A highly exothermic reaction takes place in a CSTR operating continuously. The concerm is an

upset condition resulting in a runaway exothermic reaction in the CSTR$.$ The protection against

this undesirable event is provided by two CSTR dump valves $($V$1$ and V$2)$ that should open

and quench the reaction mixture in a water$-$filled sump if the temperature inside the CSIR rises

above a preset limit$.$ The valves are actuated pneumatically and controlled by a voting logic

unit $($VLU$).$ The VLU commands the valves to open when at least one of three temperature

channels indicates a high temperature condition.

Note that successful operation of the protection system takes place if at least one of the

temperature channels, the VLU, and at least one of the valves respond to a high temperature

wendition

a$)$ Construct a fault tree for a top event: "Runaway exothermic reaction in the CSTR$".$

Determine the minimal cut sets $($Consider the following basie events only: Failure of

temperature elements, failure of VLU, failure of dump valves, and failure of electrical or

pneumatic signal lines.