Temperature and electrical stresses are important factors in affecting the lifetime of electronic devices. In field applications, device temperature and electrical stresses are usually neither constant nor consistent in the system. Many existing reliability prediction models often assume the temperature and electrical stresses as deterministic values in estimating the failure rate of electronic devices in a printed circuit board (PCB). A PCB consists of multiple identical electronic devices such as resistors, capacitors, and ICs etc, and the device temperature varies from location to location due to difference of power consumption and cooling efficiency. For the same type of device, electrical stresses often vary in different subcircuities even though they are used in the same board.This paper proposes a stochastic reliability prediction model to estimate electrical device failure rates that explicitly incorporate the variations of the temperature and electrical stresses. For the same type of electrical devices, the temperature and the electrical stress factors are treated as stochastic values, not deterministic numbers. The mean and variance of the factors are derived based on the device temperature distribution and the electrical stress profile. Then the overall PCB failure rate is estimated by appropriately aggregating all device failure rates. Finally, the confidence intervals for the PCB failure rate are obtained based on sixsigma criteria. The method was applied to the design of a broadband analog board.