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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.
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.
Replacing the weak components would prevent premature failure, infant mortality failure, or other latent defects. When the equivalent lifetime of the stress is extended into the increasing part of the bathtub-like failure-rate curve, the effect of the burn-in is a reduction of product lifetime. In a mature production it is not easy to determine ...
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.
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.
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]
This happens if there is significant "infant mortality", or defective items failing early and the failure rate decreasing over time as the defective items are weeded out of the population. In the context of the diffusion of innovations , this means negative word of mouth: the hazard function is a monotonically decreasing function of the ...