Imprecise Reliability Analysis for the Robotic Component Based on Limited Lifetime Data

Abstract

The inverse Weibull (IW) distribution has an ability to model failure rates which are quite common in reliability studies. The three-parameter generalized inverse Weibull (GIW) distribution is a promoted form of the inverse Weibull distribution which is mainly used in reliability lifetime data analysis, such as the wear life of mechanical components. With the limited lifetime data, it is difficult to estimate the accurate parameters of the GIW distribution, but we can get the imprecise ones. According to the imprecise Bayesian inference, this paper proposes a new imprecise model called imprecise Gamma-generalized inverse Weibull model, which can do reliability analysis for the component of the robotic device with incomplete lifetime data. Compared to other methods, this imprecise model can be applied to computing reliability measures when the number of events of interest or observations are very small and can provide the effective way of interval estimation. The detailed theoretical derivations for imprecise Gamma-generalized inverse Weibull model are introduced in this paper. Moreover, the impact of some parameters on the proposed model, such as the parameter s and available lifetime data size N, as well as the scale parameter and the shape parameter are also depicted. Furthermore, some convergences of the proposed model are also introduced and proved. Finally, the experimental using simulation lifetime data for the component of the robotic device validate the availability of the proposed model.