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| ====Bounds on Time====
| | #REDIRECT [[The Exponential Distribution]] |
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| The bounds around time for a given exponential percentile, or reliability value, are estimated by first solving the reliability equation with respect to time, or reliable life: | |
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| ::<math>\hat{t}=-\frac{1}{{\hat{\lambda }}}\cdot \ln (R)+\hat{\gamma }</math>
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| The corresponding confidence bounds are estimated from:
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| ::<math>\begin{align}
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| & {{t}_{U}}= & -\frac{1}{{{\lambda }_{L}}}\cdot \ln (R)+\hat{\gamma } \\
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| & {{t}_{L}}= & -\frac{1}{{{\lambda }_{U}}}\cdot \ln (R)+\hat{\gamma }
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| \end{align}</math>
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| The same equations apply for the one-parameter exponential with <math>\gamma =0.</math>
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