Reliability HotWire |
||||

Reliability Basics | ||||

In order to assess
the assumption of a common shape parameter among the data obtained at
various stress levels, the likelihood ratio (LR) test can be utilized. This
test applies to any distribution with a shape parameter. In the case of
ALTA 6, it applies to the Weibull
and lognormal distributions. When Weibull is used as the underlying life
distribution, the shape parameter, β,
is assumed to be constant across different stress levels ( The likelihood ratio test is performed by
first obtaining the LR test statistic, T. If the true shape parameters are
equal, then the distribution of T is approximately chi-square with
are the likelihood values obtained by fitting
a separate distribution to the data from each of the Once the LR statistic has been calculated, then: - If T ≤
*x*^{2}(α;*n*- 1), the*n*shape parameter estimates do not differ statistically significantly at the 100α% level. - If T >
*x*^{2}(α;*n*- 1), the*n*shape parameter estimates differ statistically significantly at the 100α% level.
Consider the following times-to-failure data at three different stress levels.
The data set was analyzed using an Arrhenius-Weibull model. The results of the analysis are:
The assumption of a common β across the different stress levels can be assessed visually using a probability plot.
In the above plot, it can be seen that the plotted data from the different stress levels seem to be fairly parallel. A better assessment can be made with the LR test, which can be performed using the Likelihood Ratio Test tool in ALTA 6. For example, the βs are compared for equality at the 10% significance level, as shown next. The individual likelihood values for each of the test stresses can be found in the Results tab of the Likelihood Ratio Test window, as shown next. The LR test statistic, T, is calculated to
be 0.481. Therefore, T = 0.481 ≤ 4.605 =
| ||||

Copyright 2004 ReliaSoft Corporation, ALL RIGHTS RESERVED | ||||