Bayesian reliability assessment of gear lifetime under fuzzy environments

It is assumed that observed lifetime data are real numbers using classical reliability estimation methods. However, some collected lifetime data are fuzzy numbers. Thus, it is necessary to generalize classical statistical estimation methods for real numbers to fuzzy numbers. There is little study on Bayesian reliability estimation based on fuzzy lifetime data. Most of the reported work in this area is limited to single parameter lifetime distributions. In this paper, we propose a new method to determine the membership function of the estimates of the reliability function of multi-parameter lifetime distributions. An artificial neural network is used to approximate the calculation process of parameter estimation and reliability prediction. The genetic algorithm is used to find the boundary values of the membership function of the estimate of interest at any cut level. The effectiveness of the proposed method is illustrated with the gear lifetime that follows the lognormal distribution.