Analysis of MTBF evaluation methods for small sample sizes

The accurate estimation of Mean Time Between Failures (MTBF) may be necessary under small sample size conditions and can be difficult. This article proposes combinations of two methods to calculate the cumulative probability using hierarchical Bayesian estimation and the mean rank order method, and two approaches to estimate parameters of the Weibull distribution using the ε-support vector regression (ε-SVR) and least square method. The relative error of these methods against a simulation are used to measure the accuracy of the parameter estimation where, according to the definition of MTBF, the expectation of the Weibull distribution is taken as the estimated value of MTBF. The article suggests approaches for further research in the reliability of aviation equipment.