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The hazard ratio is the effect on this hazard rate of a difference, such as group membership (for example, treatment or control, male or female), as estimated by regression models that treat the logarithm of the HR as a function of a baseline hazard () and a linear combination of explanatory variables:
In fact, the hazard rate is usually more informative about the underlying mechanism of failure than the other representations of a lifetime distribution. The hazard function must be non-negative, λ ( t ) ≥ 0 {\displaystyle \lambda (t)\geq 0} , and its integral over [ 0 , ∞ ] {\displaystyle [0,\infty ]} must be infinite, but is not ...
A concept closely-related but different [2] to instantaneous failure rate () is the hazard rate (or hazard function), (). In the many-system case, this is defined as the proportional failure rate of the systems still functioning at time t {\displaystyle t} (as opposed to f ( t ) {\displaystyle f(t)} , which is the expressed as a proportion of ...
The hazard rate at time is the probability per short time dt that an event will occur between and + given that up to time no event has occurred yet. For example, taking a drug may halve one's hazard rate for a stroke occurring, or, changing the material from which a manufactured component is constructed, may double its hazard rate for failure.
In survival analysis, hazard rate models are widely used to model duration data in a wide range of disciplines, from bio-statistics to economics. [1]Grouped duration data are widespread in many applications.
The 'bathtub curve' hazard function (blue, upper solid line) is a combination of a decreasing hazard of early failure (red dotted line) and an increasing hazard of wear-out failure (yellow dotted line), plus some constant hazard of random failure (green, lower solid line). The bathtub curve is a particular shape of a failure rate graph.
The "survival" of an engineering component or system is synonymous with the more commonly used term "reliability". The term "hazard rate" or "conditional failure rate" (defined as probability of survival per unit time assuming survival up to that time) is an important measure of the change in the rate of failure over time.
This page was last edited on 27 September 2019, at 07:13 (UTC).; Text is available under the Creative Commons Attribution-ShareAlike 4.0 License; additional terms may apply.