Weibull++ Standard Folio Data 1P-Weibull
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One-Parameter Weibull Like the exponential distribution, one-parameter Weibull distribution is a one-parameter model. However, the advantage of the one-parameter Weibull distribution is its ability to model products with increasing failure rate, constant failure rate and decreasing failure rate. This distribution is based on the common Weibull distribution, but assumes that the shape parameter, β, is a known value. This distribution is sometimes known as the "WeiBayes" distribution. The advantage of this distribution over the common two-parameter Weibull is that it is more robust to small sample sizes and uncertainties in fitting the parameter because it only needs to estimate one parameter, η, rather than two. The price that you pay with this approach is that you need to be able to assume a value of β. This could be based on prior comparable tests, observation and engineering knowledge. Note that the word "comparable" is key here. You cannot use a prior β if the data set you are analyzing comes from units of drastically different designs or units that fail due to different failure modes.
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