FTA, FMEA, and DRBFM
FTA, FMEA, and DRBFM are all design analysis methods used to ensure quality. For those who are familiar with the names but wonder, “How do you use them? How are they different?” I’d like to explain.
FTA (Fault Tree Analysis)
FTA (Fault Tree Analysis) is a top-down approach to failure analysis.
・Procedure
1. Determine the top event (define the event)
2. Identify the causes of the top event
3. Create the fault tree
Definition of Undesirable Events
In FTA, the first step is to define an undesirable event. This is called a top event (Top Event). In an FTA diagram, the top event is enclosed in a rectangular box and placed at the very top of the diagram.
The top event can be set to any type of incident, not limited to equipment failure—such as “fire,” “cancellation of a lecture,” or “mountain climbing accident.” In such cases, the Fault can be considered, respectively, as a failure of the fire prevention system, the occurrence of a reason for canceling the lecture, or a failure of the mountain climbing accident prevention system. It is generally accepted that top events must be events whose occurrence can be prevented; natural phenomena cannot be designated as top events. However, when the sole purpose is to analyze the occurrence frequency of those top events, it is possible to designate natural phenomena as top events.
Identification of Causes of Top Events
Below the top event, systematically list the contributing events (sufficient conditions) involved in its occurrence—that is, ensuring there are no omissions or duplicates. To list them systematically, it is best to appropriately place intermediate events and list the basic events beneath them.
When dealing with complex systems, intermediate events should be arranged hierarchically from top to bottom as primary intermediate events, secondary intermediate events, and so on. Intermediate events serve as classification categories and should be enclosed in rectangular boxes. For example, horizontal relationships—such as “left, middle, right”; “materials, machinery, people, methods, measurement”; or “engine section, steering section, hydraulic section, etc.”—should be organized by dividing the entire system into several parts. In other words, if the total does not equal the whole, it will lead to omissions in the enumeration of events.
Basic events are those for which probabilities are estimated; they should be enclosed in a circle and arranged in the bottom row.
Creating a Fault Tree Diagram
Create a fault tree diagram that represents the causal relationships between the top event and basic events using Boolean Logic to create a fault tree diagram. Place the top event at the top, arrange intermediate events hierarchically below it—such as first-order intermediate events, second-order intermediate events, and so on—and place the basic events at the bottom.
When a parent event X has child events A, B, C, etc., below it, the logical symbol that indicates the relationship where the occurrence of parent event X is contingent upon the occurrence of any one of these child events is called an OR gate. In this case, the probability of parent event X occurring is calculated by summing the probabilities of child events A, B, and C. Furthermore, the logical symbol that represents the relationship where the parent event X occurs only if all of its child events A, B, and C occur simultaneously is called the AND gate . In this case, the probability of the parent event X occurring is calculated by multiplying the probabilities of the child events A, B, and C.
A logical symbol that represents the relationship “If subordinate event A occurs, then superior event X occurs,” but only if conditional event B is satisfied, is called a constraint gate. In this case, the probability of superior event X occurring is calculated by multiplying the probabilities of subordinate events A and B.
Although these gates are typically represented by symbols, it is also acceptable to use letter symbols such as “AND,” “OR,” and “CON.”
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OR Gate
Assigning Probabilities to Events
Determine the probability of occurrence for each event. Note that this step may be omitted if the probability of the basic event cannot be quantified or if it is not necessary to quantify the probability of higher-level events.
There are two types of probability with different properties: frequency probability and state probability. Since frequency probability and state probability have different properties (units), they cannot be added together. However, they can be multiplied together.
- Frequency Probability
- This refers to assessments such as “once per hour,” “once per month,” “once per year,” or “once every 10 years.” It represents a judgment that it is reasonable to expect an occurrence frequency of this magnitude. For example, if the probability that a train will not be running on the way to work in the morning is not frequent enough to occur every month but is more frequent than once every 10 years, it is assessed as once a year.
- State Probability
- For newly designed equipment that has passed preliminary verification tests, the state probability is estimated at 0.1. If the equipment has withstood several years of use without issues, the state probability is assessed as 0.01. This state probability is used as the probability of the constraint condition, and it is multiplied by the frequency probability of a separate abnormal basic event.
- Probability of Occurrence of a Higher-Level Event
- The probability of occurrence of a higher-level event is calculated based on the probability of occurrence of lower-level events and the causal relationship expressed in Boolean logic.
For frequency probability—for example, when evaluating the probability that a train will not run during the morning commute—we assess whether such a day occurs once a year, so
- 1 day / 365 days = 3×10−3
In this way, the probabilities of all events—from the basic event to the higher-level event—are calculated on a daily basis. However, when considering an event where a building collapses due to an earthquake, killing or injuring passersby, we must assume that the building’s collapse and the people passing by occur within the same minute; therefore, the event must be placed under an AND gate. Consequently, we first evaluate the entire frequency probability on a per-minute basis before performing the calculation.
Evaluation
Finally, refer to the created FT diagram and implement countermeasures for the causes of the top event. If the probability of the top event occurring, as determined above, does not meet the target, reduce that probability by implementing countermeasures for the subordinate events.
If, for example, “materials, machinery, people, methods, and measurement” are listed as intermediate events, countermeasures are implemented with due consideration for balance so that each has a reasonable probability value. While equipment failure occurs once every 10,000 years, human error can occur about once an hour. The fundamental concept of FTA is to resolve this imbalance, thereby avoiding both excessively high probabilities and excessive countermeasures.
