Innovative Sequencing Techniques for Accurate Train Scheduling

Ultrasonic Non Destructive (NDT) inspection frequency needs to be decided based on probability of rail breaks and derailments along with cost of inspection, planned maintenance and corrective maintenance. This paper is on development of probabilistic model for NDT inspections. Undetected defects can lead to rail breaks based on the ageing, and tonnage passed through the line after the defect is initiated. Data analysed include: Rail Defect History Data (NDT testing Car and Service Defects). Expected number of defect initiation and failures are estimated. As ageing takes place in the line due to tonnage accumulation on track resulting from traffic movement, defects are developed due to the steel, axle load, maintenance of rail and wheel and material fatigue. The number of defects expected for a given rail and MGT till inspection with a predictable MGT before next inspection due to traffic flow is modelled using Weibull distribution. A model for cost benefit analysis is developed for examining the effectiveness of various inspection frequencies for reducing risk and cost. Failures are modelled as a point process with an intensity function Λ(m) where m represents Millions of Gross Tonnes (MGT) and Λ(m) is an increasing function of m indicating that the number of failures in a statistical sense increases with MGT. That means older rails with higher cumulative MGT passed through the section is expected to have more probability of initiating defects and if undetected then through further passing of traffic can lead to rail failures. As a result, N(Mi+1, Mi), the number of failures over Mi and Mi+1, is a function of MGT, m, and is a random variable. Let cumulative MGT of rail till inspection by NDT car, m, be known and Fn(m) denote the cumulative rail failure distribution modelled as Weibull distribution given by: ) ) ( exp( 1 ) ( β λm m Fn − − = (1) with the parameters β (Known as shape parameter of the distribution) > 1 and λ (Known as inverse of characteristic function for the distribution)> 0 When β is greater that 1 it indicated that there is increasing failure rate of the item under study and ageing is predominant in failure mechanism. Then failure intensity function Λ(m) is derived from (1) and is given by 1 ) ( − β λ λβ m