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Generalized Weibull DistributionsDiscrete Weibull Distributions and Their Generalizations

Generalized Weibull Distributions: Discrete Weibull Distributions and Their Generalizations [In lifetime modeling, it is common to treat failure data as being continuous, implying some degree of precision in measurement. Too often in practice, however, failures are either noted at regular inspection intervals, occur in a discrete process or are simply recorded in bins. In life testing experiments, it is sometimes impossible or inconvenient to measure the life length of a device, on a continuous scale. For example, in the case of an on/off- switching device, the lifetime of the switch is a discrete random variable. In many practical situations, reliability data are measured in terms of the number of runs, cycles, or shocks the device sustains before it fails. In survival analysis, we may record the number of days of survival for lung cancer patients since therapy, or the times from remission to relapse are also usually recorded in number of days. In this context, the geometric and negative binomial distributions are known discrete alternatives for the exponential and gamma distributions, respectively. It is well known that these discrete distributions have monotonic hazard rate functions and thus they are unsuitable for some situations.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Generalized Weibull DistributionsDiscrete Weibull Distributions and Their Generalizations

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/lp/springer-journals/generalized-weibull-distributions-discrete-weibull-distributions-and-CXZ09OZkK4
Publisher
Springer Berlin Heidelberg
Copyright
© The Author(s) 2014
ISBN
978-3-642-39105-7
Pages
97 –113
DOI
10.1007/978-3-642-39106-4_4
Publisher site
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Abstract

[In lifetime modeling, it is common to treat failure data as being continuous, implying some degree of precision in measurement. Too often in practice, however, failures are either noted at regular inspection intervals, occur in a discrete process or are simply recorded in bins. In life testing experiments, it is sometimes impossible or inconvenient to measure the life length of a device, on a continuous scale. For example, in the case of an on/off- switching device, the lifetime of the switch is a discrete random variable. In many practical situations, reliability data are measured in terms of the number of runs, cycles, or shocks the device sustains before it fails. In survival analysis, we may record the number of days of survival for lung cancer patients since therapy, or the times from remission to relapse are also usually recorded in number of days. In this context, the geometric and negative binomial distributions are known discrete alternatives for the exponential and gamma distributions, respectively. It is well known that these discrete distributions have monotonic hazard rate functions and thus they are unsuitable for some situations.]

Published: Oct 16, 2013

Keywords: Hazard Rate; Survival Function; Weibull Distribution; Discrete Version; Weibull Model

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