The 3-parameter Weibull distribution is used as a model for failure since this distribution is proper when the failure rate somewhat high in starting operation and these rates will be decreased with increasing time .

In practical side a comparison was made between (Shrinkage and Maximum likelihood) Estimators for parameter and reliability function using simulation , we conclude that the Shrinkage estimators for parameters are better than maximum likelihood estimators but the maximum likelihood estimator for reliability function is the better using statistical measures (MAPE)and (MSE) and for different sample sizes.

Note:- n_s : small sample ; n_m=median sample

This study rigorously investigates three 3d transition metal carbide (TMC) structures via LDA and GGA approximations. It examines cohesive energy (Ecoh), Vickers hardness (Hv), mechanical stability, and electronic properties. Notably, most 3d TMCs exhibit higher cohesive energy than nitrides, and rs-TiC demonstrates a Vickers hardness of 25.66 GPa, outperforming its nitride counterpart. The study employs theoretical calculations to expedite research, revealing mechanical stability in CrC and MnC (GGA) and CrC (LDA in cc structure), while all 3d TMCs in rs and seven in zb structures show stability. Charge transfer and bonding analysis reveal enhanced covalency along the series, influenced by the interplay between p orbitals of carbon and d o

Abstract

            Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t

Biosorption of lead, chromium, and cadmium ions from aqueous solution by dead anaerobic biomass (DAB) was studied in single, binary, and ternary systems with initial concentration of 50 mg/l. The metal-DAB affinity was the same for all systems. The main biosorption mechanisms were complexation and physical adsorption of metallic cations onto natural active functional groups on the cell wall matrix of the DAB. It was found that biosorption of the metallic cations onto DAB cell wall component was a surface process. The main functional groups involved in the metallic cation biosorption were apparently carboxyl, amino, hydroxyle, sulfhydryl, and sulfonate. These groups were part of the DAB cell wall structural polymers. Hydroxyle groups (–O

Background: Sex variations in coronary artery disease (CAD) are well documented. However, sex differences in coronary artery calcium (CAC) and its role in the detection of coronary artery stenosis remain controversial. Objective: To assess the impact of sex variation on coronary artery calcification and its efficacy in predicting coronary artery stenosis. Methods: This is a cross-sectional observational study including 230 consecutive patients with suspected CAD (120 men and 110 women) referred for coronary computed tomography angiography (CCTA). The study analyzed sex-based differences in the sensitivity and specificity of coronary artery calcification (CAC) for detecting moderate to severe stenosis across various coronary arteries

In this paper the centralizing and commuting concerning skew left -derivations and skew left -derivations associated with antiautomorphism on prime and semiprime rings were studied and  the commutativity of Lie ideal under certain conditions were proved.

In this paper, simulation studies and applications of the New Weibull-Inverse Lomax (NWIL) distribution were presented. In the simulation studies, different sample sizes ranging from 30, 50, 100, 200, 300, to 500 were considered. Also, 1,000 replications were considered for the experiment. NWIL is a fat tail distribution. Higher moments are not easily derived except with some approximations. However, the estimates have higher precisions with low variances. Finally, the usefulness of the NWIL distribution was illustrated by fitting two data  sets

A prey-predator interaction model has been suggested in which the population of a predator consists of a two-stage structure. Modified Holling's disk equation is used to describe the consumption of the prey so that it involves the additional source of food for the predator. The fear function is imposed on prey. It is supposed that the prey exhibits anti-predator behavior and may kill the adult predator due to their struggle against predation. The proposed model is investigated for existence, uniqueness, and boundedness. After determining all feasible equilibrium points, the local stability analyses are performed. In addition, global stability analyses for this model using the Lyapunov method are investigated. The chance of occurrence of loc