Monotone Failure Research Articles

Cyclic response of pre-failed and reinstalled single-helix piles in sand

Helical piles can be rescrewed at greater depths after failure and put back into service again as long as their integrity is preserved. However, reports on the lifetime performance after reinstallation are completely missing in the literature. This work compares the tensile cyclic response of single helix piles in dry and saturated sand after experiencing failure due to monotonic uplift and after reinstallation, using centrifuge model testing. Tensile cyclic tests were conducted on three model piles with different helix-to-shaft diameter ratios, under two different conditions: (1) cyclic loading after monotonic pile failure, and (2) cyclic loading on a pile that has been reinstalled deeper into the soil after experiencing a monotonic failure. The experiments revealed that the preceding monotonic failure causes significant influence on the post-failure cyclic performance, in which few tens of cycles are enough to lead to a critical accumulated displacement. The cyclic tests on the reinstalled helical pile at a depth of 2 D ( D = helix diameter) below the initial helix depth showed that the cyclic performance can be partially to fully recovered depending on the loading amplitude.

The Odd Ramos-Louzada Generator of distributions with applications to failure and waiting times

In this study, we have proposed a new generator called the Odd Ramos-Louzada Generator (ORL-G), which can extend many well-known distributions by applying the T-X method. Some of its basic statistical properties such as the quantile function, the rthnon-central moments and Renyi entropy are also investigated. The ORL-G has the ability to model symmetric and asymmetric data as well as non-monotonic and monotonic failure rate datasets. Three new distributions of the ORL-G family are the ORL-Burr XII (ORLBXII), ORL-Log Logistic (ORLLoL), and ORL-Weibull (ORLWei) which are respectively obtained using the Burr XII, the Log-Logistic, and Weibull as baseline models. The RL and Generalized RL distributions are sub-models of the ORLBXII and ORLLoL distributions. The ORL-G model parameters have been estimated using the maximum likelihood (ML) method. Simulation analysis carried out indicates that the ML estimation method and its asymptotic properties performed quite well. The flexibility of the ORL-G family is demonstrated through the application of three real, complete datasets, including failure and waiting times and it is evident that ORLBXII outperformed its sub-models and other competing models.

RELEVANT CONSEQUENCE RELATIONS: AN INVITATION

AbstractWe generalize the notion of consequence relation standard in abstract treatments of logic to accommodate intuitions of relevance. The guiding idea follows the use criterion, according to which in order for some premises to have some conclusion(s) as consequence(s), the premises must each be used in some way to obtain the conclusion(s). This relevance intuition turns out to require not just a failure of monotonicity, but also a move to considering consequence relations as obtaining between multisets. We motivate and state basic definitions of relevant consequence relations, both in single conclusion (asymmetric) and multiple conclusion (symmetric) settings, as well as derivations and theories, guided by the use intuitions, and prove a number of results indicating that the definitions capture the desired results (at least in many cases).

Influence of Kirschner-Wire Insertion Angle on Construct Biomechanics following Tibial Tuberosity Osteotomy Fixation in Dogs.

The aim of this study was to evaluate the effect of Kirschner wire insertion angle on the biomechanical characteristics following tibial tuberosity osteotomy fixation in dogs. Twelve pairs of cadaveric tibia were harvested and randomly assigned to two treatment groups. Kirschner wires were placed either transversely (0 degrees) or placed caudodistally (30 degrees) with respect to the tibial tuberosity osteotomy. Each limb acted as its own respective control. Radiographic analysis allowed for the calculation of Kirschner wire insertion angle variance. Constructs were tested to monotonic failure while evaluating yield, peak, and failure forces, construct stiffness, and failure mode. Kirschner wire insertion angles were 1.1 ± 2.2 degrees and 30.5 ± 2.3 degrees, respectively, for 0-degree and 30-degree groups (p <0.0001). Yield (p = 0.0095), peak (p <0.024) and failure loads (p <0.030) were all significantly greater for Kirschner wires inserted at an angle of 0 degrees compared with 30 degrees. Construct stiffness did not differ regardless of insertion angle (p = 0.068). Failure mode did not differ (p = 0.87) with tibial tuberosity avulsion and Kirschner wire pull-out seen in the majority of constructs (67%). Kirschner wires placed transversely (0 degrees) for tibial tuberosity osteotomy fixation were biomechanically superior, increasing yield, peak, and failure forces by 1.6 times, 1.3 times, and 1.4 times, respectively, to those placed in a caudodistal (30 degrees) orientation. Kirschner wire insertion angle is an important consideration following tibial tuberosity osteotomy in dogs, with Kirschner wires placed at 0 degrees conferring increased resistance of the repair to construct deformation.

