Abstract
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.
Highlights
In today’s increasingly competitive environment, designing and manufacturing reliable products is essential to the company’s survival
Results of the model will depend upon the validity of the assumed distribution forms as well as the parameter values attached to these distributions
The aggregation process uses the ratings of all the experts, considering the weights estimated in the previous step, in order to obtain unambiguous data allowing the estimation of the parameters of the assumed probability distribution
Summary
In today’s increasingly competitive environment, designing and manufacturing reliable products is essential to the company’s survival. The aggregation process uses the ratings of all the experts, considering the weights estimated in the previous step, in order to obtain unambiguous data allowing the estimation of the parameters of the assumed probability distribution. The last step of the procedure is to create a parametric model of the lifetime probability distribution sought and to use it for practical purposes, e.g., determination of the expected lifetime of new technical equipment, for which the lack of operational data precludes the use of statistical methods. The aggregation process uses the ratings of all the experts, considering the weights estimated in the previous step, to obtain unambiguous data allowing the estimation of the parameters of the assumed probability distribution
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