The process distribution of a manufacturing process which reflects past experience with the quality levels of outgoing lots is an indispensible input of the Bayesian quality audit systems. A distance-method estimator for the process distribution is developed and shown to be superior to the commonly used method-of-moments estimator. In a continuous manufacturing process, the process distribution needs to be updated after each new lot is inspected. Several updating procedures including the posterior distribution, the exponential smoothing method, the moving window method and the all periods method are proposed and compared by a simulation study.