Diagnosis of discrete event systems such as complex semiconductor manufacturing equipment has become more and more difficult such that it cannot be performed based on experience. Systematic approaches for the diagnosis problem are urgently needed. In this paper, we present an algorithm of polynomial complexity in the number of nodes for computing a sufficient condition of diagnosability of semiconductor manufacturing equipment modeled by Petri nets. Our algorithm is more efficient than previous ones since no state enumeration is necessary. This gives us an advantage to solve large real-world problems. Our algorithm is formulated as a linear programming problem, which is well-known to be of polynomial complexity in the worst case. We use a Metal-Organic Vapor Phase Epitaxy system that is simplified from real-world semiconductor manufacturing equipment applications to illustrate our proposed approach.