Number of failures for Weibull hazard function with fuzzy shape parameter Hennie Husniah (1), Rohmana (1) & Asep K. Supriatna (2)
1. Department of Industrial Engineering, Langlangbuana University, Jl. Karapitan no 116, Bandung 40261, Indonesia
2. Department of Mathematics, Padjadjaran University, Jl. Raya Bandung-Sumedang Km 21, Jatinangor 45363, Indonesia
Abstract
Number of failures play important role in maintenance strategy for industrial equipment, either repairable or non-repairable ones. There are several form of known distribution used to model the failures of an industrial equipment. Weibull distribution, and its hazard function, is among the most used distribution. Most maintenance models in literature mainly consider certain or crisp condition in a deterministic form. However, many real phenomena seem do not suitable to model in such certain or crisp condition. One approach to model a possibilistic uncertainty is by applying the fuzzy number theory. In this paper, we discuss the Weibull hazard function by assuming a fuzzy shape parameter. We look for the number of failures generating by the function using two different methods. The first one assumes that the fuzziness of the shape parameter propagates to the number of failures with the same form of fuzzy number membership. The second one use the fuzziness of the shape parameter in the computation of the number of failures directly, through the concept of alpha-cut or alpha-level. Some comparisons regarding these approaches are presented.
Keywords: Triangular fuzzy number, alpha-cut, Weinbull distribution, number of failures
