e., it is out of the experimenters’ control, such as broken equipment, lack of follow-up, etc. Experimenters typically use intentional censoring to save experimental time and cost. In this article, we develop frequentist and Bayesian statistical inferential procedures for the parameters and reliability characteristics of the Burr type XII lifetime model under the Koziol-Green model based on progressive randomly censored data. For the frequentist approach, maximum likelihood methods for point and interval estimation are developed. For the Bayesian approach, the Bayes estimates under the squared error loss function (SELF) are evaluated using the Markov Chain Monte Carlo (MCMC) and Tierney-Kadane (T-K) approximation techniques. A Monte Carlo simulation study is used to assess the performance of the proposed estimation procedures. A real data analysis is performed to illustrate the proposed methods. Moreover, obtaining progressive censoring schemes for experimental planning purposes is also discussed.

Retracted: A Family of Bayesian Estimators for the Two-Parametric Burr Type II Distribution

Retracted: A Family of Bayesian Estimators for the Two-Parametric Burr Type II Distribution

A Comparative Assessment of Five Different Distributions Based on Five Different Optimization Methods for Modeling Wind Speed Distribution

Determining wind regime distribution patterns is essential for many reasons; modelling wind power potential is one of the most crucial. In that regard, Weibull, Gamma, and Rayleigh functions are the most widely used distributions for describing wind speed distribution. However, they could not be the best for describing all wind systems. Also, estimation methods play a significant role in deciding which distribution can achieve the best matching. Consequently, alternative distributions and estimation methods are required to be studied. An extensive analysis of five different distributions to describe the wind speeds distribution, namely Rayleigh, Weibull, Inverse Gaussian, Burr Type XII, and Generalized Pareto, are introduced in this study. Further, five metaheuristic optimization methods, Grasshopper Optimization Algorithm, Grey Wolf Optimization, Moth-Flame Optimization, Salp Swarm Algorithm, and Whale Optimization Algorithm, are employed to specify the optimum parameters per distribution. Five error criteria and seven statistical descriptors are utilized to compare the good-of-fitness of the introduced distributions. Therefore, this paper provides different important methods to estimate the wind potential at any site.

Using Burr Type XII distribution for user — Nearest access point distance modelling in finite Poisson networks with edge effect

Uniform Poisson Point Processes (uPPPs) have been extensively used for performance analysis of cellular networks. Of particular importance is the distribution of the distance between a user node (UE) and its closest access point (AP), which is useful for performance evaluation purposes. In this paper, the Burr Type XII distribution is proposed as a mathematically tractable statistical model of such distances in finite Poisson networks with the presence of edge effect. This result is further employed to evaluate the outage probability and ergodic capacity of Poisson networks in the presence of Nakagami-m fading. The accuracy of the proposed model is substantiated by simulations. Our newly derived results include as limiting cases existing ones available in the literature, namely Rayleigh distributed distances.

Integrating Burr type testing effort functions in logistic reliability growth model with uncertainty factor

Integrating Burr type testing effort functions in logistic reliability growth model with uncertainty factor

Server load estimation by Burr distribution mixture analysis of TCP SYN response time

Server load estimation is key in balancing traffic between servers when optimizing data center resources. Intrusive methods are sometimes difficult or impossible to implement. Therefore, non-intrusive estimation methods are the best alternative in these cases. The objective of this paper is to present a server load estimation method based on external network traffic measurements obtained in a vantage point close to the server. Statistical distributions of TCP SYN response time, that is, the time from SYN to SYN+ACK segments at the server side, are used to fit Burr Type XII heavy tail distribution mixtures. The fitting algorithm, based on maximum likelihood estimation, is developed in detail in this paper. Experimental data shows that the median of the fitted distribution correlates within the 95% confidence interval of the server load figures and, thus, it can be used as a non-intrusive and accurate method to measure it. This new method can be applied to almost any existing load balancing algorithm, as it does not make any assumption about the server, which is considered a black box.

Characterizing prediction errors of a new tree height model for cut-to-length Pinus radiata stems through the Burr Type XII distribution

Characterizing prediction errors of a new tree height model for cut-to-length Pinus radiata stems through the Burr Type XII distribution

Investigations on burr formation mechanisms and surface quality when micro-milling duplex stainless steel (UNS S32205)

Micromilling is a high-precision machining process that has been widely used to produce components or provide micro-characteristics on macro-sized parts. It is imperative that surfaces generated by micro-machining have high specifications and quality, translated as low surface roughness and a minimum number of burrs. Deburring processes are difficult to control, and the need to assure process quality motivated a study of this work focused on burr formation and surface quality when micromilling duplex stainless steel (UNS S32205). For this purpose, slots were machined using a 4-axis computer numerically controlled (CNC) micromachining center equipped with TiN-coated carbide microtools (381 µm diameter (0.015 inch)). Optimization experiments were performed in order to choose the most suitable cutting conditions. The measurements of burr height and surface roughness were made using a profilometer. In addition, milled slots were analyzed using a scanning electron microscope (SEM). The results showed that top burrs were dominant, and the main types presented on the up-milling side were feather burrs and primary burrs. On the down-milling side, burrs presented a rather irregular shape. The width of the root of the burr presented values very close to the size of the metallurgical phases of the material, and burrs formed at distances that are comparable to the spacing between both phases, such as, α-ferrite and γ-austenite. Surface roughness is higher when using increased cutting speeds, implying that lower speeds produce a measure of surface roughness in line with component specifications that appears to be dependent on the type of burr formed during milling and associated tool wear.

The Discrete Exponentiated-Chen Model and Its Applications

A novel discrete exponentiated Chen (DEC) distribution, which is a subset of the continuous exponentiated Chen distribution, is proposed. The offered model is more adaptable to analyzing a wide range of data than traditional and recently published models. Several important statistical and reliability characteristics of the DEC model are introduced. In the presence of Type-II censored data, the maximum likelihood and asymptotic confidence interval estimators of the model parameters are acquired. Two various bootstrapping estimators of the DEC parameters are also obtained. To examine the efficacy of the adopted methods, several simulations are implemented. To further clarify the offered model in the life scenario, the two applications, based on the number of vehicle fatalities in South Carolina in 2012 and the final exam marks in 2004 at the Indian Institute of Technology at Kanpur, are analyzed. The analysis findings showed that the DEC model is the most effective model for fitting the supplied data sets compared to eleven well-known models in literature, including: Poisson, geometric, negative binomial, discrete-Weibull, discrete Burr Type XII, discrete generalized exponential, discrete-gamma, discrete Burr Hatke, discrete Nadarajah-Haghighi, discrete modified-Weibull, and exponentiated discrete-Weibull models. Ultimately, the new model is recommended to be applied in many fields of real practice.