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| ===The Exponential Reliability Function===
| | #REDIRECT [[The_Exponential_Distribution#The_Exponential_Reliability_Function]] |
| The equation for the two-parameter exponential cumulative density function, or <math>cdf,</math> is given by:
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| ::<math>F(t)=Q(t)=1-{{e}^{-\lambda (t-\gamma )}}</math>
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| Recalling that the reliability function of a distribution is simply one minus the <math>cdf</math>, the reliability function of the two-parameter exponential distribution is given by:
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| ::<math>R(t)=1-Q(t)=1-\int_{0}^{t-\gamma }f(x)dx</math>
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| ::<math>R(t)=1-\int_{0}^{t-\gamma }\lambda {{e}^{-\lambda x}}dx={{e}^{-\lambda (t-\gamma )}}</math>
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