On Unit Exponential Pareto Distribution for Modeling the Recovery Rate of COVID-19

In 2019, a new lethal and mutant virus (COVID-19) spread around the world, causing the deaths of millions of people. COVID-19 demonstrates that scientists are involved in significant research efforts to face bacteria with less effort than that dedicated to viruses. Since then, engineers and bio-materials scientists have been trying to develop antiviral research and find a suitable effective medication. Strategies and opportunities for interference diagnostics, treatment strategies, and predicting future factors became mandatory. From a statistical point of view, estimating and modelling these factors play an important role in preventing future viral epidemics. In this article, modelling the recovery rate of COVID-19 is investigated through a new distribution which is called the unit exponential Pareto distribution. The new continuous distribution with three parameters displays a prominent level of flexibility to model decreasing, symmetric, and asymmetric data with a monotone failure rate. The recovery rates of COVID-19 in Turkey and France were examined; moreover, milk production data and components’ failure rates are presented for data modeling. The obtained results proved the superiority of the newly suggested model compared to other unit-based distributions. Several statistical features are studied such as the quantile function, the moments, the moment-generating function, some entropy measures, the ordered statistics, the stress–strength, and stochastic ordering. Two classical estimation methods are used in addition to the Bayesian method. The statistical features and estimation analysis are evaluated using numerical and simulation techniques. As a result, we obtain the efficiency of using the Bayesian method over the classical ones, with respect to the bias, average squared error, and the length of confidence intervals for the unknown parameters.

A note on monotonicity and Bochner formulas in Carnot groups

In this note, we prove two monotonicity formulas for solutions of$\Delta _H f = c$and$\Delta _H f - \partial _t f = c$in Carnot groups. Such formulas involve the right-invariantcarré du champof a function and they are false for the left-invariant one. The main results, theorems 1.1 and 1.2, display a resemblance with two deep monotonicity formulas respectively due to Alt–Caffarelli–Friedman for the standard Laplacian, and to Caffarelli for the heat equation. In connection with this aspect we ask the question whether an ‘almost monotonicity’ formula be possible. In the last section, we discuss the failure of the nondecreasing monotonicity of an Almgren type functional.

Experimental assessment on the fatigue mechanical properties and fracturing mechanism of sandstone exposed to freeze-thaw treatment and cyclic uniaxial compression

The coupling problem of freeze-thaw (F-T) treatment and cyclic loading is extremely prominent for rock engineering in Tibetan Plateau, which has triggered many serious geotechnical engineering disasters. It is thus essential to systematically characterize the fatigue mechanism of rocks exposed to F-T treatment and cyclic loading. In this study, a series of cyclic uniaxial compression tests are conducted on sandstone subjected to 0, 10, 20, 30, 40 and 50 artificial F-T cycles to investigate the influence of F-T treatment on the fatigue mechanical properties of sandstone, regarding the fatigue deformation characteristics, energy evolution and coupled F-T-fatigue damage. Our testing results indicate that sandstone specimens exposed to higher F-T cycles are featured by larger irreversible strain and faster damage accumulation, leading to higher fatigue damage variable and lower fatigue life. By virtue of the digital image correlation (DIC) technique and scanning electron microscope (SEM), the progressive fatigue fracture process and the microscopic morphologies of fracture surfaces of the F-T treated sandstone specimens are revealed. During the cyclic loading process, the strain field in specimens uniformly distributes initially, and then it localizes continually with increasing cyclic number, triggering the eventual fatigue fracture. With increasing F-T cycles, the fatigue fracture of sandstone is more ductile and progressive. Moreover, the hidden linkage between microscopic fracture mechanism and macroscopic mechanical properties is further analyzed based on the test results. In addition, the microscopic fracture mechanism of F-T treated sandstone under cyclic loading and monotonic loading is also compared and discussed: the primary micro-mechanism causing the fatigue fracture of sandstone is the inter-granular (IG) fracture, while the micro-mechanism triggering the monotonic failure is the trans-granular (TG) fracture.

