Abstract:To obtain accurate product lifetime prediction results, random parameters which obey non-conjugate distributions were introduced to describe the unit-to-unit variation of products in the reliability model. For long-life products with monotonic degradation, the reliability model was proposed based on the Gamma process with non-conjugate distribution random parameters. Extending the traditional conjugate distribution of random parameters to non-conjugate distribution, unified expression of life distribution function under different parameter distributions was derived, and the lifetime prediction values were calculated by using the Monte Carlo method. Markov chain Monte Carlo method was adopted for parameter estimation. The calculation algorithm for the likelihood function under different distributions and the selection criterion for the parameter distribution were presented, and the effect of the distribution of random parameters on the product reliability was analyzed. The simulation test and the application example show that this modeling method can select an appropriate distribution. Simultaneously, the accuracy of parameter estimation and lifetime prediction of the method is validated.