Values Of Shape Parameter Research Articles

Comparison of Unsaturated Behaviour of Residual Soil in Malaysia and the Effect of Particle Size Distribution

The unsaturated behaviour of residual soil in Malaysia has been studied, yet the impact of particle size distribution (PSD) on soil-water characteristics still needs to be more adequately explored. Previous research highlights the significance of fine particles in controlling geotechnical properties. This study investigates how the PSD of five soil samples influences the Soil-Water Characteristic Curve (SWCC) parameters, water retention, storage properties and permeability. The study involved five samples, four samples from Ibrahim et al., [1] research, such as reserved forest, gravelly sand, silty sand, kaolin and silty clay soil from the Garinono Formation soil. A pressure plate extractor determined the samples' Soil-Water Characteristic Curve (SWCC) and bulk density. The van Genutchen (1980) model fitted experimental data and the hydraulic response was studied on the five soil samples. The results show that Kaolin and silty clay have higher volumetric water content than gravelly and silty sand due to a higher percentage of silty and clay particles. However, the reserve forest sample has volumetric water content like kaolin and silty clay due to its natural location. Reserved forest, kaolin and silty clay samples have higher water storage, i.e., effective soil porosity (ESP) values than gravelly sand due to higher clay and silty contents. Silty sand, reserve forest and gravelly sand have higher shape parameter (n) values due to their higher sand and gravel content. Clay-rich samples had smaller (n) values, indicating a more uniform distribution. Hydraulic conductivity function (K(θ)) is influenced by scale parameter (α), Air-Entry Value (AEV) and Saturated Hydraulic Conductivity K_s. Kaolin and silty clay samples exhibit lower α values, resulting in higher suction at AEV than other soils as they contain high silty and clay contents. Saturated conductivity values directly affect hydraulic conductivity function, while AEV inversely affects the unsaturated flow. Understanding unsaturated hydraulic responses and SWCC characteristics could assist in anticipating slope instability and ground stabilisation in residual soil and soil behaviour during and after rainfall.

Control chart for generalized exponential distribution based on modified chain sampling

Abstract In recent years, modern statistical process control has established higher concentration, and this approach is reinforced by new control charts to efficiently monitor the process. The goal of this article is to create a control chart based on a modified chain sampling plan (MchSP) when product quality dimensions are followed by a generalized exponential distribution. There was a brief overview of the generalized exponential distribution (GED) and the modified chain sampling strategy. The chart parameters were presented for several sample sizes at various average run length (ARL) values. A variety of tables were provided for the actual application of the produced control chart in industrial applications at various shift values of scale and form parameters. The real data set was used to demonstrate the application of the created MchSP control chart process. In addition, the proposed MchSP control chart process was developed using simulated data. The average run length (ARL) results of the established control chart for shifting both scale and shape parameters were computed for various sample sizes. The results show that when the shift constant (both scale and form) increases, the ARL values decrease. Also, it was discovered that ARL1 values tend to decrease as the shape parameter value increases.

Evaluation of reliability and characteristics measure using exponential decay distribution of non‐series parallel network

AbstractThe purpose of this paper is to analyze the reliability and characteristics of the non‐series‐parallel network. The illustrative non‐series parallel networks, that is, the Twin T‐Network and the network with six components of resistor and capacitor, have been converted into a series of parallel network combinations by use of the minimal path technique. The stochastic variables related to component failure rate have been demonstrated using exponential decay distribution. We obtain the reliability, mean time to failure, and sensitivity with the use of the exponential decay distribution. The reliability and its attributes are examined by assuming different values of scale and shape parameters at different points of time. Using Owen's methodology, we obtained minimal signature, tail signature, expected time, expected cost, and Barlow‐Proschan index were determined. The performance of all reliability characteristics has been observed graphically for arbitrary values of parameters. A real‐world example is used to introduce the point.

