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