Keywords: condition-based maintenance, predictive maintenance, railway maintenance, statistical approach, track defects, track monitoring, track surveying.

Reliability and availability requirements of transport systems are growing greater and greater. Even though railways are not an exception, many railway companies still maintain their tracks with middle twentieth century techniques. This is at odds with the need to bring both service quality and the reduction of maintenance costs. The only way to solve this is by introducing updated maintenance techniques which act on the tracks only when they are required. Such techniques are based on predictive maintenance methods, which imply the need of a track surveying system, a statistical analysis of the data obtained and a decision making process.

The statistical approach features the use of a specific track parameter by fitting a known probability density distribution to the empirical probability distribution created from the registered dataset, so that it is possible to identify a track with a certain degree of deterioration with only a few parameters. Among the different parameters which characterise a given length of track, only track vertical alignment is addressed in the present paper, for which rail vertical defects are registered. Real data were registered from line 2 of Madrid's underground by means of optical sensors implemented in the monitoring infrastructure vehicle VAI.

Two main issues are discussed. On the one hand, the selection procedure for the most suitable probability distribution which represents the rail defects is described, together with the most appropriate measuring step that will give the best fitting coefficient. It is found that, for the case of track vertical alignment data from line 2 of Madrid's underground, measured using the VAI, the most appropriate probability function is the gamma function with a measuring step of 3 metres. It was noticed that the best fitting coefficient for the different probability distributions may be obtained with different measuring steps, and that no evidence is found in order to identify the cause of this difference.

On the other hand, the influence of load cycles applied by passing trains on the evolution of track deterioration is also considered. To achieve this, three different track surveys were been carried out. Although the results show almost a linear dependence of track deterioration with respect to time, the track measurements were taken too close in time. In order to have significant evidence of the evolution of track conditions and come up with some reliable relationship, the time between track surveys should be extended from six to twelve months.

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