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A method for estimating the probability distribution of the lifetime for new technical equipment based on expert judgement

Andrzejczak Karol, Bukowski Lech

Eksploatacja i Niezawodność

2021

Vol. 23, no. 4

757--769

Managing the exploitation of technical equipment under conditions of uncertainty requires the use of probabilistic prediction models in the form of probability distributions of the lifetime of these objects. The parameters of these distributions are estimated with the use of statistical methods based on historical data about actual realizations of the lifetime of examined objects. However, when completely new solutions are introduced into service, such data are not available and the only possible method for the initial assessment of the expected lifetime of technical objects is expert methods. The aim of the study is to present a method for estimating the probability distribution of the lifetime for new technical facilities based on expert assessments of three parameters characterizing the expected lifetime of these objects. The method is based on a subjective Bayesian approach to the problem of randomness and integrated with models of classical probability theory. Due to its wide application in the field of maintenance of machinery and technical equipment, a Weibull model is proposed, and its possible practical applications are shown. A new method of expert elicitation of probabilities for any continuous random variable is developed. A general procedure for the application of this method is proposed and the individual steps of its implementation are discussed, as well as the mathematical models necessary for the estimation of the parameters of the probability distribution are presented. A practical example of the application of the developed method on specific numerical values is also presented.

Quantile analysis of the operating costs of the public transport fleet

Andrzejczak K., Selech J.

Transport Problems

2017

T. 12, z. 3

103--111

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.