View source for Template:Effect of beta on the cdf

'''The Effect of <span class="texhtml">β</span> on the <math>cdf</math> and Reliability Function'''


[[Image:lda6.2.gif|thumb|center|350px| Effect on <math>\beta</math> on the <math>cdf</math> on the Weibull probability plot with a fixed value of <math>\eta</math> ]]
 
The above Figure shows the effect of the value of <span class="texhtml">β</span> on the <math>cdf</math>, as manifested in the Weibull probability plot. It is easy to see why this parameter is sometimes referred to as the slope. Note that the models represented by the three lines all have the same value of <span class="texhtml">η</span>. The followng figure shows the effects of these varied values of <span class="texhtml">β</span> on the reliability plot, which is a linear analog of the probability plot.

[[Image:lda6.3.gif|thumb|center|350px| The effect of values of <math>\beta</math> on the Weibull reliability plot. ]]
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:*<span class="texhtml">''R''(''t'')</span> decreases sharply and monotonically for <span class="texhtml">0 &lt; β &lt; 1</span> and is convex. 
:*For <span class="texhtml">β = 1</span>, <span class="texhtml">''R''(''t'')</span> decreases monotonically but less sharply than for <span class="texhtml">0 &lt; β &lt; 1</span> and is convex. 
:*For <span class="texhtml">β &gt; 1</span>, <span class="texhtml">''R''(''t'')</span> decreases as  increases. As wear-out sets in, the curve goes through an inflection point and decreases sharply.

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