Ordered durability functions estimation for inspection-based data: a computational issue

Abstract

This contribution is framed in, and is part of, the Durabiltiy of Building Facades studies carried out in the last decade in the Institut d’Estadística i Matemàtica Aplicada a l’Edificació and the Laboratori d’Edificació at the Universitat Politècnica de Catalunya, Spain. The goal of this paper is to incorporate in the analysis of the estimation of the durability of building facades respect the severity degrees (low, medium or high) the order of the events of interest. In other words, we will take into account preliminary estimates of the survival probabilities of previous events (e.g. initial severities) as order constraints for the estimation of survival probabilities for subsequent events of interest (e.g. more advanced severities). Standard statistical analyses for this type of interval censored data are usually conducted by using the R statistical software, however it does not include libraries or packages neither for simultaneous estimation nor for the use of order constraints. For this reason, we will use AMPL language and the solver SNOPT and we will develop and implement a Survival Estimator Algorithm with Restrictions (SEAR), for the estimation of the survival function of each event of interest taking into account the information given by the survival function of some previous event of interest. The proposed methodology solves the inconsistency problem associated with a separate estimation of the respective survival probabilities. Application of the methodology to a simulated dataset, which reproduces a real collection data, will be presented and discussed.