System Reliability Theory. Marvin Rausand
that occur during a transition. The types of failures occurring in a state are illustrated in Examples 3.3, 3.4, and 3.5.
Consider an electric driven water pump. The essential function of the pump is to pump water at a certain rate. Assume that the target rate is 100 l/min, with performance criterion saying that the rate need to be between 95 and 105 l/min. In case of internal fouling, the pumping rate may decrease such that the performance criterion is no longer met. When the rate passes the lower threshold rate, a pump failure occurs and the pump has to be stopped. The pump remains in this state until it has been cleaned/repaired. This process is illustrated in Figure 3.3.
Figure 3.3 Illustration of the difference between failure and fault for a degrading item.
Example 3.4 (Light bulb–continuously “on”)
Consider a light bulb that is always switched on. The function of the bulb is to provide light. When the light bulb fails, the failure occurs in an operating state. If someone is present and can observe the loss of light event, the precise time of the failure can be recorded.
Example 3.5 (Light bulb–“on” only on demand)
Reconsider a light bulb, similar to the one in Example 3.4, but assume that the light bulb is very seldom switched on and that it each time is energized for a short time period. The bulb may also fail in passive state (e.g. due to vibrations). A failure in passive state is not observable and leaves a hidden fault. The hidden fault is not revealed until the light bulb is switched on next time. The time
3.2.2 Failures During Transition
A failure during transition may either be caused by an existing hidden fault or an erroneously performed transition, as illustrated in Examples 3.6 and 3.7.
Consider a lawn mower with a petrol engine that is started by pulling a rope. To start the lawn mower involves a transition from a passive to an active state of the mower. A failure during this transition may be caused by an internal defect (e.g. corrosion, or contaminated petrol), but may also be due to incorrect starting procedure.
Reconsider the safety valve in Example 3.1 and assume that the valve is in fully open state when an emergency occurs on the downstream side of the valve. The valve receives a signal to close and the transition is initiated. Due to debris in the valve cavity, the movement is stopped before the valve reaches the closed state.
3.3 Faults
The term fault is mentioned in Section 3.2, but without a proper definition. We define a fault as:
Definition 3.2 (Fault of an item)
A state of an item, where the item is not able to perform as required.
The duration of the fault may range from negligible to permanent. There are two main types of faults.
Type 1 fault is a fault that occurs as a consequence of a failure. The failure causes a transition from a functioning state into a fault, which is also called a failed state. In Example 3.4, the failure of the light bulb left the bulb in a state where it cannot give light. In this example, the bulb has to be replaced to function again.
Type 2 fault is a fault that is introduced in the item due to human error or misjudgment in the specification, design, manufacture, transportation, installation, operation, or maintenance of the item. This type of fault enters the item without any preceding item failure and is a dormant fault that remains hidden until the item is activated or inspected. A type 2 fault is also called a systematic fault. A software bug is a typical example of such a fault. Another example is faults caused by design errors or installation errors.
3.4 Failure Modes
We define a failure mode of an item as:
Definition 3.3 (Failure mode)
The manner in which a failure occurs, independent of the cause of the failure.
A failure mode is a description of how a failure occurs but does not say anything about why the failure occurred. Example 3.8 illustrates how the failure mode concept is usually interpreted.
Example 3.8 (Failure modes of a sink faucet)
Consider a sink faucet used in a bathroom. The main functions of the faucet are to open/close the water supply, to contain the water, and to regulate the water temperature and flow. We consider only the faucet (the item) and assume that cold and hot water are available.
The faucet may have a number of failure modes. Among these are:
1 Fail to open (on demand) and supply water
2 Fail to close (on demand) and stop the flow of water
3 Leakage through the faucet (i.e. dripping)
4 Leakage out (from faucet seals)
5 Fail to regulate water flow
6 Fail to regulate temperature
The faucet has two main states, closed and open. The first two failures (1 and 2) occur during intended transitions between these states. The next two failure modes (3 and 4) occur in a state. For these failure modes, the faucet is in a state where it is leaking and not able to perform as required. The two last failure modes (5 and 6) may be interpreted to be somewhere between the two other