Search Results (382)

Limitations inherent to existing statistical distributions in capturing the complexities of real-world data often necessitate the development of novel models. This paper introduces the new exponential generalized inverse generalized Weibull (NEGIGW) distribution. The NEGIGW distribution boasts significant flexibility with symmetrical and asymmetrical shapes, allowing its hazard rate function to be adapted to many failure patterns observed in various fields such as medicine, biology, and engineering. Some statistical properties of the NEGIGW distribution, such as moments, quantile function, and Renyi entropy, are studied. Three methods are used for parameter estimation, including maximum likelihood, maximum product of spacing, and percentile methods. The performance of the estimation methods is evaluated via Monte Carlo simulations. The NEGIGW distribution excels in its ability to fit real-world data accurately. Five medical and engineering datasets are applied to demonstrate the superior fit of NEGIGW distribution compared to competing models. This compelling evidence suggests that the NEGIGW distribution is promising for lifetime data analysis and reliability assessments across different disciplines. Full article

Large-tow carbon fiber-reinforced polymer composites (CFRP) have great application potential in civil engineering due to their low price, but their basic mechanical properties are still unclear. The tensile properties of large-tow CFRP rods and plates were investigated in this study. First, the tensile properties of unidirectional CFRP rods and plates were studied, and the test results of the relevant mechanical properties were statistically analyzed. The tensile strength of the CFRP rod and plate are 2005.97 MPa and 2069.48 MPa. Second, the surface of the test specimens after failure was observed using a scanning electron microscope to analyze the type of failure and damage evolution process. Finally, the probabilistic characteristics of the mechanical properties were analyzed using normal, lognormal, and Weibull distributions for parameter fitting. Quasi-optimality tests were performed, and a probability distribution model was proposed for the mechanical properties of large-tow CFRP rods and plates. Full article

Measuring the flexural strength of restorative materials such as zirconia is crucial for providing proper indications for clinical applications and predicting performance. Great variations in specimen preparation for flexural strength measurements exist among laboratories. The aim was to evaluate how the processing method, surface treatment, and test method of the specimens affect the flexural strength of zirconia. Zirconia specimens (VITA YZ HT) (n = 270) were processed using CAD/CAM or were conventionally milled with three different surface treatments (machined, ground, polished) and were measured with three-point bending (non-chamfered/chamfered) or biaxial flexural strength test. Weibull statistics were conducted. The mean flexural strength values ranged from 612 MPa (conventional, machined, three-point bending non-chamfered) to 1143 MPa (CAD/CAM, polished, biaxial flexural strength). The highest reliability is achieved when specimens are prepared using thoroughly controllable processing with CAD/CAM and subsequently polished. Higher strength values are achieved with the biaxial flexural strength test method because the stress concentration in relation to the effective volume is smaller. Polishing reduces surface microcracks and therefore increases the strength values. Full article

In this paper, four probability functions are compared with the purpose of establishing a methodology to improve the accuracy of wind energy estimations in a desert city in Northwestern Mexico. Three time series of wind speed data corresponding to 2017, 2018, and 2019 were used for statistical modeling. These series were recorded with a sonic anemometer at a sampling frequency of 10 Hz. Analyses based on these data were performed at different stationarity periods (5, 30, 60, and 600 s). The estimation of the parameters characterizing the probability density functions (PDFs) was carried out using different methods; the statistical models were evaluated by the coefficient of determination and Nash–Sutcliffe efficiency coefficient, and their accuracy was estimated by the measured quadratic error, mean square error, mean absolute error, and mean absolute percentage error. Weibull, using the energy pattern factor method, and Gamma, using the Method of Moments, were the probability density functions that best described the statistical behavior of wind speed and were better at estimating the generated energy. We conclude that the proposed methodology will increase the confidence of both wind speed estimation and the energy supplied by small-scale wind installations. Full article

