Stochastic Petri Nets and Generalized Stochastic Petri Nets as well as other extensions to Stochastic Petri Nets have been widely applied as a model of asynchronous concurrent process, or as an aid to analyze or design concurrent systems. This paper presents an Extended Stochastic Petri Net model for a shift processing system in which three kinds of sink may occur and an arbitrary time distribution is incorporated, provides an analytical method based on a Markov renewal process with some non-regeneration points to clarify the probabilistic behavior of the system, and finally evaluates the performance of the system with numerical values.