This paper describes a formal safety analysis technique which is demonstrated by performing empirical formal safety analysis with the case study of beamline hutch door Interlock system that is developed by using PLC (Programmable Logic Controller) systems at the Pohang Accelerator Laboratory. In order to perform formal safety analysis, we have built the Z formal specifications representation from user requirement written in ambiguous natural language and target PLC ladder logic, respectively. We have also studied the effective method to express typical PLC timer component by using specific Z formal notation which is supported by temporal history. We present a formal proof technique specifying and verifying that the hazardous states are not introduced into ladder logic in the PLC-based safety critical system. And also, we have found that some errors or mismatches in user requirement and final implemented PLC ladder logic while analyzing the process of the consistency and completeness of Z translated formal specifications. In the case of relatively small systems like Beamline hutch door interlock system, a formal safety analysis including explicit proof is highly recommended so that the safety of PLC-based critical system may be enhanced and guaranteed. It also provides a helpful benefits enough to comprehend user requirement expressed by ambiguous natural language.