Mixture reliability analysis of a product consisting of new and remanufactured components

PurposeThe rapid increase in importance of the remanufacturing operation in the present scenario is just because of its ability to retrieve the functional value of the End-of-Use or End-of-Life products which is as good as the original product. However, customers are still concerned about the reliability of the remanufactured product which is considered as one of the major problems in the area of remanufacturing. The purpose of this paper is to study and analyse the behavioural pattern of the mixture failure rate of a remanufactured product.Design/methodology/approachIn order to analyse the behavioural pattern of the mixture failure rate, different proportions of new and remanufactured products are mixed. In this paper, a two-parameter Weibull distribution is used to observe the mixture failure rate characteristics. Also, the mixture failure rate of the remanufactured product is evaluated under two conditions, that is when the shape parameter of new and remanufactured components is the same and when the shape parameter values are different.FindingsFrom the analysis, it is observed that the mixture failure rate is always decreasing in nature when the shape parameter values are same. In that case, the value of the mixture failure rate depends only on the proportion of the new components. When the shape parameter values are different, the mixture failure rate characteristics depend upon the shape parameter value of the remanufactured product.Originality/valueThe results of the research can be applied to any remanufactured automotive product. This study also shows the behavioural characteristics of the mixture failure rate of a remanufactured product at different mixture proportions.

An in-depth analysis of the Radial Point Interpolation Method’s parameters in relation to the accuracy of fracture problem

The fracture problem has been modeled using Radial Point Interpolation Method (RPIM) to examine the effects of support domain size and shape parameter value on the calculation of Stress Intensity Factor (SIF). The study focuses on an edge crack problem subjected to normal load and shear loads, determining that the support domain size of ‘ α ≥ 3.5 and shape parameter value between ‘ n = 1.9 -2.1’ yield results of accuracy with error % ≤ 3 % . Additionally, research extended by varying the problem domain size and crack location to verify consistency. The findings indicate that selecting the optimal shape parameter value will ensure better accuracy over the enrichment techniques with lesser computational cost.

The influence of vesicularity on grain morphology in basaltic pyroclasts from Mauna Loa and Kīlauea volcanoes

Vesicularity of individual pyroclasts from airfall tephra deposits is an important parameter that is commonly measured at basaltic volcanoes. Conventional methods used to determine pyroclast vesicularity on a large number of clasts has the potential to be time consuming, particularly when rapid analysis is required. Here we propose dynamic image analysis on two-dimensional (2D) projection shapes of crushed pyroclasts from tephra deposits as a new method to estimate vesicularity. This method relies on the influence of vesicles and uses grain morphology as a proxy for vesicle size and abundance. Pyroclasts from a variety of basaltic tephra deposits from the volcanoes of Mauna Loa and Kīlauea were analyzed. Vesicularities between 52–98% were measured via nitrogen-gas pycnometry. The same pyroclasts were then crushed and sieved, and their grain shapes measured using dynamic image analysis on a CAMSIZER®. This yields values for the mean sphericity, elongation, compactness, and Krumbein roundness of the grains. Our data show that grains become increasingly irregular with increasing vesicularity, with the degree of correlation between shape parameters and vesicularity depending on the size of measured grains. Shape irregularities in small grains (60–250 µm) are mostly area-based, with elongation being the best vesicularity indicator, whereas shape irregularities in large grains (250–700 µm) are mostly perimeter-based, with Krumbein roundness as the best vesicularity indicator. Using mean shape parameter values with all grain sizes included, grain elongation is the most well-correlated shape parameter with vesicularity, with the best fitted model explaining 76% of variation in the observations. Microscope images of thin sections of intact pyroclasts, as well as from crushed pyroclasts, were analyzed using CSDCorrections 1.6 software in ImageJ to find local vesicularity, vesicle size, grain size, grain elongation, and vesicle spatial distribution by stereological conversion. Observed correlation between grain shape and vesicularity can be explained by the local effect of vesicles on the shape of the solid structure in between those vesicles. Grain shape depends not only on vesicularity, but also on vesicle to grain size ratio and the spatial distribution of vesicles. The influence of vesicles on grain shape is best captured by grains with the size of the solid structure in between vesicles, which generally increases with decreasing vesicularity. Dynamic image analysis is a useful tool to quickly gauge vesicularity, which could be used in near-real-time during an eruption response. However, this method is best suited for highly vesicular (> 80%) basaltic pyroclasts from tephra deposits with few microlites and phenocrysts. Further research on crushing techniques, optimum grain size for shape measurements, and Krumbein roundness measurements for the grain size range of 250–700 µm might enable application of this method to lower vesicularity pyroclasts.

