The Rayleigh distribution, serving as a special case of the Weibull distribution, is
known to have wide applications in survival analysis, reliability theory and commu-
nication engineering. In this paper, Bayesian estimators (including shrinkage esti-
mators) of the unknown parameter of the censored Rayleigh distribution are derived
using the Al-Bayyati loss function, whilst simultaneously considering different objec-
tive prior distributions. Comparisons are made between the proposed estimators by
calculating the risk functions using simulation studies and an illustrative example.