Reliability and Availability Models of Belt Drive Systems Considering Failure Dependence

Conventional reliability models of belt drive systems in the failure mode of fatigue are mainly based on the static stress strength interference model and its extended models, which cannot consider dynamic factors in the operational duration and be used for further availability analysis. In this paper, time-dependent reliability models, failure rate models and availability models of belt drive systems are developed based on the system dynamic equations with the dynamic stress and the material property degradation taken into account. In the proposed models, dynamic failure dependence and imperfect maintenance are taken into consideration. Furthermore, the issue of time scale inconsistency between system failure rate and system availability is proposed and addressed in the proposed system availability models. Besides, Monte Carlo simulations are carried out to validate the established models. The results from the proposed models and those from the Monte Carlo simulations show a consistency. Furthermore, the case studies show that the failure dependence, imperfect maintenance and the time scale inconsistency have significant influences on system availability. The independence assumption about the belt drive systems results in underestimations of both reliability and availability. Moreover, the neglect of the time scale inconsistency causes the underestimate of the system availability. Meanwhile, these influences show obvious time-dependent characteristics.

Characterizing the Relationship between Weibull Location Parameter and the Minimal Observation in a Small Size of Sample Based on Stochastic Simulation

Three-parameter Weibull distribution is one of the preferable distribution models to describe product life. However, it is difficult to estimate its location parameter in the situation of a small size of sample. This paper presents a stochastic simulation method to estimate the Weibull location parameters according to a small size of sample of product life observations and a large amount of statistically simulated life date. Big data technique is applied to find the relationship between the minimal observation in a product life sample of size n (n ≥ 3) and the Weibull location parameter. An example is presented to demonstrate the applicability and the value of the big data based stochastic simulation method. Comparing with other methods, the stochastic simulation method can be applied to very small size of sample such as the sample size of three, and it is easy to apply.