System Reliability Theory. Marvin Rausand

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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.

      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.

      We define a failure mode of an item as:

      Definition 3.3 (Failure mode)

      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 types.

Schematic illustration of the doorbell and associated circuitry.

      1 No sound when the pushbutton is activated (by a finger.)

      2 Doorbell sound does not stop when finger is lifted from pushbutton.

      3 Doorbell sounds without activating the pushbutton.

      A similar doorbell system is analyzed in NASA (2002).

Schematic illustration of the relation between failure causes, failure modes, and failure effects.

      3.5.1 Failure Causes

      All failures have at least one cause. We define failure cause as follows.

      Definition 3.4 (Failure cause)

      Set of circumstances that leads to failure.

      The failure cause may originate during specification, design, manufacture, installation, operation, or maintenance of an item (IEV 192‐03‐11). The failure cause may be an action, an event, a condition, a factor, a state, or a process that is – at least partly – responsible for the occurrence of a failure. To be responsible for a failure, the cause must be present before the failure occurs, and the presence of the cause should increase the likelihood of the failure.

      When studying several similar failures, we should see a positive correlation between the presence of the cause and the occurrence of the failure(s), but positive correlation is not a sufficient condition for claiming that something is a cause of a failure. It is very easy to find correlated factors that are totally unrelated. The correlation may, for example, be that the two factors are both caused by the same third factor. Causality is a complicated philosophical subject. A lot more information may be found by searching the Internet. The authors especially recommend consulting (Pearl 2009).

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