Bayesian Point Estimation of Linear/Circular Consecutive k-out-of-n : F System Reliability Under Vague Environment

The paper proposes a Bayesian approach to estimate the reliability and mean time to failure (MTTF) of linear and circular consecutive [Formula: see text]-out-of-[Formula: see text]:[Formula: see text] systems under vague environments, where uncertainties are represented using vague sets. By assuming model parameters as vague random variables with vague prior distributions, the study employs the Resolution Identity theorem for vague sets to resolve and structure this vagueness within the Bayesian framework. The proposed method uses the squared error loss function to derive vague Bayesian estimates, providing a more realistic and comprehensive analysis of system reliability in the presence of uncertainty. Numerical illustrations are included to demonstrate the applicability and effectiveness of the approach, highlighting its potential for handling vague information in complex system reliability analysis.