Based on high nonlinearity

hard convergence

low computational efficiency in the computational process by the classic maximum entropy probability density function model

a method called dual maximum entropy probability density function model+sequential updating method was proposed. Because of the unsteady optimization routine

a transformation formula of Lagrangian coefficient was rededuced. The probability density function and reliability of several common distributions and one complex distribution was calculated by classic and dual maximum entropy probability density function models. This shows that compared with classic maximum entropy probability density function model

the optimization function of dual maximum entropy probability density function model has advantages of low nonlinearity and simple form

the sequential updating method not only overcomes the sensitivity problem of initial value but exhibits high computational efficiency; dual maximum entropy probability density function model+sequential updating method has the highest computational accuracy

and can be well applied to the reliability problems of complex distribution.