1P-Exponential Data Analysis with No Failures

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1P-Exponential Data Analysis with No Failures

This example validates the calculations for the case when no failures are observed.


Reference Case

The formulas on page 168 in the book Statistical Methods for Reliability Data by Dr. Meeker and Dr. Escobar, John Wiley & Sons, 1998.


[math]\theta = \frac{2TTT}{x^{2}_{(1-\alpha; 2)}}\,\![/math]


where TTT is the total test time and [math]x^{2}_{(1-\alpha; 2)}\,\![/math] is the [math]1 - \alpha \,\![/math] percentile of a chi-squared distribution with degree of freedom of 2. [math]1 - \alpha \,\![/math] is also the confidence level. The equation above gives the lower 1-sided confidence bound for [math]\theta \,\![/math].


Data

A total of 70 fans are tested for 200 hours and no failure is observed.


Result


[math]\theta = \frac{2TTT}{X^{2}_{1-\alpha; 2}} = \frac{28000}{5.99146} = 4673.31\,\![/math]


Results in Weibull++


1PE no failures.png