Optimal and economic design of multiple deferred state repetitive group sampling plan for assuring mean life under a family of lifetime distributions

In this paper, a designing methodology of the multiple deferred (dependent) state repetitive group sampling plan is developed to ensure the mean lifetime of the products under the truncated life test, which follows a family of different lifetime distributions. An approach of two points on the operating characteristic curve is followed to obtain the optimal plan parameters with the known shape parameter values for various mean life ratios under different lifetime models. The proposed sampling plan is illustrated with a numerical example. The application of the proposed sampling plan is explained with a real-life example based on Burr XII distribution. Comparison is made among the performances of the proposed sampling plan using the different lifetime distributions; these performances are also compared with a single sampling plan using Burr XII distribution based on mean life assurance. Finally, an economic design of the proposed sampling plan is discussed, along with some cost models to minimize the total cost.

Generalized Bézier-like model and its applications to curve and surface modeling.

The subject matter of surfaces in computer aided geometric design (CAGD) is the depiction and design of surfaces in the computer graphics arena. Due to their geometric features, modeling of Bézier curves and surfaces with their shape parameters is the most well-liked topic of research in CAGD/computer-aided manufacturing (CAM). The primary challenges in industries such as automotive, shipbuilding, and aerospace are the design of complex surfaces. In order to address this issue, the continuity constraints between surfaces are utilized to generate complex surfaces. The parametric and geometric continuities are the two metrics commonly used for establishing connections among surfaces. This paper proposes continuity constraints between two generalized Bézier-like surfaces (gBS) with different shape parameters to address the issue of modeling and designing surfaces. Initially, the generalized form of C3 and G3 of generalized Bézier-like curves (gBC) are developed. To check the validity of these constraints, some numerical examples are also analyzed with graphical representations. Furthermore, for a continuous connection among these gBS, the necessary and sufficient G1 and G2 continuity constraints are also developed. It is shown through the use of several geometric designs of gBS that the recommended basis can resolve the shape and position adjustment problems associated with Bézier surfaces more effectively than any other basis. As a result, the proposed scheme not only incorporates all of the geometric features of curve design schemes but also improves upon their faults, which are typically encountered in engineering. Mainly, by changing the values of shape parameters, we can alter the shape of the curve by our choice which is not present in the standard Bézier model. This is the main drawback of traditional Bézier model.

Future Prediction for Tax Complaints to Turkish Ombudsman by Models from Polynomial Regression and Parametric Distribution

The aim of this study is to forecast the amount of tax complaints filed with the Turkish Ombudsman in the future and whether or not policymakers require a specific tax Ombudsman. The polynomial regression for discrete data set is proposed to fit the number of events of tax complaints in the period from years $2013$ to $2021$. The artificial data set is generated by models which are polynomial regression and parametric distribution. The location, scale and shape parameters are determined according to the smallest value between the observed and predicted dependent variable. After determining the smallest value for the tried values of shape parameter and the parameters of polynomial regression, the best value determined by grid search for shape parameter is around $1.07$. Thus, the heavy-tailed from of exponential power distribution is gained. The artificial data sets are generated and sorted from the smallest to biggest ones. The maximum values are around $700$ and $800$ which can be regarded as future prediction because the distance among observations is taken into account by models from polynomial regression and parametric distribution. Since the polynomial regression and the parametric models are used simultaneously for modelling, the distance among observations can also be modelled by parametric model as an alternative approach provided.

A stable meshless numerical scheme using hybrid kernels to solve linear Fredholm integral equations of the second kind and its applications

The main challenge in kernel-based approximation theory and its applications is the conflict between accuracy and stability. Hybrid kernels can be used as one of the simplest and most effective tools to manage this challenge. This article uses a meshless scheme based on hybrid radial kernels (HRKs) to solve second kind Fredholm integral equations (FIEs). The method estimates the solution via the discrete collocation procedure based on a hybrid kernel that combines appropriate kernels with suitable weight parameters. The optimal parameters in the hybrid kernels can be calculated using the particle swarm optimization (PSO) algorithm based on the root mean square (RMS) error. This technique converts the problem under investigation into a system of linear equations. Moreover, the convergence of the suggested hybrid approach is studied. Lastly, some numerical experiments are included to reveal the accuracy and stability of the hybrid kernels approach. The numerical results demonstrate that the presented hybrid procedure meaningfully reduces the ill-conditioning of the operational matrices, at the same time, it maintains the accuracy and stability for all values of shape parameters.

