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Tsallis Entropy of a Used Reliability System at the System Level.

Mohamed Kayid¹, Mashael A Alshehri²

¹Department of Statistics and Operations Research, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia.

Entropy (Basel, Switzerland)

|May 16, 2023

Summary

Predicting technical system lifetime is crucial. This study uses Tsallis entropy and system signatures to measure the predictability of a coherent system

Keywords:

Shannon entropy coherent system residual Tsallis entropy system signature

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Area of Science:

Reliability Engineering
Information Theory
System Dynamics

Background:

Assessing the lifetime uncertainty of technical systems is increasingly vital for predictability.
Coherent systems, where all components must function for system success, are common in engineering.
Existing methods may not fully capture the nuances of lifetime predictability.

Purpose of the Study:

To introduce and apply Tsallis entropy to quantify the remaining lifetime uncertainty of coherent systems.
To utilize the system signature as a key tool in this entropy-based analysis.
To investigate the properties and bounds of Tsallis entropy in this context.

Main Methods:

Modeling a coherent system with n components, all functional at time t.
Applying the system signature concept to define system behavior.
Calculating and analyzing the Tsallis entropy of the remaining system lifetime.

Main Results:

Tsallis entropy provides a measure for the predictability of a coherent system's remaining lifetime.
Established bounds and order properties for the Tsallis entropy of the system's remaining lifetime.
Demonstrated the utility of the approach for comparing predictability between different systems.

Conclusions:

Tsallis entropy, in conjunction with system signatures, offers a robust method for assessing lifetime predictability.
The derived results facilitate comparative analysis of system reliability and predictability.
This framework enhances the understanding and measurement of uncertainty in technical system lifetimes.