The exponential-dispersion (ED) process is a generalized stochastic process, including Wiener, gamma, and inverse Gaussian processes as special cases. This paper studies the reliability evaluation problem for products based on the ED process with random effects and covariates. The expectation maximization algorithm is applied to estimate the parameters of the ED processes. The probability density functions, the cumulative distribution functions of the lifetime and the remaining useful life distributions of products are derived based on Birnbaum–Saunders distribution. Finally, two illustrative examples are presented to show the effectiveness of the developed methods.