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Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...
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Tsallis Entropy in Consecutive k-out-of-n Good Systems: Bounds, Characterization, and Testing for Exponentiality.

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This study applies Tsallis entropy to analyze uncertainty in k-out-of-n systems. New methods and bounds offer insights into system reliability and statistical inference.

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Rényi entropyShannon entropyTsallis entropyconsecutive k-out-of-n good systemsstochastic orders

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Area of Science:

  • Reliability Engineering
  • Information Theory
  • Statistical Inference

Background:

  • Consecutive k-out-of-n systems are crucial in reliability and engineering.
  • Evaluating system uncertainty requires robust entropy measures.

Purpose of the Study:

  • To apply Tsallis entropy for uncertainty evaluation in consecutive k-out-of-n systems.
  • To derive analytical expressions and bounds for Tsallis entropy.
  • To develop an entropy-based test for exponentiality.

Main Methods:

  • Derivation of analytical expressions and bounds for Tsallis entropy.
  • Establishing theoretical connections with Shannon and Rényi entropies.
  • Developing a nonparametric estimator for Tsallis entropy.
  • Monte Carlo simulations for performance evaluation.

Main Results:

  • New analytical expressions and bounds for Tsallis entropy in k-out-of-n systems.
  • Theoretical links between Tsallis, Shannon, and Rényi entropies.
  • A validated nonparametric estimator for Tsallis entropy.
  • A novel entropy-based test for exponentiality.

Conclusions:

  • Tsallis entropy is a flexible tool for reliability characterization.
  • The proposed methods enhance uncertainty evaluation in complex systems.
  • This work provides a foundation for comparing systems using stochastic orders.