Contributions Towards New Families of Distributions: An Investigation, Further Developments, Characterizations and Comparative Study

In the past couple of years, statistical models have been extensively used in applied areas for analyzing real data sets. However, in numerous situations, the traditional distributions are not flexible enough to cater to different aspects of the real phenomena. For example, (i) in the practice of reliability engineering and biomedical analysis, some distributions provide the best fit to the data having monotonic failure rate function, but fails to provide the best fit to the data having non-monotonic failure rate function, (ii) some statistical distributions provide the best fit for small insurance losses, but fails to provide an adequate fit to large claim size data, and (iii) some distributions do not have closed forms causing difficulties in the estimation process. To address the above issues, therefore, several methods have been suggested to improve the flexibility of the classical distributions. In this article, we investigate some of the former methods of generalizing the existing distributions. Further, we propose nineteen new methods of extending the classical distributions to obtain flexible models suitable for modeling data in applied fields. We also provide certain characterizations of the newly proposed families. Finally, we provide a comparative study of the newly proposed and some other existing well-known models via analyzing three real data sets from three different disciplines such as reliability engineering, medical, and financial sciences.

Bayesian and frequentist approach for the generalized log-logistic accelerated failure time model with applications to larynx-cancer patients

The log-normal, log-logistic and Weibull distributions are commonly utilized to model survival data. Unimodal (or non-monotone) failure rate functions are modeled using the log-normal and the log-logistic families, whereas monotone failure rate functions are modeled using the Weibull family. The growing availability of survival data with a variety of features encourages statisticians to propose more flexible parametric models that can accommodate both monotone (increasing or decreasing), and non-monotone (unimodal or bathtub) failure rate functions. One such model is the generalized log-logistic distribution which not only accommodates unimodal failure rates but also allows for a monotone and non-monotone failure rate functions. This distribution has shown to have a lot of potential in univariate analysis of survival data. However, many studies are primarily concerned with determining the link between survival time and one or more explanatory variables. This leads to the study of hazard-based regression models in survival and reliability analysis, which can be formulated in a variety of ways. One such method concerns formulating hazard-based regression models for the accelerated failure time (AFT) family of continuous probability distributions. The log-logistic, Weibull and log-normal distributions are the most widely utilized this framework. In this paper, we show that the generalized log-logistic distribution is closed under the accelerated failure time framework. We then formulate an accelerated failure time model based on the generalized log-logistic distribution. Furthermore, we show parameter estimation for the model using Bayesian and frequentist approaches. An extensive simulation study is conducted to illustrate the inferential properties of the proposed model, more specifically, the tendency to recover the baseline hazard shapes, parameter estimation, as well as the effect of censoring proportions on inference. The simulation results demonstrate that the generalized log-logistic accelerated failure time model can be capable of modeling survival data with various hazard rate shapes. Finally, a real-life survival data relating to larynx-cancer patients was used.

