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Related Concept Videos

Stress: General Loading Conditions01:15

Stress: General Loading Conditions

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To grasp the intricacy of real-world conditions where multiple loads are applied simultaneously to a structure, one might visualize a section passing through a specific point within a body, aligned parallel to the xy plane. This section is subjected to various forces, including original loads, normal forces, and shearing forces.
The shearing force, possessing potential directionality within the plane of the section, is simplified into two component forces running parallel to the x and y axes....
293
Components of Stress01:23

Components of Stress

194
Stress analysis under multiple loading conditions is intricate, necessitating a comprehensive grasp of normal and shearing stresses. Consider a small cube at point O, subjected to stress on all six faces, visible or not. Normal stress components σx, σy, σz act perpendicularly to the x, y, and z axes. Shearing stress components τxy and τxz are exerted on faces perpendicular to these axes.
Interestingly, the hidden cube faces also experience these stresses, equal and...
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Censoring Survival Data01:09

Censoring Survival Data

54
Survival analysis is a statistical method used to analyze time-to-event data, often employed in fields such as medicine, engineering, and social sciences. One of the key challenges in survival analysis is dealing with incomplete data, a phenomenon known as "censoring." Censoring occurs when the event of interest (such as death, relapse, or system failure) has not occurred for some individuals by the end of the study period or is otherwise unobservable, and it might have many different...
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Generalized Hooke's Law01:22

Generalized Hooke's Law

756
The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of...
756
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

233
Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
233
Stresses under Combined Loadings01:23

Stresses under Combined Loadings

137
When analyzing a bent tube with a circular cross-section subjected to multiple forces, it is crucial to determine the stress distribution in order to maintain structural integrity under varied load conditions.
The process begins by slicing the tube at critical points and analyzing the internal forces and stress components at these sections, focusing on the centroid. Normal stresses, generated by axial forces and bending moments, are either compressive or tensile and vary across the section from...
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Reliability inference for multi-component stress-strength systems with heterogeneous Lomax-distributed components

Akram Kohansal1, Hassan S Bakouch2, Reza Pakyari3

  • 1Department of Statistics, Imam Khomeini International University, Qazvin, Iran.

Scientific Reports
|May 16, 2025
PubMed
Summary

This study estimates the m-component stress-strength reliability using the Lomax distribution under progressive first failure censoring. Various estimation methods were compared via simulation and real data analysis.

Keywords:
Data analysis.Lindley’s approximationLomax distributionMCMC methodMulti-component stress-strength parameterProgressive first failure censoringSimulation

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Area of Science:

  • Reliability Engineering
  • Statistical Inference
  • Probability Distributions

Background:

  • The m-component stress-strength parameter is crucial for system reliability assessment.
  • Progressive first failure (PFF) censoring is a practical data collection scheme in reliability studies.
  • The Lomax distribution is frequently used to model lifetime data due to its flexibility.

Purpose of the Study:

  • To estimate the m-component stress-strength parameter under PFF censoring.
  • To compare the performance of classical and Bayesian estimation methods.
  • To analyze real-world datasets using the developed methodologies.

Main Methods:

  • Maximum Likelihood Estimation (MLE) for parameter estimation.
  • Bayesian estimation utilizing Markov Chain Monte Carlo (MCMC) and Lindley's approximation.
  • Derivation of asymptotic confidence intervals and Highest Posterior Density (HPD) credible intervals.
  • Uniformly Minimum Variance Unbiased Estimator (UMVUE) considered for known parameters.
  • Monte Carlo simulation for performance evaluation.
  • Real data analysis for practical illustration.

Main Results:

  • Performance comparison of MLE and Bayesian methods under different scenarios.
  • Evaluation of interval estimation techniques (confidence and credible intervals).
  • Demonstration of the applicability of the methods on real-world stress-strength data.

Conclusions:

  • The study provides a comprehensive framework for stress-strength reliability estimation under PFF censoring.
  • Both classical and Bayesian approaches offer viable estimation strategies, with performance varying by scenario.
  • The findings are applicable to engineering systems where component failures follow Lomax distribution and data is PFF censored.