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A multi-stage two-machines replacement strategy using mixture models, bayesian inference, and stochastic dynamic programming

Fallah Nezhad, M. S ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1080/03610920903453459
  3. Abstract:
  4. If at least one out of two serial machines that produce a specific product in manufacturing environments malfunctions, there will be non conforming items produced. Determining the optimal time of the machines' maintenance is the one of major concerns. While a convenient common practice for this kind of problem is to fit a single probability distribution to the combined defect data, it does not adequately capture the fact that there are two different underlying causes of failures. A better approach is to view the defects as arising from a mixture population: one due to the first machine failures and the other due to the second one. In this article, a mixture model along with both Bayesian inference and stochastic dynamic programming approaches are used to find the multi-stage optimal replacement strategy. Using the posterior probability of the machines to be in state γ1,γ 2 (the failure rates of defective items produced by machine 1 and 2, respectively), we first formulate the problem as a stochastic dynamic programming model. Then, we derive some properties for the optimal value of the objective function and propose a solution algorithm. At the end, the application of the proposed methodology is demonstrated by a numerical example and an error analysis is performed to evaluate the performances of the proposed procedure. The results of this analysis show that the proposed method performs satisfactorily when a different number of observations on the times between productions of defective products is available
  5. Keywords:
  6. Bayesian inference ; Gamma distribution ; Mixture models ; Production processes ; Replacement strategy ; Stochastic dynamic programming ; Bayesian networks ; Computer programming ; Defects ; Error analysis ; Inference engines ; Mixtures ; Optimization ; Probability distributions ; Production ; Stochastic models ; Stochastic systems ; Dynamic programming
  7. Source: Communications in Statistics - Theory and Methods ; Volume 40, Issue 4 , 2011 , Pages 702-725 ; 03610926 (ISSN)
  8. URL: http://www.tandfonline.com/doi/abs/10.1080/03610920903453459?journalCode=lsta20