Estimation of Weibull Parameters for Wind Energy Application in Al Shihabi City

Wind energy is environmentally friendly and low-cost energy compared to other renewable energy technologies and is easily exploited by different users. Al-Shihabi ia a city with high potential wind resources. The aim of the research is to assess the mean winds and Weibull parameters such as shape parameter and scale parameter. The assessment helps in understanding the wind behavior for the application of the wind energy project. Field data for year 2019 were collected at an interval of 10 minutes at altitudes of 50 and 100 meters. Then the data was analyzed using the statistical Weibull distribution function. The annual average of monthly means at 50 m and 100 m heights are 5.04 m/s and 5.56 m/s, respectively. While the annual average of monthly maximum winds at 50 m and 100 m heights were 13.65 m/s and 15.05 m/s. The larger values were in summer months. The mean wind speed and maximum wind speed values suggest that Al-Shihabi City is a promising site to install a wind farm. Estimating Weibull distribution parameters showed for 50 m and 100 heights that the annual average of monthly values of shape parameter and scale parameter were 5.6840, and 2.4035, respectively. At 100 m height, It was found that the annual average of monthly values of shape parameter, scale parameter were 6.2634 and 2.3215, respectively. It can also be noted that the values of parameters are higher in summer than in winter. It was found that the Weibull distribution is applicable to describe the probability density of wind speed.

Quantitative Assessment of Ailia coila (Hamilton, 1822) Fish Population in Kaptai Lake: A Length‐Based Approach

ABSTRACTThe Ailia coila, a small indigenous freshwater fish species in Kaptai Lake, plays a crucial role in providing employment, food, and financial security for the local people. With a high market demand, the average production of this species over the last 5 years reached about 112.27 metric tons. However, there has been a notable decline in Ailia coila fish production in Kaptai Lake in recent years. Therefore, to understand the current stock status of this species, this study employed a length‐based stock assessment method the “length‐based spawning potential ratio (LB‐SPR)”. Between August 2022 and March 2023, a total of 1219 individuals were collected through fortnightly sampling from two fish landing centers (BFDC fishery ghat and Kaptai boat ghat) and two local markets (Banarupa Bazar and Reserve Bazar). The maximum length of Ailia coila was recorded at 15.7 cm in total length, with an average length of 11.1 (±4) cm. The length‐weight relationship was estimated as W = 0.01084 L2.599 (R2 = 0.75). The value of shape parameter ‘b’ is smaller than three which indicate a negative allometric growth pattern. The estimated asymptotic length (L∞) and length at first maturity (L50%) were found to be 16.84 and 10.54 cm, respectively. The LB‐SPR revealed that the fishery is currently experiencing overfishing, with the spawning biomass (SPR = 32%) below the target reference point. The mean estimate of fishing mortality relative to natural mortality (F/M) was 3.07, more than three times the threshold F/M = 1, indicating extreme fishing mortality in this fishery. The estimated length at first capture (SL50%) was significantly higher than the length at first maturity (L50%), suggesting that the fishing is predominantly targeting mature fishes. To enhance the spawning biomass and ensure the sustainability of the fishery, it is imperative to reduce the current fishing pressure and implement appropriate management measures.

Preserving monotone or convex data using quintic trigonometric Bézier curves

<abstract><p>Bézier curves are essential for data interpolation. However, traditional Bézier curves often fail to detect special features that may exist in a data set, such as monotonicity or convexity, leading to invalid interpolations. This study aims to improve the deficiency of Bézier curves by imposing monotonicity or convexity-preserving conditions on the shape parameter and control points. For this purpose, the quintic trigonometric Bézier curves with two shape parameters are used. These techniques constrain only one of the shape parameters, leaving the other free to provide users with more freedom and flexibility in modifying the final curve. To guarantee smooth interpolation, the curvature profiles of the curves are analyzed, which aids in selecting the optimal shape parameter values. The effectiveness of the developed schemes was evaluated by implementing real-life data and data obtained from the existing schemes. Compared with the existing schemes, the developed schemes produce low-curvature interpolation curves with unnoticeable wiggles and turns. The proposed methods also work effectively for both nonuniformly spaced data and negative-valued convex data in real-life applications. When the shape parameter is correctly chosen, the developed interpolants exhibit continuous curvature plots, assuring $ C^2 $ continuity.</p></abstract>

