Reliability estimation in a two-unit hot standby system under classical and Bayesian inferential framework

Hot stand-by systems play a critical role in reliability engineering, ensuring uninterrupted operation in applications where system failure is not an option. This study focuses on the reliability assessment of a two-unit hot stand-by system with a perfect switch, using failure time data modeled by the Weighted Exponential-Lindley Distribution (WXLD). Bayesian reliability estimators are proposed under two loss functions: the Squared Error Loss Function (SELF) and the Linear Exponential (LINEX) Loss Function. These estimators are contrasted with Maximum Likelihood Estimators (MLEs) obtained by optimizing the likelihood function. Monte Carlo simulations are utilized to generate synthetic failure time data, facilitating a comparative analysis of the estimators based on their mean squared errors (MSEs). The findings highlight the performance and robustness of the Bayesian estimators relative to the classical MLEs. This comprehensive evaluation contributes to the advancement of reliability estimation techniques, offering practical insights into the effective analysis of hot stand-by systems.