Lomax gamble type two distributions with applications to lifetime data

The Gumbel Type-Two (GTT) distribution among many classical distributions has been found to lack the capacity to adequately fit some random phenomenon due to its monotonic failure rates thereby limiting its application. The Lomax-Generator was employed in this study to generalize the GTT distribution in order to derive the Lomax Gumbel Type-Two (LGTT) distribution capable of providing better modeling fits to real dataset. The new distribution has the Lomax Inverse Exponential distribution as a special case; the reliability and hazard rates functions were investigated. The distribution is unimodal, positively skewed and close to bell shape depending on parameter values. The quantile, median and order statistics were derived while the method of maximum likelihood estimation was used for estimating the parameters of the distribution. The proposed distribution demonstrated its potentials for modeling events whose distributions tends to be platykurtic, leptokurtic and approximately symmetric. Two lifetime survival datasets were analyzed using the distribution and results revealed the importance of application of LGTT distribution to the datasets with superior modeling fits than other four generalizations of GTT distributions existing in literatures derived using other generator. Three additional real life datasets were also used to compare the performance of LGTT with some distributions derived using Lomax as generator, results of analysis revealed that LGTT exhibits greater flexible potentials for modelling the real life datasets.

The Exponentiated XGamma Distribution: a New Monotone Failure Rate Model and Its Applications to Lifetime Data

The Exponentiated XGamma Distribution: a New Monotone Failure Rate Model and Its Applications to Lifetime Data

On the Discrete Weibull Marshall–Olkin Family of Distributions: Properties, Characterizations, and Applications

In this article, we introduce a new flexible discrete family of distributions, which accommodates wide collection of monotone failure rates. A sub-model of geometric distribution or a discrete generalization of the exponential model is proposed as a special case of the derived family. Besides, we point out a comprehensive record of some of its mathematical properties. Two distinct estimation methods for parameters estimation and two different methods for constructing confidence intervals are explored for the proposed distribution. In addition, three extensive Monte Carlo simulations studies are conducted to assess the advantages between estimation methods. Finally, the utility of the new model is embellished by dint of two real datasets.

The Marshall-Olkin Extended Gumbel-weibull Distribution: Properties And Applications

We introduce a new lifetime distribution called Marshall-Olkin extended Gumbel-Weibull. Some properties of distribution such as moments, TL-moments, quantile function, en- tropy, and order statistics are studied. The fexibility of the distribution to model unimodal, monotone shapes as well as unimodal, bimodal, monotone failure rates are presented. The estimators of the parameters of the distribution were obtained using the maximum likeli- hood estimation method. The performance of the maximum likelihood estimates of the Marshall-Olkin extended Gumbel-Weibulll parameters was observed through simulation studies. Two real life applications to illustrate the potentials of the new distribution are presented, and comparison with other distribution having the same baseline is done using goodness-of-test statistics.

New Lindley Half Cauchy Distribution Theory and Applications

In this paper, we have defined a new two-parameter new Lindley half Cauchy (NLHC) distribution using Lindley-G family of distribution which accommodates increasing, decreasing and a variety of monotone failure rates. The statistical properties of the proposed distribution such as probability density function, cumulative distribution function, quantile, the measure of skewness and kurtosis are presented. We have briefly described the three well-known estimation methods namely maximum likelihood estimators (MLE), least-square (LSE) and Cramer-Von-Mises (CVM) methods. All the computations are performed in R software. By using the maximum likelihood method, we have constructed the asymptotic confidence interval for the model parameters. We verify empirically the potentiality of the new distribution in modeling a real data set.

Lindley Gompertz distribution with properties and applications

In this article, we have presented a new three-parameter probability distribution called the Lindley Gompertz distribution. The proposed model can exhibit increasing, increasing-decreasing, j-shaped, and bathtub, and a broad variety of monotone failure rates. Some properties of this model are studied and calculated. Three extensively used estimation methods are used to estimate the model parameters namely maximum likelihood estimators (MLE), least-square (LSE), and Cramer-Von-Mises (CVM) methods. By using the maximum likelihood estimate we have constructed the asymptotic confidence interval for the model parameters. All the computations are performed in R software. The potentiality of the proposed distribution is revealed by using some graphical methods and statistical tests taking a real dataset, where the proposed distribution provided a better fit and more flexible in comparison with some other lifetime distributions.

