This paper addresses the problem of discovering and modeling a manufacturing process from the timed data contained in a monitoring data base. The modeling approach, called the stochastic approach, aims at producing temporal patterns under the form of abstract chronicle models from a homogenous Markov chain and its corresponding superposition of Poisson processes representing a sequence of timed data generated by supervision system. The paper presents the BJT4R algorithm (Backward Jump with Timed constraints For Road) that implements the stochastic approach to discover the most probable paths linking a discrete event class to another and its application to the wafer manufacturing process of a production plant of the STMicroelectronics Company1. The aim of this application is to discover models of "manufacturing roads" with the associated timed constraints to improve the wafer manufacturing process. This paper shows that the stochastic approach and the BJT4R is applicable to this aim.