Alex:
After 53 years as a practicing engineer, I want to take this opportunity to address your query for your sake as a student (as well as all other students reading this) because I consider this topic as a very important one for chemical engineering students.
I strongly endorse and back up what Fallah has categorically answered - and in precisely the same tone: there is no such thing as calling an operation a "normal" one while a safety relief device is being activated and venting excess pressure. THAT IS NEVER to be considered as a normal operation. That is either a major process upset and/or an emergency situation where remedial action must be taken to relieve and stop the cause of the upset. A Pressure Safety Valve relieves excess pressure; unfortunately it cannot stop the cause of the excess pressure. This is an ABnormal operation - not a normal operation.
For your sake as a student studying process safety, I highly stress the need for your acceptance of the above fact: a PSV is used to protect the human and machinery environment in the event of an abnormal process pressure increase. The specific PSV is designed to have a relief capacity for a specific worst case scenario and that scenario is studied and identified as to credibility and flow capacity by process design engineers (probably you or other chemical engineers) encharged with that duty.
As Fallah infers, in the event that there might occur an extreme and sudden pressure spike (such as a runaway reaction, a deflagration and/or detonation, a process blow-through, etc.) a rupture disk or buckling pin might have to be incorporated in the system as a means to handle that possibility. It is also the Chemical Engineers designing the process to identify the possibility of that occurring and size the appropriate relief device.
A normal operation is one where there are no relief devices in operation and all steady state flows, temperatures, pressures, and compositions are well within the design range for the unit. When a process pressure upset occurs, the immediate response is to relieve the source of the pressure to atmosphere. In the special case of toxic fluids, this relief must be done in a controlled manner - i.e., to scrubbers or containment systems where the gases or vapors can be handled and managed safely without entering the atmosphere. Flaring a gas relief is used to avoid the gas proper entering the atmosphere as such, but rather as an oxide of the components - which generally are acceptable as emergency contaminants to the atmosphere - such as CO2. How you control and manage such emissions is another subject and one that is also assigned to Chemical Engineers. This requires a thorough knowledge of all available Unit Operations and Unit Processes in order to identify one that can be applied to the relieved gases.
I do not agree with Sparsha's comment about not designing your system to withstand explosions. I have designed acetylene generation plant piping systems to withstand deflagration AND detonation. This is a normal piping design requirement for acetylene generation plants and existing standards and codes exist. I don't know where Sparsha got his/her belief, but it is not true. If an internal detonation is possible, then you MUST design for it. Otherwise, to design such a system without that capability would be a crime.