The problem of reconstruction of the past failure times in the left-censored set-up is considered. Various reconstructors of time to failure of units censored in a left-censored sample from the proportional reversed hazard rate models are demonstrated. The maximum-likelihood, best unbiased and conditional median reconstructors are obtained. We also present two methods, non-Bayesian and Bayesian, for obtaining reconstruction intervals for the past failure times. Numerical example and a Monte Carlo simulation study are given to illustrate all the reconstruction methods discussed in this paper