The Modified Kumaraswamy Weibull Distribution: Properties and Applications in Reliability and Engineering Sciences

We introduce the Kumaraswamy alpha power-G (KAP-G) family which extends the alpha power family (Mahdavi and Kundu, 2017) and some other families. We consider the Weibull as baseline for the KAP family and generate Kumaraswamy alpha power Weibull distribution which has right-skewed, left-skewed, symmetrical, and reversed-J shaped densities, and decreasing, increasing, bathtub, upside-down bathtub, increasing-decreasing–increasing, J shaped and reversed-J shaped hazard rates. The proposed distribution can model non-monotone and monotone failure rates which are quite common in engineering and reliability studies. Some basic mathematical properties of the new model are derived. The maximum likelihood estimation method is used to evaluate the parameters and the observed information matrix is determined. The performance and flexibility of the proposed family is illustrated via two real data applications.

Effect of partial vs complete circumferential epitendinous suture placement on the biomechanical properties and gap formation of canine cadaveric tendons.

To determine the effect of partial vs complete circumferential epitendinous suture (ES) placement in addition to a core suture on the biomechanical strength and gapping characteristics of repaired canine tendinous constructs. Ex vivo, biomechanical study. Thirty-six canine superficial digital flexor tendons. Superficial digital flexor tendons were randomly assigned to three groups (n = 12), sharply transected and repaired with a core locking-loop suture with Group 1 a partial circumferential ES, 180° on the palmar side; Group 2 a complete circumferential ES, 360° and double knotting technique; or Group 3 a complete circumferential ES, 360° and single knotting technique. After preloading, constructs were distracted to monotonic failure. Failure mode, gap formation, yield, peak, and failure forces were analyzed. Mean yield (group 1 = 68.6 N, group 2 = 106.5 N, group 3 = 114 N, P < .013), peak (group 1 = 92.8 N, group 2 = 134.6 N, group 3 = 147.3 N; P < .001), and failure (group 1 = 88.7 N, group 2 = 133.0 N, group 3 = 145.5 N, P < .001) loads differed between groups. No difference in yield (P = .874), peak (P = .434), or failure load (P = .434) was detected between complete circumferential ES groups. Force to create 1-mm (P < .001) and 3-mm (P < .038) gap formation was greater in specimens with complete vs partial circumferential ES placement. Complete circumferential ES repairs failed primarily by suture pull-through compared with suture breakage in most partial circumferential ES constructs. Addition of a complete circumferential ES with a single or double knotting technique increased the biomechanical strength of normal tendon repairs while reducing gap formation compared with partial ES placement alone. Complete circumferential ES is recommended over partial ES placement.

Generalising Exponential Distributions Using an Extended Marshall–Olkin Procedure

This paper presents a three-parameter family of distributions which includes the common exponential and the Marshall–Olkin exponential as special cases. This distribution exhibits a monotone failure rate function, which makes it appealing for practitioners interested in reliability, and means it can be included in the catalogue of appropriate non-symmetric distributions to model these issues, such as the gamma and Weibull three-parameter families. Given the lack of symmetry of this kind of distribution, various statistical and reliability properties of this model are examined. Numerical examples based on real data reflect the suitable behaviour of this distribution for modelling purposes.

On the non-monotonicity of entropy for a class of real quadratic rational maps

We prove that the entropy function on the moduli space of real quadratic rational maps is not monotonic by exhibiting a continuum of disconnected level sets. This entropy behavior is in stark contrast with the case of polynomial maps, and establishes a conjecture on the failure of monotonicity for bimodal real quadratic rational maps of shape $(+-+)$ which was posed in arXiv:1901.03458 based on experimental evidence.

The alpha-mixture of survival functions

AbstractThis paper presents a flexible family which we call the $\alpha$ -mixture of survival functions. This family includes the survival mixture, failure rate mixture, models that are stochastically closer to each of these conventional mixtures, and many other models. The $\alpha$ -mixture is endowed by the stochastic order and uniquely possesses a mathematical property known in economics as the constant elasticity of substitution, which provides an interpretation for $\alpha$ . We study failure rate properties of this family and establish closures under monotone failure rates of the mixture’s components. Examples include potential applications for comparing systems.