System Reliability Theory. Marvin Rausand

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System Reliability Theory - Marvin Rausand

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rel="nofollow" href="#ulink_b2f16cfb-8f64-582d-a572-3d756b207a8b">Definition 3.1 may be given:

      1 Definition 3.1 is mainly a rephrasing of IEV's definition of a failure: “loss of ability to perform as required” (IEV 192‐03‐01), but the expression “loss of ” is replaced with the expression “the termination of” to make it even more clear that a failure is an event that takes place at a certain point in time (e.g. at time ).

      2 In the context of reliability, the expression “ability to perform as required” does not imply that all aspects of the item are perfect, but that the item must be able to perform the functions that are required for a given purpose.

      3 The item may deteriorate as a slow process. Failure occurs when a required function no longer fulfills its performance requirements, and it may not be any significant change in performance when the threshold is passed, as shown in Example 3.2.

      4 One user may interpret “as required” different from another user. A failure that is important (and costly) in a warranty context may, for example, be irrelevant in a risk assessment context.The performance requirements for an item are usually available in the item specification document and partly in the user's manuals, but users seldom read the specifications and the complete user's manual.

      5 We use the verb fail to express that a failure occurs. When a failure occurs at time , the item fails at time .

Schematic illustration of the failure as a transition from a functioning state to a failed state.

      When a car is used, the tires wear and the tire tread depth is continuously reduced and thereby the performance of the tires is degrading. When the depth becomes smaller than a certain legal limit images (may be different in the different countries), the tires have to be replaced. A failure occurs when the tread depth passes images. In this case, it is not possible to determine exactly the time of failure, and there is no dramatic change of performance when the failure occurs, but the risk of water planning and of puncture is considered to be unacceptable with a smaller depth than images.

      3.2.1 Failures in a State

Graph depicts the difference between failure and fault for a degrading item.

      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.

      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 images of the occurrence of the failure is unknown. When we try to switch on the light and observe that it has failed, we only know that the failure occurred in the time interval since the preceding use of the light bulb. (In this example, we assume that the switch is functioning without failure.)

      3.2.2 Failures During Transition

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