Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Classification of Systems-I01:26

Classification of Systems-I

319
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
319
Routh-Hurwitz Criterion II01:19

Routh-Hurwitz Criterion II

424
In the application of the Routh-Hurwitz criterion, two specific scenarios can arise that complicate stability analysis.
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...
424
Wald-Wolfowitz Runs Test II01:17

Wald-Wolfowitz Runs Test II

329
The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
For binary data, runs are identified using symbols such as + and −, or equivalently, 1s and...
329
Routh-Hurwitz Criterion I01:15

Routh-Hurwitz Criterion I

339
Consider an electrical power grid, where stability is essential to prevent blackouts. The Routh-Hurwitz criterion is a valuable tool for assessing system stability under varying load conditions or faults. By analyzing the closed-loop transfer function, the Routh-Hurwitz criterion helps determine whether the system remains stable.
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
339
Wald-Wolfowitz Runs Test I01:17

Wald-Wolfowitz Runs Test I

748
The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
The test works...
748
Linear time-invariant Systems01:23

Linear time-invariant Systems

441
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
441

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

An exact and interpretable test for detecting aging behavior in reliability and survival data.

PloS one·2026
Same author

Information-Theoretic Reliability Analysis of Consecutive <i>r</i>-out-of-<i>n</i>:G Systems via Residual Extropy.

Entropy (Basel, Switzerland)·2025
Same author

Entropy-Based Uncertainty Quantification in Linear Consecutive k-out-of-n:G Systems via Cumulative Residual Tsallis Entropy.

Entropy (Basel, Switzerland)·2025
Same author

Tsallis Entropy in Consecutive <i>k</i>-out-of-<i>n</i> Good Systems: Bounds, Characterization, and Testing for Exponentiality.

Entropy (Basel, Switzerland)·2025
Same author

Some New Results Involving Past Tsallis Entropy of Order Statistics.

Entropy (Basel, Switzerland)·2023
Same author

Cumulative Residual Entropy of the Residual Lifetime of a Mixed System at the System Level.

Entropy (Basel, Switzerland)·2023

Related Experiment Video

Updated: Sep 18, 2025

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
11:09

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

Published on: July 17, 2021

3.1K

Information-Theoretic Reliability Analysis of Linear Consecutive r-out-of-n:F Systems and Uniformity Testing.

Ghadah Alomani1, Faten Alrewely2, Mohamed Kayid3

  • 1Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia.

Entropy (Basel, Switzerland)
|June 26, 2025
PubMed
Summary

This study uses extropy to analyze the reliability of r-out-of-n:F systems. A new test for uniformity in system lifetimes is proposed and validated through simulations.

Keywords:
Shannon entropyconsecutive r-out-of-n:F systemsextropygoodness-of-fit teststochastic orders

More Related Videos

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
08:00

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Published on: October 25, 2017

7.0K
Author Spotlight: Validation of SICOLE-R for Assessing Cognitive and Reading Skills in Spanish-Speaking Children and Its Role in Personalized Education
09:00

Author Spotlight: Validation of SICOLE-R for Assessing Cognitive and Reading Skills in Spanish-Speaking Children and Its Role in Personalized Education

Published on: August 16, 2024

921

Related Experiment Videos

Last Updated: Sep 18, 2025

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans
11:09

RBDT: A Computerized Task System based in Transposition for the Continuous Analysis of Relational Behavior Dynamics in Humans

Published on: July 17, 2021

3.1K
DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers
08:00

DNA Nanotubes as a Versatile Tool to Study Semiflexible Polymers

Published on: October 25, 2017

7.0K
Author Spotlight: Validation of SICOLE-R for Assessing Cognitive and Reading Skills in Spanish-Speaking Children and Its Role in Personalized Education
09:00

Author Spotlight: Validation of SICOLE-R for Assessing Cognitive and Reading Skills in Spanish-Speaking Children and Its Role in Personalized Education

Published on: August 16, 2024

921

Area of Science:

  • Reliability Engineering
  • Information Theory
  • Statistical Inference

Background:

  • Linear consecutive r-out-of-n:F systems are crucial in reliability analysis.
  • Understanding system lifetime uncertainty is vital for accurate reliability assessment.
  • Extropy, a measure complementary to entropy, offers unique insights into uncertainty.

Purpose of the Study:

  • To explore the reliability of linear consecutive r-out-of-n:F systems using extropy.
  • To develop and validate a new statistical test for uniformity in system lifetimes.
  • To investigate the impact of component lifetime distributions and heterogeneity on system extropy.

Main Methods:

  • Derivation of general expressions for extropy in r-out-of-n:F systems.
  • Development of theoretical bounds and characterization results for extropy.
  • Proposal of a nonparametric extropy estimator and a uniformity test statistic.
  • Simulation studies to evaluate the power of the proposed test against alternatives.

Main Results:

  • General expressions for extropy in linear consecutive r-out-of-n:F systems were derived.
  • The study identified unique properties of the uniform distribution within the extropy framework.
  • The proposed nonparametric test for uniformity demonstrated effectiveness in simulation studies.

Conclusions:

  • Extropy provides valuable insights into the reliability and uncertainty of r-out-of-n:F systems.
  • The developed statistical test offers a practical tool for assessing uniformity in system lifetimes.
  • Findings contribute to both theoretical understanding of information measures and applied reliability analysis.