Comparative Analysis of Fuzzy Dagum Hazard Function Approaches for Estimating Failure Rates

Abstract

When analysing the maintenance plan for a manufacturing system, the number of failures is a crucial consideration. There are frequently some uncertainties that have an impact on this number. The category of probabilistic uncertainty is distinct from probabilistic uncertainty, which encompasses most uncertainties. By using the fuzzy theoretical framework, this uncertainty is frequently modelled. With a fuzzy shape parameter, the failure numbers of the Dagum system under study in this paper is exhausted to calculate several failures.
Here, the figure is computed via two distinct approaches. With the first approach, the quality of failure receives the exact same membership values based on fuzziness of DGM shape parameter.  To determine membership, using level of α-cut of the shape parameter approach and estimate formula for failure number from the second method. For the Dagum shape parameter, we employ the Triangular Fuzzy Number (TrFN) without losing generality. We demonstrate that both approaches were successful in calculating the failure rate. When we deliberate failures as an operating time, both methodologies show that as time increases, the ambiguity (or fuzziness) of the various failures that arise rises.
The failure numbers that result as using the first method has a TrFN form. The second method's output failure rate, however, has a TrFN-like form rather than necessarily having a TrFN form. The Generalised Mean Value Defuzzification (GMDF) method is used to compare some aspects of these two approaches. The results reveal that the focal point of these fuzzy numbers of failures of corresponding DGM (Dagum distribution) are the same for any given GMDF weighting factor.