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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".
A product is said to follow the bathtub curve if in the early life of a product, the failure rate decreases as defective products are identified and discarded, and early sources of potential failure such as manufacturing defects or damage during transit are detected. In the mid-life of a product the failure rate is constant.
For example, a common specification for PATA and SATA drives may be an MTBF of 300,000 hours, giving an approximate theoretical 2.92% annualized failure rate i.e. a 2.92% chance that a given drive will fail during a year of use. The AFR for a drive is derived from time-to-fail data from a reliability-demonstration test (RDT). [3]
The probability of an event is a number between 0 and 1; the larger the probability, the more likely an event is to occur. [note 1] [1] [2] This number is often expressed as a percentage (%), ranging from 0% to 100%. A simple example is the tossing of a fair (unbiased) coin.
If a binary classifier (potentially enhanced with a different likelihood to take more structure of the problem into account) is calibrated, then the classifier score is the hazard function (i.e. the conditional probability of failure). [17] Description of the transformation of continuous-time survival data to discrete-time survival data.
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]
Performing a probabilistic risk assessment starts with a set of initiating events that change the state or configuration of the system. [3] An initiating event is an event that starts a reaction, such as the way a spark (initiating event) can start a fire that could lead to other events (intermediate events) such as a tree burning down, and then finally an outcome, for example, the burnt tree ...
Thus the force of mortality at these ages is zero. The force of mortality μ(x) uniquely defines a probability density function f X (x). The force of mortality () can be interpreted as the conditional density of failure at age x, while f(x) is the unconditional density of failure at age x. [1]