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A hybrid variable neighborhood search and simulated annealing algorithm to estimate the three parameters of the Weibull distribution

Abbasi, B ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1016/j.eswa.2010.07.022
  3. Publisher: 2011
  4. Abstract:
  5. The Weibull distribution plays an important role in failure distribution modeling of reliability research. While there are three parameters in the general form of this distribution, for simplicity, one of its parameters is usually omitted and as a result, the others are estimated easily. However, due to its more flexibility, when the general form of the Weibull distribution is of interest, the estimation procedure is not an easy task anymore. For example, in the maximum likelihood estimation method, the likelihood function that is formed for a three-parameter Weibull distribution is very hard to maximize. In this paper, a new hybrid methodology based on a variable neighborhood search and a simulated annealing approach is proposed to maximize the likelihood function of a three-parameter Weibull distribution. The performance of the proposed methodology in terms of both the estimation accuracy and the required CPU time is then evaluated and compared to the ones of an existing current method through a wide range of numerical examples in which a sensitivity analysis is performed on the sample size. The results of the comparison study show that while the proposed method provides accurate estimates as well as those of the existing method, it requires significantly less CPU time
  6. Keywords:
  7. Comparison study ; CPU time ; Estimation procedures ; Existing method ; Failure distributions ; Hybrid methodologies ; Likelihood functions ; Maximum likelihood estimation method ; Numerical example ; Sample sizes ; Simulated annealing algorithms ; Three parameter Weibull distribution ; Three parameters ; Variable neighborhood search ; Weibull probability distribution ; Annealing ; Maximum likelihood estimation ; Numerical analysis ; Parameter estimation ; Probability ; Sensitivity analysis ; Weibull distribution ; Simulated annealing
  8. Source: Expert Systems with Applications ; Volume 38, Issue 1 , January , 2011 , Pages 700-708 ; 09574174 (ISSN)
  9. URL: http://www.sciencedirect.com/science/article/pii/S0957417410006391