Objective Bayesian estimation for multistate stress‐strength model's reliability with various kernel functions

Abstract The paper discusses the objective Bayesian estimation of the reliability of a multistate stress‐strength model (MSSM) based on different kernel functions. For the MSSM, we first derive the reliability function and Fisher information matrix. The Jeffreys prior, reference prior, and probability matching prior for the reliability function of the MSSM are constructed based on the objective Bayesian paradigm. Subsequently, we demonstrated that these priors are improper density, then evaluated the effects of these priors on Bayes estimates for MSSM's reliability based on a complete sample. The Bayesian estimates are calculated using random walk Metropolis–Hastings techniques. We employ Monte Carlo simulation to examine the effectiveness of Bayes estimates for MSSM's reliability in terms of average bias and mean squared error, meanwhile the highest posterior density credible intervals are investigated in terms of average length and coverage probability. Finally, two real datasets were examined, demonstrating the viability of the objective Bayes technique for small sample data.