IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v96y2011i8p949-957.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832011000421
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2011.03.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    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. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Huynh, K.T. & Barros, A. & Bérenguer, C. & Castro, I.T., 2011. "A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events," Reliability Engineering and System Safety, Elsevier, vol. 96(4), pages 497-508.
    2. Huynh, K.T. & Castro, I.T. & Barros, A. & Bérenguer, C., 2012. "Modeling age-based maintenance strategies with minimal repairs for systems subject to competing failure modes due to degradation and shocks," European Journal of Operational Research, Elsevier, vol. 218(1), pages 140-151.
    3. Chang, Miaoxin & Huang, Xianzhen & Coolen, Frank P.A. & Coolen-Maturi, Tahani, 2021. "Reliability analysis for systems based on degradation rates and hard failure thresholds changing with degradation levels," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    4. Guillermo Martínez-Flórez & Artur J. Lemonte & Germán Moreno-Arenas & Roger Tovar-Falón, 2022. "The Bivariate Unit-Sinh-Normal Distribution and Its Related Regression Model," Mathematics, MDPI, vol. 10(17), pages 1-26, August.
    5. Tianyu Liu & Zhengqiang Pan & Quan Sun & Jing Feng & Yanzhen Tang, 2017. "Residual useful life estimation for products with two performance characteristics based on a bivariate Wiener process," Journal of Risk and Reliability, , vol. 231(1), pages 69-80, February.
    6. Jorge A. Sefair & Oscar Guaje & Andrés L. Medaglia, 2021. "A column-oriented optimization approach for the generation of correlated random vectors," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 43(3), pages 777-808, September.
    7. Hajipour, Yassin & Taghipour, Sharareh, 2016. "Non-periodic inspection optimization of multi-component and k-out-of-m systems," Reliability Engineering and System Safety, Elsevier, vol. 156(C), pages 228-243.
    8. Xiaojia Wang & Ting Huang & Keyu Zhu & Xibin Zhao, 2022. "LSTM-Based Broad Learning System for Remaining Useful Life Prediction," Mathematics, MDPI, vol. 10(12), pages 1-13, June.
    9. Wang, Changxi & Elsayed, Elsayed A., 2020. "Stochastic modeling of corrosion growth," Reliability Engineering and System Safety, Elsevier, vol. 204(C).
    10. Wang, Xiaofei & Wang, Bing Xing & Jiang, Pei Hua & Hong, Yili, 2020. "Accurate reliability inference based on Wiener process with random effects for degradation data," Reliability Engineering and System Safety, Elsevier, vol. 193(C).
    11. Finkelstein, Maxim & Ludick, Zani, 2014. "On some steady-state characteristics of systems with gradual repair," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 17-23.
    12. Alaswad, Suzan & Xiang, Yisha, 2017. "A review on condition-based maintenance optimization models for stochastically deteriorating system," Reliability Engineering and System Safety, Elsevier, vol. 157(C), pages 54-63.
    13. Yanwei Zhang & Vanja Dukic, 2013. "Predicting Multivariate Insurance Loss Payments Under the Bayesian Copula Framework," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 80(4), pages 891-919, December.
    14. Liu, Yongchao & Wang, Guanjun & Liu, Peng, 2024. "A condition-based maintenance policy with non-periodic inspection for k-out-of-n: G systems," Reliability Engineering and System Safety, Elsevier, vol. 241(C).
    15. Savage, Gordon J. & Zhang, Xufang & Son, Young Kap & Pandey, Mahesh D., 2016. "Reliability of mechanisms with periodic random modal frequencies using an extreme value-based approach," Reliability Engineering and System Safety, Elsevier, vol. 150(C), pages 65-77.
    16. Wang, Zhonglai & Liu, Jing & Yu, Shui, 2020. "Time-variant reliability prediction for dynamic systems using partial information," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    17. Song, Sanling & Coit, David W. & Feng, Qianmei, 2014. "Reliability for systems of degrading components with distinct component shock sets," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 115-124.
    18. Guo, Chiming & Wang, Wenbin & Guo, Bo & Si, Xiaosheng, 2013. "A maintenance optimization model for mission-oriented systems based on Wiener degradation," Reliability Engineering and System Safety, Elsevier, vol. 111(C), pages 183-194.
    19. Wang, Liying & Song, Yushuang & Zhang, Wenhua & Ling, Xiaoliang, 2023. "Condition-based inspection, component reallocation and replacement optimization of two-component interchangeable series system," Reliability Engineering and System Safety, Elsevier, vol. 230(C).
    20. Christian Paroissin & Landy Rabehasaina, 2015. "First and Last Passage Times of Spectrally Positive Lévy Processes with Application to Reliability," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 351-372, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:96:y:2011:i:8:p:949-957. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.