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Weibull Distribution
The Weibull distribution is one of the most commonly used distributions in reliability engineering. There are two versions of this distribution: two-parameter Weibull and three-parameter Weibull distributions.
Parameters
- shape parameter
(
)
- scale parameter
()
- location parameter
(
yields the two-parameter Weibull distribution)
Domain
Probability Density Function (PDF)
Weibull Distribution Fitting
EasyFit allows to automatically or manually fit the Weibull distribution and 40 additional distributions to your data, compare the results, and select the best fitting model using the goodness of fit tests and interactive graphs.
Weibull Distribution Graphs and Properties
EasyFit displays all graphs and properties of the Weibull distribution, presenting the results in an easy to read & understand manner. EasyFit calculates statistical moments (mean, variance etc.), quantiles, tail probabilities depending on the distribution parameters you specify.
Random Numbers from the Weibull Distribution
You can easily generate random numbers from the Weibull distribution in a variety of ways:
- directly from EasyFit
- in Excel sheets using the worksheet functions provided by EasyFitXL
- in your VBA applications using the EasyFitXL library
Excel Worksheet and VBA Functions
EasyFitXL enables you to use the following functions in your Excel sheets and VBA applications:
WeibullPdf |
Probability Density Function |
WeibullCdf |
Cumulative Distribution Function |
WeibullHaz |
Hazard Function |
WeibullInv |
Inverse CDF (Quantile Function) |
WeibullRand |
Random Numbers |
WeibullMean |
Mean |
WeibullVar |
Variance |
WeibullStdev |
Standard Deviation |
Applications
The Weibull distribution is often used to model the time until a given technical device fails:
- if alpha<1, then the failure rate of the device decreases over time;
- if alpha=1, then the failure rate of the device is constant over time;
- if alpha>1, then the failure rate of the device increases over time.