Abstract: Reliabilities of force condition analysis of vehicle axles and Bayes statistics are both discussed with the intention of determining the axle diameter on given reliability basis and vice versa, the posterior expectation of Bayes statistics is simplified in order in sequence: (1) converting the non-normal distribution into equivalent normal one by use of conventional approaches to reliability; (2) calculating the prior and posterior parameters of normal distribution by use of the characteristics of exponent group in conjugate distribution; (3) getting numerical solutions with very high convergence by use of symbolic integration by substitution and Newton-Ralphson iteration method. The solution is verified through an instance. The algorithm is implemented on computer with VB programming, thus avoiding out-of-date methods and rationalizing conventional design procedure. In particular the method proposed here applies to the personalized/specialized designs to which the classical statistics method is unavailable, and it may provide more accurate solutions than traditional methods for those designs which will be changed frequently or poor in either experimental or in-site data.