Windchill Risk and Reliability Desktop Help > Windchill ALT > ALT Analysis > ALT Data Set How-Tos > Running a Likelihood Ratio Test
Running a Likelihood Ratio Test
ALT analysis assumes that the scale parameter of a life distribution is dependent on stress levels and that the shape parameter is independent of them. In the Likelihood Ratio Test window, you use the likelihood ratio test to assess whether the shape parameter of the Weibull or lognormal distribution is constant across stress levels.
1. Ensure that either the Weibull or lognormal distribution is selected for the data set and that it is calculated.
2. Select ALT > Likelihood Ratio Test. The Likelihood Ratio Test window opens.
The following table describes all options in the Likelihood Ratio Test window.
Option
Description
Significance level
The statistical criterion used for rejecting the null hypothesis, which is the assumption of a common shape parameter for all stress levels. The significance level of the likelihood ratio test indicates that the probability of mistakenly rejecting the null hypothesis can be no greater than the value entered here.
[Shape parameter]
The shape parameter for the distribution, which is read-only and from the calculation results.
• When Weibull is the distribution, β (Beta) is the shape parameter.
• When Lognormal is the distribution, σ (Sigma) is the shape parameter.
Results
The next three options are display-only results. They are computed when you click Calculate.
T
The test statistic of the likelihood ratio test. If the shape parameters at different stress levels are equal, T approximately follows the Chi-Square distribution with j − 1 degrees of freedom.
alpha
Alpha (α) is the significance of the likelihood ratio test.
Chi-Square (alpha, j-1)
The 100α percentile of the Chi-Square distribution with j - 1 degrees of freedom.
L0
The likelihood value obtained by fitting the life stress model with the shape parameter.
Stress results
The table under this heading has a row for each stress level for the data set. Once you click Calculate, it shows display-only results for likelihood values. These values are obtained by fitting a separate distribution to the data corresponding to each of the stress levels with two or more exact failure points. The failure distribution obtained for each stress level produces a separate scale parameter for each stress level but not a common shape parameter.
Stress Level
The stress level for the data set.
Likelihood Value
The likelihood value calculated for the stress level.
3. In the first field, enter the significance level and then click Calculate.
Below Stress results, a display-only table shows the likelihood values calculated for each stress level.
4. When finished, click Close.