Mathematical models to forecast temporal variations of power law shape parameters of a PV module working in real weather conditions: Prediction of maximum power and comparison with single-diode model

In this study, an innovative approach has been proposed to generate real time current–voltage characteristics and forecast peak power of photovoltaic (PV) modules working outdoors beneath real meteorological conditions. Power-Law Model (PLM) including four unknown parameters, two PV metrics (ISC, VOC), and two profile parameters (γ, m), has been used for fast, accurate and reliable modelling of PV modules. Explicit expressions giving γ and m parameters as functions of cardinal point coordinates (IMPP,VMPP, ISC and VOC) have been established. A daily monitoring of PV quantities, throughout one reference day, has been used to derive novel mathematical models of γ and m depending on module temperature and solar irradiance. To describe PV module behavior under changing meteorological conditions during an arbitrary day, mathematical models have been called to reproduce dynamical values of PLM shape parameters γ and m. Reliability of the approach has been assessed by comparing current–voltage characteristics and maximum power coming from PLM and Single-Diode Model (SDM) to experimental data of twenty-two PV modules measured at NREL. Comparison also reveals that I-V characteristics generated and predicted separately by PLM and SDM parameters are very close. In some cases, I-V characteristics generated by PLM parameters are more accurate. Furthermore, NRMSE values for generated and predicted I-V characteristics for all kinds of PV modules evaluated for different working conditions do not exceed 4% for both PLM and SDM, and determination coefficient values for long-term prediction of maximum power are close to one and annual average value is greater than 0,95.

Economic design of multiple deferred state sampling plan for two parameter Lindley distributed mean life assurance

In this study, we propose a multiple deferred state sampling plan under two parameter Lindley distribution based on time truncated life test. One of the principal objectives of the proposed plan is to ensure that the products have higher mean life. The procedure for determining the optimal plan parameters of the proposed plan is described by two points on the operating characteristics curve approach. Tables are constructed to select the optimal plan parameters of the proposed plan for different values of shape parameters, consumer’s risk and producer’s risk. The implementation of the proposed plan is illustrated with a real life time data. In addition, the performance of the proposed plan is evaluated by comparing the average sample number and operating characteristic curve of the proposed plan to that of single sampling plan. Finally, a mathematical model for economic design of the proposed plan is developed by considering the waiting time to reduce the total inspection cost while satisfying both the producer and consumer requirements and a sensitivity analysis is also explored.

Formation and manipulation of optical soliton pulse in a self- and cross-phase modulated four-level inverted Y-type system

We have proposed a theoretical model for controllable optical soliton pulse formation in a magnetic-field-assisted four-level inverted Y-type atomic system. The probability amplitudes of the pertinent levels are used to analyze the contrast between self- and cross-phase modulated probe absorption signals. The absorption profiles obtained from the probability amplitudes and the zeroth-order of the pulse propagation constant in the Taylor series are appropriately congruent. The nonlinear Schrödinger equation derived from the Maxwell–Bloch equation determines the respective bright and dark soliton conditions with positive and negative values of the pulse shape parameter. It is demonstrated that the coupling laser field strengths, laser frequency detunings, and the external magnetic field’s direction are the controlling parameters to produce both bright and dark optical soliton pulses. Alongside, the shape of the optical soliton pulses in self- and cross-phase modulation is influenced by the polarization angle of the probe and coupling fields. It is also found that the variation of coupling field strengths may be used to regulate the group velocity of the soliton probe pulse from superluminal to subluminal modes or vice-versa.

