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The reliability of a product/component constitutes an important aspect of product quality. Of particular interest is the quantification of product reliability, so that one can derive estimates of the product expected useful life. Knowing the probability of product/ component failures at different stages of its life can be very useful to make a decision about when to replace or overhaul the component.
A useful general distribution for describing failure time data is the Weibull distribution named after the Swedish professor Waloddi Weibull (1887-1979), who demonstrated the appropriateness of this distribution for modeling a wide variety of different data sets.
It is often meaningful to consider the function that describes the probability of failure during a very small time increment (assuming that no failures have occurred prior to that time). This function is called the hazard function (or, sometimes, also the conditional failure, intensity, or force of mortality function), and is generally defined as:
h(t) = f(t)/(1-F(t))
where h(t) stands for the hazard function (of time t), and f(t) and F(t) are the probability density and cumulative distribution functions, respectively. The hazard (conditional failure) function for most components or devices can best be described in terms of the "bathtub" curve: Very early during the life of a device, the rate of failure is relatively high (so-called Infant Mortality Failures); after all components settle, and the electronic parts are burned in, the failure rate is relatively constant and low. Then, after some time of operation, the failure rate again begins to increase (Wear-out Failures), until all components or devices will have failed.
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