Template:Alta weibull distribution: Difference between revisions

Latest revision as of 01:42, 16 August 2012

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-== The Weibull Distribution  ==
+#REDIRECT [[Distributions_Used_in_Accelerated_Testing#The_Weibull_Distribution]]
-The Weibull distribution is one of the most commonly used distributions in reliability engineering because of the many shapes it attains for various values of <span class="texhtml">β</span> (slope). It can therefore model a great variety of data and life characteristics [[Reference Appendix D: References|[18]]].
-The 2-parameter Weibull ''pdf'' is given by:
-<br>
-::<math>f(T)=\frac{\beta }{\eta }{{\left( \frac{T}{\eta } \right)}^{\beta -1}}{{e}^{-{{\left( \tfrac{T}{\eta } \right)}^{\beta }}}}</math>
-<br>
-where:
-<br>
-::<math>f(T)\ge 0,\text{ }T\ge 0,\text{ }\beta >0,\text{ }\eta >0\text{ }</math>
-<br> and:
-<br>
-:*<span class="texhtml">η = </span> scale parameter.
-:*<span class="texhtml">β = </span> shape parameter (or slope).
-<br> {{aw statistical properties summary}}
-{{aw characteristics}}
-=== Parameter Estimation  ===
-The estimates of the parameters of the Weibull distribution can be found graphically on probability plotting paper, or analytically using either least squares or maximum likelihood. (Parameter estimation methods are presented in detail in [[Appendix B: Parameter Estimation|Appendix B]].) <br> {{aw probability plotting}}
-{{mle alta for ed}}