Bayesian Estimation of Stress Strength Modeling Using MCMC Method Based on Outliers

In reliability literature and engineering applications, stress-strength (SS) models are particularly important. This paper aims to estimate the SS reliability for an inverse Weibull distribution having the same shape parameters but different scale parameters when the strength (X) and stress (Y) random variables are independent. In the presence of outliers and in a homogeneous situation, the maximum likelihood reliability estimator is computed. With independent gamma priors, a Bayesian estimation approach for SS reliability is also proposed. The symmetric and asymmetric loss functions are used to derive the Bayesian estimators of SS reliability. Some sophisticated calculations are carried out using Markov chain Monte Carlo methods. Simulations are used to investigate the precision of Bayesian and non-Bayesian estimates for SS reliability. Further, a comparative study among the Bayesian estimates in the case of uniform and gamma priors is carried out utilizing a simulation methodology. The provided methodology is ultimately applied to the actual data using the discussed model and data from head-neck cancer. According to the results of a study, larger sample sizes resulted in better reliability estimates for both techniques. Generally, as the number of outliers increased, the precision measures from both methods decreased. In all circumstances, the Bayesian estimates under the precautionary loss function outperformed the observed estimates under alternative loss functions. The actual data analysis assured the theoretical and simulated studies.