The Quadratic Trigonometric Bezier like Curve With two Shape Parameters

The quadratic trigonometric Bezier model serves as a potent and valuable tool in computer-aided geometric design, boasting exceptional geometric properties. In this study, Novel functions are introduced by leveraging a trigonometric Bezier-like curve with adjustable shape parameters. Each curve segment is formed by three consecutive control points, providing precise control over shape by adjusting these parameters while keeping the control polygon unchanged. These curves exhibit superior proximity to the control polygon compared to quadratic Bezier curves across all shape parameter values, gradually approaching the control polygon as the shape parameter increases. Moreover, for practical application, the quadratic trigonometric Bezier-like curve was utilized to artfully design the Arabic word "الله" (Allah) and define flower contours, employing MATHEMATICA software. The results underscore the model's effectiveness in accurately representing intricate shapes, offering a versatile and efficient solution for diverse design challenges. Furthermore, the fusion of the quadratic trigonometric Bezier-like curve with shape parameters significantly augments design flexibility and adaptability, making it a valuable asset in computer graphics, geometric modeling, and artistic design across multiple domains.

Testing the annual rainfall dispersion in Chaiyaphum, Thailand, by using confidence intervals for the coefficient of variation of an inverse gamma distribution

In Thailand, droughts are regular natural disasters that happen nearly every year due to several factors such as precipitation deficiency, human activity, and the global warming. Since annual rainfall amount fits an inverse gamma (IG) distribution, we wanted to try testing annual rainfall dispersion via the coefficient of variation (CV). Herein, we propose two statistics for testing the CV of an IG distribution based on the Score and Wald methods. We evaluated their performances by means of the Monte Carlo simulations conducted under several shape parameter values for an IG distribution based on empirical type I error rates and powers of the tests. The simulation results reveal that the Wald-method test statistic performed better than the Score-method one in terms of the attained nominal significance level, and is thus recommended for analysis in similar scenarios. Furthermore, the efficacy of the proposed test statistics was illustrated by applying them to the annual rainfall amounts in Chaiyaphum, Thailand.

Mathematical modeling of oscillating water column wave energy converter devices placed over an undulated seabed in a two-layer fluid system

The present study investigates the hydrodynamic performance of the two types of oscillating water column wave energy converter devices, namely (i) INP (interface non-piercing) OWC device and (ii) IP (interface piercing) OWC device placed over an undulated seabed in a two-layer fluid system. The boundary element method is used to handle the associated boundary value problems. Major emphasis is given to analyze the efficiency of the OWC devices for various values of incident wave parameters and shape parameters associated with the OWC devices and undulated seabed. Further, the time-domain analysis is provided in which the free surface and interface elevations are demonstrated for different instants of time. It is observed that the efficiency of both the OWC devices associated with the internal wave mode is highly oscillatory and periodic in nature. Further, the resonating pattern in the efficiency curve occurs due to the exchange of wave energy between the surface and internal waves and also due to the multiple resonances and near-resonance interactions of waves with the bottom ripples. Moreover, the results show that the incoming wave energy associated with the internal wave mode is distributed to cover a broadband spectrum, and consequently, the multiple resonances occur in the efficiency curve. In addition, air compressibility significantly influences the hydrodynamic efficiency of the OWC devices.

A Class of Rational Quartic Splines and their Local Tensor Product Extensions

This work describes a new class of rational quartic splines with local shape parameters as well as their local tensor product extensions. The important local shape preserving properties of the new rational quartic spline curves, including monotonicity-preserving and convexity-preserving, are discussed in detail. With a simple knot vector, the resulting rational quartic spline curves are G2 continuous at the knots in general, and by setting the values of local shape parameters, the spline curves can be C2 or C2∩FC3 continuous at the specified knots. Local Bézier curve segments representation form with respect to the new spline curves is developed, based on which exact formulations for representing conic segments and straight line segments are given. And the local subdivision algorithm is also developed. Based on the presented rational quartic splines, tensor product rational splines and local tensor product rational splines are constructed. The non-negativity conditions for the local tensor product rational splines are deduced. Without solving a linear system, the resulting local tensor product spline surfaces can interpolate arbitrary selected control points partly or entirely by specifying some values of local shape parameters. Some experiments of fitting 3D triangular mesh models demonstrate that the tensor product and local tensor product rational spline surfaces have better performances concerning energy-loss functional involving accuracy and smoothness than the classical bi-cubic B-spline surfaces.