This study proposes a non-parametric estimation of the survival function of road facilities using observed survival periods with unknown service origins based on the length-biased sampling in which the number of observations depend on lengths of survival periods. In medicine and statistics areas, the estimation of the survival function has been intensively analyzed. However, in their non-parametric estimation, previous studies assume that the origins of survival periods are known, since the origins may be known by the interview of patients in medical field even if the observation starts after the origins. For the road facilities however, starting dates (origins) of facility services may not be always known. This study therefore proposes a non-parametric estimation method of the survival function even with unknown origins of facility services, and reveals its property based on the validation using real inspection data. Also, the comparison and selection of several estimation methods are discussed.