Reliasoft Weibull Crack
- In other words, the Weibull routine reveals, rather than masks, the correct shape of the data's density curve. For example, a Weibull shape factor of 1.0 represents an exponential distribution. A shape factor of 2.0 is a Raleigh distribution, while a Weibull shape factor of about 3.0 or above represents an approximately normal distribution.
- ReliaSoft's ALTA PRO employs a physics of failure approach and can be used to analyze test data for single or multiple stress conditions. (Weibull distribution), mean (exponential distribution) or median (lognormal distribution). 40 electronic components were tested to failure due to crack growth in solder joints as a result of repeated.
- The ReliaSoft Weibull fit crosses the x-axis at a nonzero energy value (i.e., γ 0). Based on the analysis, the scale parameter, η, equals 22.6. Φ (E ˆ) equals 10% when E ˆ = 1.97. The goodness of Weibull fit equals 0.97, suggesting a very good fit despite the fact that the failure records cluster early in time.
ReliaSoft's Weibull software tool is the industry standard in life data analysis (Weibull analysis) for thousands of companies worldwide. The software performs life data analysis utilizing multiple lifetime distributions (including all forms of the Weibull distribution), with a clear and concise interface geared toward reliability engineering.
The Weibull is a very flexible life distribution model with two parameters.It has CDF and PDF and other key formulas given by:$$ begin{array}{ll}mbox{PDF:} & f(t, gamma, alpha) = frac{gamma}{t} left( frac{t}{alpha} right)^gamma e^{- left( frac{t}{alpha} right)^gamma} & mbox{CDF:} & F(t) = 1-e^{- left( frac{t}{alpha} right)^gamma} & mbox{Reliability:} & R(t) = e^{- left( frac{t}{alpha} right)^gamma} & mbox{Failure Rate:} & h(t) = frac{gamma}{alpha} left( frac{t}{alpha} right) ^{gamma-1} & mbox{Mean:} & alpha Gamma left(1+frac{1}{gamma} right) & mbox{Median:} & alpha (mbox{ln} , 2)^{frac{1}{gamma}} & mbox{Variance:} & alpha^2 Gamma left( 1+frac{2}{gamma} right) - left[ alpha Gamma left( 1 + frac{1}{gamma}right) right]^2 end{array} $$
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).
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. Usb write protection removal tool free download. Some authors even parameterize the density function differently, using a scale parameter (theta = alpha^gamma).
Special Case: When (gamma) = 1,the Weibull reduces to the Exponential Model, with (alpha = 1/lambda)= the mean time to fail (MTTF).
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.
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