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A method for estimating the probability distribution of the lifetime for new technical equipment based on expert judgement
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Poznan University of Technology, Faculty of Control, Robotics and Electrical Engineering, Institute of Mathematics, ul. Piotrowo 3A, 60-965 Poznań, Poland
WSB University, ul. Zygmunta Cieplaka 1c, 41-300 Dabrowa Górnicza, Poland
Publication date: 2021-12-31
Eksploatacja i Niezawodność – Maintenance and Reliability 2021;23(4):757-769
  • A new method for estimating the probability distribution of the lifetime based on expert assessments is developed.
  • The expert lifetime elicitation procedure is developed and applied to the Weibull lifetime.
  • The quantile function is used to develop the expert method.
  • The subjective Bayesian approach with models of classical probability theory is integrated.
  • The objectification of the evaluation of experts to assign weights to their opinions is proposed.
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.
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