Computing the Number of Failures for Fuzzy Weibull Hazard Function

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 u...

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Autores principales:	Hennie Husniah, Asep K. Supriatna
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Weibull hazard function number of failures <i>TFN</i> α-cut defuzzification Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b65aa71a5c854f9aa6d8a49fabaa0255
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spelling	oai:doaj.org-article:b65aa71a5c854f9aa6d8a49fabaa02552021-11-25T18:16:36ZComputing the Number of Failures for Fuzzy Weibull Hazard Function10.3390/math92228582227-7390https://doaj.org/article/b65aa71a5c854f9aa6d8a49fabaa02552021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2858https://doaj.org/toc/2227-7390The 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 (<i>TFN</i>) 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 <i>TFN</i> form. Meanwhile, the resulting number of failures from the second method does not necessarily have a <i>TFN</i> form, but a <i>TFN-like</i> form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification (<i>GMVD</i>) method. The results show that for certain weighting factor of the <i>GMVD</i>, the cores of these fuzzy numbers of failures are identical.Hennie HusniahAsep K. SupriatnaMDPI AGarticleWeibull hazard functionnumber of failures<i>TFN</i>α-cutdefuzzificationMathematicsQA1-939ENMathematics, Vol 9, Iss 2858, p 2858 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Weibull hazard function number of failures <i>TFN</i> α-cut defuzzification Mathematics QA1-939
spellingShingle	Weibull hazard function number of failures <i>TFN</i> α-cut defuzzification Mathematics QA1-939 Hennie Husniah Asep K. Supriatna Computing the Number of Failures for Fuzzy Weibull Hazard Function
description	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 (<i>TFN</i>) 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 <i>TFN</i> form. Meanwhile, the resulting number of failures from the second method does not necessarily have a <i>TFN</i> form, but a <i>TFN-like</i> form. Some comparisons between these two methods are presented using the Generalized Mean Value Defuzzification (<i>GMVD</i>) method. The results show that for certain weighting factor of the <i>GMVD</i>, the cores of these fuzzy numbers of failures are identical.
format	article
author	Hennie Husniah Asep K. Supriatna
author_facet	Hennie Husniah Asep K. Supriatna
author_sort	Hennie Husniah
title	Computing the Number of Failures for Fuzzy Weibull Hazard Function
title_short	Computing the Number of Failures for Fuzzy Weibull Hazard Function
title_full	Computing the Number of Failures for Fuzzy Weibull Hazard Function
title_fullStr	Computing the Number of Failures for Fuzzy Weibull Hazard Function
title_full_unstemmed	Computing the Number of Failures for Fuzzy Weibull Hazard Function
title_sort	computing the number of failures for fuzzy weibull hazard function
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b65aa71a5c854f9aa6d8a49fabaa0255
work_keys_str_mv	AT henniehusniah computingthenumberoffailuresforfuzzyweibullhazardfunction AT asepksupriatna computingthenumberoffailuresforfuzzyweibullhazardfunction
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Computing the Number of Failures for Fuzzy Weibull Hazard Function

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