Bayesian Estimation of Exponentiated Exponential Strength and Exponentiated Weibull Stress Reliability Model for Real Data

Abstract

Stress-strength reliability is an important concept in reliability analysis, quantifies the probability that the strength of a system surpasses its applied stress. This paper focuses on the reliability analysis for exponentiated exponential distribution strength variable and the exponentiated Weibull distribution stress variable. The study explores the estimation of the parameters in stress-strength reliability model using maximum likelihood estimation and Bayesian estimation. In particular, the Bayesian estimator of stress-strength reliability is obtained by utilizing Lindley’s approximation by considering both linear exponential loss function and squared error loss function for informative and non-informative priors. A comprehensive simulation study is conducted and the performances of estimators are compared using mean squared errors. The stress-strength reliability for real datasets is also investigated for real-time data sets.

Introduction

VI. ACKNOWLEDGMENT

I would like to thank my supervisor for her continuous support and encouragement in preparing the manuscript.

Conclusion

The study focuses on estimating the stress-strength reliability using EED as the strength variable and EWD as the stress variable. The estimation is performed using MLE and Bayesian methods under LINEX loss function and SELF using Lindley’s approximation. The performance of these estimators is compared based on the mean squared errors. The simulation study reveals the following findings. 1) Increasing the values of while keeping other parameters fixed leads to an increase in stress-strength reliability. 2) Decreasing the values of and while keeping the remaining parameters fixed results in an increase in stress-strength reliability. 3) The Bayes estimator with a gamma prior under LLF demonstrates better performance with smaller mean squared errors across all three sets of hyperparameters. Hence, it can be concluded that the Bayes estimators for the gamma prior under the LINEX loss function with a positive loss parameter outperform other estimation methods. Additionally, the stress-strength reliability) of the EED with EWD is investigated using real data sets of breaking strength in carbon fibers with different gauge lengths. The findings reveal that the 10 mm length carbon fibers exhibit greater strength compared to the 20 mm length fibers.

References

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Copyright

Copyright © 2023 Mekala Sony, Dr. P. R. Jayashree. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.