Estimation of Reliability under Conditional Stress - Strength Setup based on Weibull Distribution

Architha M

Department of Statistics, Bangalore University, India.

Parameshwar V Pandit *

Department of Statistics, Bangalore University, India.

*Author to whom correspondence should be addressed.


Abstract

The Weibull distribution has been extensively studied and applied across various fields due to its versatility in modeling a wide range of phenomena, especially in reliability engineering, survival analysis, and lifetime modeling. The concept of Rl a,b , which represents a system's reliability in a conditional stress-strength setup, was proposed by Sabre and Khorshidian (2021). In this research, the problem of estimating reliability of the component is considered when strength variable X and stress variable Y follow independent Weibull distributions with common shapes and different scale parameters under conditional stress-strength setup. The maximum likelihood estimator, asymptotic confidence interval, Bootstrap estimators, Boot-p estimators, and Bayes estimator under-squared error loss function with associated highest posterior density interval are constructed for conditional stress-strength reliability. Simulation study is conducted to estimate mean square error (MSE) of estimator of conditional stress-strength reliability. The real data analysis is also carried out.

Keywords: Weibull distribution, stress-strength reliability, conditional stress-strength model, maximum likelihood estimator, bootstrap confidence interval Bayes estimator, MCMC technique


How to Cite

Architha M, & Pandit, P. V. (2024). Estimation of Reliability under Conditional Stress - Strength Setup based on Weibull Distribution. Asian Journal of Probability and Statistics, 26(3), 28–43. https://doi.org/10.9734/ajpas/2024/v26i3598

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