Mechanical Components Example

Mechanical Components Example
A mechanical component was put into an accelerated test with temperature as the accelerated stress. The following times-to-failure were observed.

1) Determine the parameters of the Arrhenius-Weibull model.

2) What is your observation?

Solution
The parameters of the Arrhenius Weibull model were estimated using ALTA with the following results:


 * $$\begin{align}

\beta =1.771460,\text{ }B=86.183591,\text{  }C=1170.423770. \end{align}$$

A small value for $$B$$  was estimated. The following observations can then be made:


 * Life is not accelerated with temperature, or


 * the stress increments were not sufficient, or


 * the test stresses were well within the "specification limits" for the product (see discussion here).

A small value for $$B$$  is not the only indication for this behavior. One can also observe from the data that at all three stress levels, the times-to-failure are within the same range. Another way to observe this is by looking at the Arrhenius plot. The scale parameter, $$\eta $$, and the mean life are plotted next.

It can be seen that life ( $$\eta $$, and the mean life) is almost invariant with stress.