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The Weibull modulus is a dimensionless parameter of the Weibull distribution. ... which can be intrinsic or extrinsic in origin, arising from factors such as cavity ...
The Weibull distribution (usually sufficient in reliability engineering) is a special case of the three parameter exponentiated Weibull distribution where the additional exponent equals 1. The exponentiated Weibull distribution accommodates unimodal, bathtub shaped [33] and monotone failure rates.
A fundamental derivation of Eq. 5 for a general structural geometry has been given by applying dimensional analysis and asymptotic matching to the limit case of energy release when the initial macro-crack length tends to zero. For general structures, the following effective size may be substituted in Eq. (5):
The Kaniadakis κ-Weibull distribution is exhibits power-law right tails, and it has the following probability density function: [3] = + ()valid for , where | | < is the entropic index associated with the Kaniadakis entropy, > is the scale parameter, and > is the shape parameter or Weibull modulus.
They showed that the exponentiated Weibull distribution has increasing, decreasing, bathtub, and unimodal hazard rates. The exponentiated exponential distribution proposed by Gupta and Kundu (1999, 2001) is a special case of the exponentiated Weibull family.
The yield stress of a material is often only known to a certain precision, meaning that there is an uncertainty and therefore a probability distribution associated with the known value. [ 6 ] [ 8 ] Let the probability distribution function of the yield strength be given as f ( R ) {\displaystyle f(R)} .
The Discrete Weibull Distribution, first introduced by Toshio Nakagawa and Shunji Osaki, is a discrete analog of the continuous Weibull distribution, predominantly used in reliability engineering. It is particularly applicable for modeling failure data measured in discrete units like cycles or shocks.
The folded normal distribution is a probability distribution related to the normal distribution.Given a normally distributed random variable X with mean μ and variance σ 2, the random variable Y = |X| has a folded normal distribution.