EM Approach for Weibull Analysis in a Strongly Censored Data Context - Application to Road Markings

摘要

Road surface markings organize road traffic and therefore play a major role in road safety. This is one reason why a part of the current guidance system is to model traffic lanes based on pavement marking detection. Consequently, road managers must guarantee detectable marking lines. An adapted maintenance strategy is a potential solution. Today, marking lines are inspected periodically. A direct consequence of this is that the failure moment of a given marking is generally strongly censored (left, interval or right). Sathyanarayanan et al. present the first Weibull approach for road markings. Weibull distributions are estimated by the maximum likelihood estimation (MLE) method adapted to this censored problem. The MLE is computed by a numerical approach such as the Newton-Raphson algorithm. In the context of interval-censored data, Pradhan and Kundu proposed an alternative method based on an Expectation-Maximisation EM algorithm. This paper proposes replacing this EM approach in the road markings context. A case study regarding the broken center line of a section of French National Road 4 illustrates this methodology. Lifetime markings are distributed by the Weibull distribution.