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The bathtub curve is a particular shape of a failure rate graph. This graph is used in reliability engineering and deterioration modeling. The 'bathtub' refers to the shape of a line that curves up at both ends, similar in shape to a bathtub. The bathtub curve has 3 regions: The first region has a decreasing failure rate due to early failures.
E model, 1/E model and power law exponential model are common models which depict the breakdown behavior. The failure types for integrated circuit (IC) components follow the classic bath tub curve. There is infant mortality, which is decreasing failure rate typically due to manufacturing defects. A low constant failure rate which is random in ...
A well-known model to show the probability of failure of an asset throughout its life is called bathtub curve. This curve is made of three main stages: infant failure, constant failure, and wear out failure. In infrastructure asset management the dominant mode of deterioration is because of aging, traffic, and climatic attribute.
However, this is only valid if the failure rate () is actually constant over time, such as within the flat region of the bathtub curve. In many cases where MTBF is quoted, it refers only to this region; thus it cannot be used to give an accurate calculation of the average lifetime of a system, as it ignores the "burn-in" and "wear-out" regions.
An example is the bathtub curve hazard function, which is large for small values of , decreasing to some minimum, and thereafter increasing again; this can model the property of some mechanical systems to either fail soon after operation, or much later, as the system ages.
Examples are maximum one-day rainfalls and the time a user spends on a web page. The distribution is named after Swedish mathematician Waloddi Weibull , who described it in detail in 1939, [ 1 ] [ 2 ] although it was first identified by René Maurice Fréchet and first applied by Rosin & Rammler (1933) to describe a particle size distribution .
The occurrence of infant mortality in a population can be described by the infant mortality rate (IMR), which is the number of deaths of infants under one year of age per 1,000 live births. [1] Similarly, the child mortality rate , also known as the under-five mortality rate, compares the death rate of children up to the age of five.
Each behavioural change theory or model focuses on different factors in attempting to explain behaviour change. Of the many that exist, the most prevalent are learning theories, social cognitive theory, theories of reasoned action and planned behaviour, transtheoretical model of behavior change, the health action process approach, and the BJ Fogg model of behavior change.