The performance and reliability of lithium thionyl chloride (Li/SOCl₂) batteries are significantly affected by temperature, but the reliability level and failure mechanisms of Li/SOCl₂ batteries remain unclear. In this study, Weibull distribution statistics were used to infer the life expectancy of Li/SOCl₂ batteries at different temperatures. Additionally, the battery failure mechanism was analyzed using electrochemical impedance spectroscopy (EIS). It is found that under the discharge condition of 7.5 kΩ load, the mean time between failures (MTBF) and reliable life of the battery decreased with increasing operating temperature. Under the discharge condition of 750 Ω load, the MTBF of the battery peaked at 60 °C. Furthermore, the influence of temperature on the voltage output characteristics of Li/SOCl₂ batteries and the voltage hysteresis were analyzed. Both the battery output voltage and the hysteresis effect increased with rising temperature. This is because high temperature accelerates internal battery reactions, thus altering the formation process of the passivation film on the lithium metal negative electrode. Full article

The gyroid structure is a bio-inspired structure that was discovered in butterfly wings. The geometric design of the gyroid structure in butterfly wings offers a unique combination of strength and flexibility. This study investigated sandwich panels consisting of a 3D-printed gyroid structure core and carbon fiber-reinforced polymer (CFRP) facing skin. A filament fused fabrication 3D printer machine was used to print the gyroid cores with three different relative densities, namely 10%, 15%, and 20%. Polylactic acid (PLA) was used as the printing material for the gyroid. The gyroid structure was then sandwiched and joined by an epoxy resin between CFRP laminates. Polyurethane foam (PUF) was filled into the gyroid core to fill the cavity on the core for another set of samples. Flexural and compression tests were performed on the samples to investigate the mechanical behavior of the sandwiches. Moreover, the two-parameter Weibull distribution was used to evaluate the results statistically. As a result, the sandwich-specific facing stress and core shear strength from the three-point bending test of the composites increased with the increase in sandwich density. Core density controls the flexural characteristics of the sandwich. Adding PUF improves the deflection at the maximum stress and the sustained load after fracture of the sandwich. Compression strength, modulus, and energy absorbed by gyroid core sandwiches and their specific properties are higher than the PUF-filled gyroid core sandwiches at equal sandwich density. Full article

A complete framework of predicting the attributes of sea clutter under different operational conditions, specified by wind speed, wind direction, grazing angle, and polarization, is proposed for the first time. This framework is composed of empirical spectra to characterize sea-surface profiles under different wind speeds, the Monte Carlo method to generate realizations of sea-surface profiles, the physical-optics method to compute the normalized radar cross-sections (NRCSs) from individual sea-surface realizations, and regression of NRCS data (sea clutter) with an empirical probability density function (PDF) characterized by a few statistical parameters. JONSWAP and Hwang ocean-wave spectra are adopted to generate realizations of sea-surface profiles at low and high wind speeds, respectively. The probability density functions of NRCSs are regressed with K and Weibull distributions, each characterized by two parameters. The probability density functions in the outlier regions of weak and strong signals are regressed with a power-law distribution, each characterized by an index. The statistical parameters and power-law indices of the K and Weibull distributions are derived for the first time under different operational conditions. The study reveals succinct information of sea clutter that can be used to improve the radar performance in a wide variety of complicated ocean environments. The proposed framework can be used as a reference or guidelines for designing future measurement tasks to enhance the existing empirical models on ocean-wave spectra, normalized radar cross-sections, and so on. Full article

