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Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes

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  • Pan, Zhengqiang
  • Balakrishnan, Narayanaswamy

Abstract

Many highly reliable products usually have complex structure, with their reliability being evaluated by two or more performance characteristics. In certain physical situations, the degradation of these performance characteristics would be always positive and strictly increasing. In such a case, the gamma process is usually considered as a degradation process due to its independent and non-negative increments properties. In this paper, we suppose that a product has two dependent performance characteristics and that their degradation can be modeled by gamma processes. For such a bivariate degradation involving two performance characteristics, we propose to use a bivariate Birnbaum–Saunders distribution and its marginal distributions to approximate the reliability function. Inferential method for the corresponding model parameters is then developed. Finally, for an illustration of the proposed model and method, a numerical example about fatigue cracks is discussed and some computational results are presented.

Suggested Citation

  • Pan, Zhengqiang & Balakrishnan, Narayanaswamy, 2011. "Reliability modeling of degradation of products with multiple performance characteristics based on gamma processes," Reliability Engineering and System Safety, Elsevier, vol. 96(8), pages 949-957.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:8:p:949-957
    DOI: 10.1016/j.ress.2011.03.014
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    References listed on IDEAS

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    1. van Noortwijk, J.M. & van der Weide, J.A.M. & Kallen, M.J. & Pandey, M.D., 2007. "Gamma processes and peaks-over-threshold distributions for time-dependent reliability," Reliability Engineering and System Safety, Elsevier, vol. 92(12), pages 1651-1658.
    2. Barker, C.T. & Newby, M.J., 2009. "Optimal non-periodic inspection for a multivariate degradation model," Reliability Engineering and System Safety, Elsevier, vol. 94(1), pages 33-43.
    3. Belmansour, Ahmed-Tidjani & Nourelfath, Mustapha, 2010. "An aggregation method for performance evaluation of a tandem homogenous production line with machines having multiple failure modes," Reliability Engineering and System Safety, Elsevier, vol. 95(11), pages 1193-1201.
    4. Bruce W. Schmeiser & Ram Lal, 1982. "Bivariate Gamma Random Vectors," Operations Research, INFORMS, vol. 30(2), pages 355-374, April.
    5. Savage, Gordon J. & Kap Son, Young, 2011. "The set-theory method for systems reliability of structures with degrading components," Reliability Engineering and System Safety, Elsevier, vol. 96(1), pages 108-116.
    6. Kundu, Debasis & Balakrishnan, N. & Jamalizadeh, A., 2010. "Bivariate Birnbaum-Saunders distribution and associated inference," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 113-125, January.
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