Alternative Weibull analysis for road markings: an EM approach

ESREL2018 - European Safety and Reliability Conference, Trondheim, NORVEGE, 17-/06/2018 - 21/06/2018The quality and reliability of road infrastructure and its equipment play a major role in road safety. This is especially true for autonomous car traffic guided mainly by a GPS system that is, unfortunately, neither precise nor reliable. In order to improve the guidance systems, one option could be to equip the vehicle with a camera reading road markings. Such solution requires maintenance strategies guaranteeing markings' perceptibility to the human eye or the autonomous car camera. Currently, the retroreflection luminance of markings is measured for evaluating marking degradation. An important remaining step is a life time analysis depending on the inspection strategy. Since the exact failure time isn't generally observed, feedback database contain many censured data: the left-censure corresponding to a marking failing before the first inspection, the interval censure that corresponds to markings failing between two inspections, and the right-censure corresponding to a marking that never fails. In the literature, a Weibull analysis was proposed to estimate the markings reliable distributions using the Maximum Likelihood through the Newton-Raphson method. Facing with censored data, this approach couldn't be computed without introducing strong bias in the reliability estimation. For generic interval-censored data, Pradhan and Kundu proposed an alternative, based on the EM algorithm. In our study an extension of the EM algorithm processing left and right censures is proposed. Finally, this algorithm is applicable for all kind of observations, whatever the censure nature. After introducing this EM extension, the paper focuses on the fact that computations are simpler than the Newton-Raphson methods and censored-data are directly estimated. The French National Road 4 markings case is considered to illustrate the proposed approach. Moreover, the proposed algorithm being generic, its application is, of course, not limited to our road marking case study