The present paper investigates flaw strength distributions established using various flexural tests on batches of SiC bar test specimens, namely four-point bending as well as three-point bending tests with different span lengths. Flaw strength is provided by the elemental stress operating on the critical flaw at the fracture of a test specimen. Fracture-inducing flaws and their locations are identified using fractography. A single population of pores was found to dominate the fracture. The construction of diagrams of p-quantile vs. elemental strengths was aimed at assessing the Gaussian nature of flaw strengths. Then, empirical cumulative distributions of strengths were constructed using the normal distribution function. The Weibull distributions of strengths are then compared to the normal reference distributions. The parameters of the Weibull cumulative probability distributions are estimated using maximum likelihood and moment methods. The cumulative distributions of flexural strengths for the different bending tests are predicted from the flaw strength density function using the elemental strength model, and from the cumulative distribution of flexural strength using the Weibull function. Flaw strength distributions that include the weaker flaws that are potentially present in larger test pieces are extrapolated using the p-quantile diagrams. Implications are discussed regarding the pertinence of an intrinsically representative flaw strength distribution, considering failure predictions. Finally, the influence of the characteristics of fracture-inducing flaw populations expressed in terms of flaw strength interval, size, dispersion, heterogeneity, and reproducibility with volume change is examined. Full article

Moments of order statistics (OSs) characterize the Weibull–geometric and half-logistic families of distributions, of which the extended exponential–geometric (EEG) distribution is a particular case. The EEG distribution is used to create the log-extended exponential–geometric (LEEG) distribution, which is bounded in the unit interval (0, 1). In addition to the generalized Stirling numbers of the first kind, a few years ago, the polylogarithm function and the Lerch transcendent function were used to determine the moments of order statistics of the LEEG distributions. As an application based on the L-moments, we expand the features of the LEEG distribution in this work. In terms of the Gauss hypergeometric function, this work presents the precise equations and recurrence relations for the single moments of OSs from the LEEG distribution. Along with recurrence relations between the expectations of function of two OSs from the LEEG distribution, it also displays the truncated and conditional distribution of the OSs. Additionally, we use the L-moments to estimate the parameters of the LEEG distribution. We further fit the LEEG distribution on three practical data sets from medical and environmental sciences areas. It is seen that the estimated parameters through L-moments of the OSs give a superior fit. We finally determine the correspondence between the entropies and the OSs. Full article

While it is well known that the Weibull distribution is a good model for wind-speed measurements and can be explained through simple statistical arguments, how such a model holds for shorter time periods is still an open question. In this paper, we present a systematic investigation of the accuracy of the Weibull distribution to wind-speed measurements, in comparison with other possible “cousin” distributions. In particular, we show that the Gaussian distribution enables one to predict wind-speed histograms with higher accuracy than the Weibull distribution. Two other good candidates are the Nakagami and the Rice distributions, which can be interpreted as particular cases of the Weibull distribution for particular choices of the shape and scale parameters. These findings hold not only when predicting next-point values of the wind speed but also when predicting the wind energy values. Finally, we discuss such findings in the context of wind power forecasting and monitoring for power-grid assessment. Full article

Reactor pressure vessel (RPV) steels are highly susceptible to irradiation embrittlement due to prolonged exposure to high temperature, high pressure, and intense neutron irradiation. This leads to the shift in nil-ductility transition reference temperature—∆RT_NDT. The change in ∆RT_NDT follows a certain distribution pattern and is impacted by factors including chemical composition, neutron fluence, and irradiation temperature. Existing empirical procedures can estimate ∆RT_NDT based on fitting extensive irradiation embrittlement data, but their reliability has not been thoroughly investigated. Probability statistical distributions and the Gamma stochastic process were performed to model material property degradation in RPV steels from a pressurized water reactor due to irradiation embrittlement, with the probability models considered being normal, Weibull, and lognormal distributions. Comparisons with existing empirical procedures showed that the Weibull distribution model and the Gamma stochastic model demonstrate good reliability in predicting ∆RT_NDT for RPV steels. This provides a valuable reference for studying irradiation embrittlement in RPV materials. Full article

