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Computing the Number of Failures for Fuzzy Weibull Hazard Function

Author

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  • Hennie Husniah

    (Department of Industrial Engineering, Langlangbuana University, Bandung 40261, Indonesia)

  • Asep K. Supriatna

    (Department of Mathematics, Padjadjaran University, Jatinangor 45363, Indonesia)

Abstract

The number of failures plays an important factor in the study of maintenance strategy of a manufacturing system. In the real situation, this number is often affected by some uncertainties. Many of the uncertainties fall into the possibilistic uncertainty, which are different from the probabilistic uncertainty. This uncertainty is commonly modeled by applying the fuzzy theoretical framework. This paper aims to compute the number of failures for a system which has Weibull failure distribution with a fuzzy shape parameter. In this case two different approaches are used to calculate the number. In the first approach, the fuzziness membership of the shape parameter propagates to the number of failures so that they have exactly the same values of the membership. While in the second approach, the membership is computed through the α-cut or α-level of the shape parameter approach in the computation of the formula for the number of failures. Without loss of generality, we use the Triangular Fuzzy Number ( TFN ) for the Weibull shape parameter. We show that both methods have succeeded in computing the number of failures for the system under investigation. Both methods show that when we consider the function of the number of failures as a function of time then the uncertainty (the fuzziness) of the resulting number of failures becomes larger and larger as the time increases. By using the first method, the resulting number of failures has a TFN form. Meanwhile, the resulting number of failures from the second method does not necessarily have a TFN form, but a TFN-like form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification ( GMVD ) method. The results show that for certain weighting factor of the GMVD , the cores of these fuzzy numbers of failures are identical.

Suggested Citation

  • Hennie Husniah & Asep K. Supriatna, 2021. "Computing the Number of Failures for Fuzzy Weibull Hazard Function," Mathematics, MDPI, vol. 9(22), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:22:p:2858-:d:676381
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    References listed on IDEAS

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    1. Bermawi P. Iskandar & Nat Jack & D. N. Pra Murthy, 2012. "Two New Servicing Strategies For Products Sold With Warranty," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-16.
    2. Harish Garg & S.P. Sharma & Monica Rani, 2013. "Weibull fuzzy probability distribution for analysing the behaviour of pulping unit in a paper industry," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 14(4), pages 395-413.
    3. Juhyun Lee & Byunghoon Kim & Suneung Ahn, 2019. "Maintenance Optimization for Repairable Deteriorating Systems under Imperfect Preventive Maintenance," Mathematics, MDPI, vol. 7(8), pages 1-17, August.
    4. Toshio Nakagawa, 2005. "Maintenance Theory of Reliability," Springer Series in Reliability Engineering, Springer, number 978-1-84628-221-8, March.
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