Mechanical Components Example

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A mechanical component was put into an accelerated life test with temperature as the stress type. The objective is to fit the Arrhenius-Weibull relationship model to the observed data and analyze the result of the test. The following times-to-failure data were observed.


343 K 363 K 383 K
266.66 618.54 351.12
430.09 666.72 355.1
570.45 724.4 672.69
890.42 950.89 923.35
1046.65 1148.4 948.22
1158.14 1202.94 1277.04
1396.01 1492.56 1538.81
1918.38 1619.59 2020.34
2028.86 2592.29 2099.03
2785.58 3596.85 2173.04


The parameters of the Arrhenius Weibull model were estimated using the ALTA standard folio. The results are:


[math]\displaystyle{ \begin{align} \beta =1.771460,\text{ }B=86.183591,\text{ }C=1170.423770. \end{align} }[/math]


The estimate shows a small value for [math]\displaystyle{ \beta }[/math]. The following observations can then be made:

  • Life is not accelerated with temperature, or
  • The stress increments were not sufficient, or
  • The stress values used in the test were well within the "specification limits" for the product (see discussion here).


The value of [math]\displaystyle{ \beta }[/math] is not the only indicator for the observed behavior. As you can see from the data that was obtained from the test, the times-to-failure at all three stress levels fall within the same ranges. Another way to observe this is by looking at the Arrhenius plot. The following plot shows the scale parameter, [math]\displaystyle{ \eta }[/math], and the mean life. As you can see, the life ( [math]\displaystyle{ \eta }[/math] and the mean life) are almost invariant with stress.

Eta and Mean Life vs. Stress.