Symmetrical as well as asymmetrical statistical models play a prominent role in describing and predicting the real-world phenomena of nature. Among other fields, these models are very useful for modeling data in the sector of civil engineering. Due to the applicability of the statistical models in civil engineering and other related sectors, this paper offers a statistical methodology to improve the distributional flexibility of traditional models. The suggested method/approach is called the extended-X family of distributions. The proposed method has the ability to generate symmetrical and asymmetrical probability distributions. Based on the extended-X family approach, an updated version of the Weibull model, namely, the extended Weibull model, is studied. The proposed model is very flexible and has the ability to capture the symmetrical and asymmetrical shapes of its density function. For the extended-X method, the estimation of parameters, a simulation study, and some mathematical properties are derived. Finally, the practical illustration/usefulness of the suggested model is shown by analyzing two data sets taken from the field of engineering. Both data sets represent the fracture toughness of alumina (Al₂O₃). Full article

Improvement of the surface quality of machined parts is essential in order to avoid excessive and costly post-processing. Although non-conventional processes can efficiently carry out the machining of difficult-to-cut materials with high productivity, they may also, for various reasons, be related to increased surface roughness. In order to optimize the surface quality of generated surfaces in a reliable way, surface profiles obtained during these processes must be adequately modeled. However, given that most studies have focused on Ra or Rz indicators or are based on the assumption of a normal distribution for the profile heights, relevant models cannot accurately represent the surface characteristics that exist in a real machined surface with a high degree of accuracy. Thus, in the present study, a new modeling approach based on the use of a statistical probability distribution for the surface profile height is proposed. After six different distributions were evaluated on the basis of a three-stage procedure involving different roughness indicators pertaining to the abrasive waterjet (AWJ) milling of pockets, it was found that, although it is not possible to model the nominal values of every roughness parameter simultaneously, in several cases, it is possible to approximate the values of critical indicators such as Ra, Rz, Rsk, Rku and Rp/Rv ratio by Weibull distribution with a sufficient degree of accuracy. Full article

For complex equipment, it is easy to over-evaluate the impact of failure on production by estimating the reliability level only through failure probability. To remedy this problem, this paper proposes a statistical evaluation method based on fuzzy failure data considering the multi-state characteristics of equipment failures. In this method, the new reliability-evaluation scheme is firstly presented based on the traditional statistical analysis method using the Weibull distribution function. For this scheme, the failure-grade index is defined, and a fuzzy-evaluation method is also proposed by comprehensively considering failure severity, failure maintenance, time, and cost; this is then combined with the time between failures to characterize the failure state. Based on the fuzzy failure data, an improved adaptive-failure small-sample-expansion method is proposed based on the classical bootstrap method and the deviation judgment between distributions of the original and newborn samples. Finally, a novel reliability-evaluation model, related to the failure grade and its membership degree, is established to quantify the reliability level of equipment more realistically. Example cases for three methods of the scheme (the failure-grade fuzzy-evaluation method, the sample-expansion method, and the reliability-evaluation modeling method) are presented, respectively, to validate the effectiveness and significance of the proposed reliability-evaluation technology. Full article

The deformation and damage process of rocks is accompanied by crack extension and penetration. The rock strength criterion, as a macroscopic characterization of the rock strength microelement, is the basis for establishing the damage constitutive modeling of rock. Aiming at the problem of the Hoek–Brown (H–B) strength criterion having a large strength prediction value under high confining pressure, the H–B strength criterion is corrected by considering the influence of the initial cracks on the development of the rock strength, and its applicability is verified. Based on the damage theory, assuming that the rock strength microelement obeys the Weibull distribution and considering the influence of residual strength, the damage correction coefficient is introduced, and a thermal damage statistical constitutive model that can reflect the whole process of the development of initial cracks inside the rock is established. The degree of penetration up to the damage is established, and the method of determining the parameters of the model is given. The theoretical curves of the established model are compared and analyzed with the curves of a conventional triaxial compression test of rock samples, and the study shows that the statistical constitutive model of the thermal damage of rock, established based on the modified H–B strength criterion, can better simulate the stress–strain relationship of rock under a conventional triaxial test. It also verifies the reasonableness and applicability of the model, which is expected to provide a basis for the exploitation of deep resources and the safety assessment of underground engineering. Full article