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| === Characteristics ===
| | #REDIRECT [[Distributions_Used_in_Accelerated_Testing#Characteristics_of_the_Exponential_Distribution]] |
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| The characteristics of the 1-parameter exponential distribution can be exemplified by examining its parameter, lambda (<span class="texhtml">λ<span style="font-family: sans-serif;">)</span></span> and the effect lambda has on the <span class="texhtml">''p''''d''''f''</span>, reliability and failure rate functions.<br>
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| ==== Effects of <span class="texhtml">λ</span> on the ''pdf'' ====
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| <br>
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| [[Image:ALTA4pdf.gif|thumb|center|400px]] <br> | |
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| :*The scale parameter is <math>\tfrac{1}{\lambda }</math> .
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| :*As <span class="texhtml">λ</span> is decreased in value, the distribution is stretched out to the right, and as <span class="texhtml">λ</span> is increased, the distribution is pushed toward the origin.
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| :*This distribution has no shape parameter, as it has only one shape (i.e., the exponential). Its only parameter is the failure rate, <span class="texhtml">λ</span> .
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| :*The distribution starts at <span class="texhtml">''T'' = 0</span> at the level of <span class="texhtml">''f''(''T'' = 0) = λ</span>, and it decreases thereafter exponentially and monotonically as <span class="texhtml">''T''</span> increases. The distribution is convex.
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| :*As <math>T\to \infty </math> , <math>f(T)\to 0</math>.
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| :*This ''pdf'' can be thought of as a special case of the Weibull<span class="texhtml"</span> ''pdf'' with <span class="texhtml">β = 1</span>.
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| <br> [[Image:ALTA4reliabilityvstimeplot.gif|thumb|center|400px]] <br>
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| ==== Effects of <span class="texhtml">λ</span> on the Reliability Function ====
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| :*The 1-parameter exponential reliability function starts at the value of 1 at <span class="texhtml">''T'' = 0</span> . It decreases thereafter monotonically and is convex.
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| :*As <math>T\to \infty </math> , <math>R(T\to \infty )\to 0</math>.
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| ==== Effects of <span class="texhtml">λ</span> on the Failure Rate Function ====
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| The failure rate function for the exponential distribution is constant and it is equal to the parameter <span class="texhtml">λ</span> .
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| <br> [[Image:ALTA4FRvsTP.gif|thumb|center|400px]] <br>
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