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The Weibull is a very flexible life distribution model with two parameters.It has CDF and PDF and other key formulas given by:$$ begin{array}{ll}mbox{PDF:} & f(t, gamma, alpha) = frac{gamma}{t} left( frac{t}{alpha} right)^gamma e^{- left( frac{t}{alpha} right)^gamma} & mbox{CDF:} & F(t) = 1-e^{- left( frac{t}{alpha} right)^gamma} & mbox{Reliability:} & R(t) = e^{- left( frac{t}{alpha} right)^gamma} & mbox{Failure Rate:} & h(t) = frac{gamma}{alpha} left( frac{t}{alpha} right) ^{gamma-1} & mbox{Mean:} & alpha Gamma left(1+frac{1}{gamma} right) & mbox{Median:} & alpha (mbox{ln} , 2)^{frac{1}{gamma}} & mbox{Variance:} & alpha^2 Gamma left( 1+frac{2}{gamma} right) - left[ alpha Gamma left( 1 + frac{1}{gamma}right) right]^2 end{array} $$
Free reliasoft weibull 7 download. Education software downloads - ReliaSoft DOE by ReliaSoft Corporation and many more programs are available for instant and free download. Failure is defined as a crack of length 30 mm or greater. Using Weibull Degradation Analysis folio and Quick Calculation Pad (QCP), determine the B10 life for the blades using degradation analysis with an exponential model for the extrapolation. ReliaSoft Weibull is a comprehensive life data analysis tool that performs life data analysis utilizing multiple lifetime distributions, warranty and degradation data analysis, design of experiment and more with a clear and intuitive interface geared toward reliability engineering.
with (alpha)the scale parameter (the Characteristic Life), (gamma)(gamma) the Shape Parameter, and (Gamma)is the Gamma function with (Gamma(N) = (N-1)!)for integer (N).
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The cumulative hazard function for the Weibull is the integral of the failurerate or $$ H(t) = left( frac{t}{alpha} right)^gamma , . $$
A more general three-parameter form of the Weibull includes an additionalwaiting time parameter (mu)(sometimes called a shift or location parameter). The formulas for the 3-parameterWeibull are easily obtained from the above formulas by replacing (t) by ((t-mu))wherever (t)appears. No failure can occur before (mu)hours,so the time scale starts at (mu),and not 0. If a shift parameter (mu)is known (based, perhaps, on the physics of the failure mode), then all you have to do is subtract (mu)from all the observed failure times and/or readout times and analyze the resulting shifted data with a two-parameter Weibull.
NOTE: Various texts and articles in the literature use a varietyof different symbols for the same Weibull parameters. For example, thecharacteristic life is sometimes called (c) ((nu) = nu or (eta) = eta)and the shape parameter is also called (m) (or (beta) = beta).To add to the confusion, some software uses (beta)as the characteristic life parameter and (alpha)as the shape parameter. Some authors even parameterize the density function differently, using a scale parameter (theta = alpha^gamma).
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Special Case: When (gamma) = 1,the Weibull reduces to the Exponential Model, with (alpha = 1/lambda)= the mean time to fail (MTTF).
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Depending on the value of the shape parameter (gamma),the Weibull model can empirically fit a wide range of data histogramshapes. This is shown by the PDF example curves below.