Using the response surface method (RSM)

input parameters-output responses equations of a type 6408 ball bearing were created to simulate different random error distributions; meanwhile

using matrix test method

sample point positions in input parameters spacing were located

and then it carried out a series of deterministic fitting tests to get the input parameters-output responses equations compositions and coefficients

by the method of regression analysis (least square method)

in software LS-DYNA dynamic simulations for the ball bearing. To solve these stochastic functional equations

the ball bearing service-reliability ratio at any time was calculated. Result shows that the service-reliability ratio of 6408 ball bearing at 0.020008s is 97.062%.