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Load-Sharing Model under Lindley Distribution and Its Parameter Estimation Using the Expectation-Maximization

Chanseok Park1, Min Wang2, Refah Mohammed Alotaibi3

  • 1Applied Statistics Laboratory, Department of Industrial Engineering, Pusan National University, Busan 46241, Korea.

Entropy (Basel, Switzerland)
|December 3, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical method for load-sharing systems, improving parameter inference for component lifetimes. The developed expectation maximization algorithm offers a more effective approach for maximum likelihood estimation compared to existing methods.

Keywords:
Lindley distributionNewton–Raphson methodexpectation-maximization algorithmhypothetical latent random variablemaximum likelihood estimation

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Area of Science:

  • Reliability Engineering
  • Statistical Inference
  • System Dynamics

Background:

  • Load-sharing systems redistribute load to surviving components upon failure.
  • Statistical inference for component lifetime distribution parameters is crucial for system reliability.
  • Existing methods may face challenges in parameter estimation for complex systems.

Purpose of the Study:

  • To develop a novel methodology for statistical inference of parameters in load-sharing systems.
  • To integrate latent random variables into the analysis of load-sharing systems.
  • To enhance the accuracy and efficiency of parameter estimation for Lindley-distributed component lifetimes.

Main Methods:

  • Introduction of a methodology integrating latent random variables.
  • Development of an expectation maximization algorithm for maximum likelihood estimation.
  • Comparison with Newton-Raphson-type algorithms using simulation techniques.

Main Results:

  • The proposed methodology demonstrates superior performance in parameter estimation.
  • The expectation maximization algorithm consistently reaches a global maximum.
  • Numerical results validate the effectiveness of the new approach.

Conclusions:

  • The novel methodology provides a more effective approach for statistical inference in load-sharing systems.
  • The expectation maximization algorithm is a robust tool for maximum likelihood estimation.
  • This work advances the reliability analysis of systems with load-sharing capabilities.