This paper presents an aggregate method of selecting a theoretical cumulative distribution function (CDF) for an empirical CDF.
The method was intended to identify the time of reliable operation of a renewable technical object by applying three criteria based
on the following statistics: the modified Kolmogorov–Smirnov (MK-S) statistic, the mean absolute deviation of the theoretical
CDF from the empirical CDF, and a statistic calculated on the basis of a log-likelihood function. The values of these statistics
were used to rank eleven probability distributions. The data for which calculations were made concerned failures of the driver’s
cab lock recorded during five years of operation of a fleet of 45 trams. Before calculating the statistics, the empirical CDF of the
examined component was determined using the Kaplan–Meier estimator, and then, using the method of Maximum Likelihood Estimation, the parameters of the analysed theoretical distributions were estimated. The theoretical distributions were then ranked
according to the values obtained for each of the assumed criteria: the lower the value for a given criterion, the higher the ranking
position, indicating a better fit according to that criterion. Then, based on the three rankings and on weights assigned to the individual criteria, an aggregate criterion (referred to as DESV) was implemented to select the best-fitting probability distribution.
The method assumes that the lowest DESV value corresponds to the best-fitting theoretical distribution. In the case of the examined
component, this was found to be the generalised gamma distribution. It is shown that if the final decision is based on the aggregate criterion, which takes into account the three criteria for goodness of fit, the reliability of the estimation of the time-to-failure
distribution increases, and thus mistakes resulting from the use of only one of the criteria can be avoided.
The aim of this paper is to develop a quantile method of cost analysis allowing identification of the most cost-generating malfunctions occurring in a fleet of public transport vehicles. The exemplification of this method has been performed for a fleet of a specified type of trams. The idea behind the quantile method of public transport vehicle operating cost analysis is the reversing of the accumulated function of costs, for the determination of which a cost database from a given operating time of a public transport vehicle fleet has been used. The paper presents data on the malfunctions from the first five years of operation of trams in a large transport company. The assumed time of five years results from the warranty period provided by the manufacturer. The recorded number of indexes of replaced parts was 547. The group contained inoperative parts that were renewed several times.
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