Gamma Distribution Example

From ReliaWiki
Jump to navigation Jump to search
Weibull Examples Banner.png


This example appears in the Life Data Analysis Reference book.

24 units were reliability tested, and the following life test data were obtained:

[math]\begin{matrix} \text{61} & \text{50} & \text{67} & \text{49} & \text{53} & \text{62} \\ \text{53} & \text{61} & \text{43} & \text{65} & \text{53} & \text{56} \\ \text{62} & \text{56} & \text{58} & \text{55} & \text{58} & \text{48} \\ \text{66} & \text{44} & \text{48} & \text{58} & \text{43} & \text{40} \\ \end{matrix}\,\![/math]

Fitting the gamma distribution to this data, using maximum likelihood as the analysis method, gives the following parameters:

[math]\begin{align} & \hat{\mu }= 7.72E-02 \\ & \hat{k}= 50.4908 \end{align}\,\![/math]

Using rank regression on [math]X,\,\![/math] the estimated parameters are:

[math]\begin{align} & \hat{\mu }= 0.2915 \\ & \hat{k}= 41.1726 \end{align}\,\![/math]

Using rank regression on [math]Y,\,\![/math] the estimated parameters are:

[math]\begin{align} & \hat{\mu }= 0.2915 \\ & \hat{k}= 41.1726 \end{align}\,\![/math]