Solution to the Storage Tank System Problem
Problem Summary:
The storage tank system is equipped with:
1. High-level alarm.
2. High-level shutdown system (connected to a solenoid valve to stop input stock flow).
Questions Asked:
1. Develop an event tree for the system using "failure of level indicator" as the initiating event.
2. Estimate the number of overflows expected per year.
3. Develop a fault tree for the top event of "storage tank overflows".
4. Determine the failure probability, expected occurrences per year, and minimal cut sets.
Step 1: Develop an Event Tree
- Event Tree starts with "Failure of Level Indicator" as the initiating event.
- Possible paths:
- High-Level Alarm either functions or fails.
- If alarm functions, risk is reduced; if fails, operator intervention is needed.
- Operator may successfully stop flow or fail.
- If operator fails, the high-level switch system activates or fails, leading to overflow.
Step 2: Estimate the Number of Overflows per Year
- Given Data:
- Level Indicator Failure: 4 times/year.
- High-Level Alarm Failure Probability: 0.01.
- Operator Failure Probability: 0.1.
- High-Level Switch System Failure Probability: 0.01.
- Calculation:
Probability of Overflow = (4 times/year) * (0.01) * (0.1) * (0.01)
Probability of Overflow = 0.00004 overflows/year.
Step 3: Develop a Fault Tree for "Storage Tank Overflows"
- Fault Tree Top Event: Storage Tank Overflows.
- Contributing Events:
- Failure of Level Indicator.
- Failure of High-Level Alarm.
- Failure of Operator to Stop Flow.
- Failure of High-Level Switch System.
Step 4: Determine Failure Probability and Expected Occurrences
- Failure Probability: 0.00004 overflows/year.
- Expected Occurrences per Year: 0.00004 occurrences/year (very low likelihood).
Minimal Cut Sets:
- Failure of Level Indicator.
- Failure of High-Level Alarm.
- Failure of Operator to Stop Flow.
- Failure of High-Level Switch System.
Most Likely Failure Modes:
1. Operator fails to stop the flow (Probability = 0.1).
2. High-Level Alarm failure (Probability = 0.01).
3. High-Level Switch failure (Probability = 0.01).
Design Improvement Suggestions:
- Improve the reliability of the high-level alarm.
- Automate the shutdown process to reduce reliance on the operator.
- Add redundant level indicators for better detection.
