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In real-world applications, the failure probability of a system usually differs over time; failures occur more frequently in early-life ("burning in"), or as a system ages ("wearing out"). This is known as the bathtub curve, where the middle region is called the "useful life period".
For example, in an automobile, the failure of the FM radio does not prevent the primary operation of the vehicle. It is recommended to use Mean time to failure (MTTF) instead of MTBF in cases where a system is replaced after a failure ("non-repairable system"), since MTBF denotes time between failures in a system which can be repaired. [1]
Annualized failure rate (AFR) gives the estimated probability that a device or component will fail during a full year of use. It is a relation between the mean time between failure ( MTBF ) and the hours that a number of devices are run per year.
For an exponential survival distribution, the probability of failure is the same in every time interval, no matter the age of the individual or device. This fact leads to the "memoryless" property of the exponential survival distribution: the age of a subject has no effect on the probability of failure in the next time interval.
Software reliability is the probability that software will work properly in a specified environment and for a given amount of time. Using the following formula, the probability of failure is calculated by testing a sample of all available input states. Mean Time Between Failure(MTBF)=Mean Time To Failure(MTTF)+ Mean Time To Repair(MTTR)
The probability of failure was obtained through the multiplication of each of the failure probabilities along the path under consideration. HRA event tree for aligning and starting emergency purge ventilation equipment on in-tank precipitation tanks 48 or 49 after a seismic event.
Obtain event failure probabilities: If the failure probability can not be obtained use fault tree analysis to calculate it. Identify the outcome risk: Calculate the overall probability of the event paths and determine the risk. Evaluate the outcome risk: Evaluate the risk of each path and determine its acceptability.
– probability of component i failing – the probability of all components failing (system failure) This formula assumes independence of failure events. That means that the probability of a component B failing given that a component A has already failed is the same as that of B failing when A has not failed.