# Likelihood Ratio Test Example

### From ReliaWiki

*This example appears in the Accelerated Life Testing Data Analysis Reference book.*

Consider the following times-to-failure data at three different stress levels.

Stress | 406 K | 416 K | 426 K |
---|---|---|---|

Time Failed (hrs) | 248 | 164 | 92 |

456 | 176 | 105 | |

528 | 289 | 155 | |

731 | 319 | 184 | |

813 | 340 | 219 | |

543 | 235 |

The data set was analyzed using an Arrhenius-Weibull model. The analysis yields:

The assumption of a common across the different stress levels can be visually assessed by using a probability plot. As you can see in the following plot, 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. For example, in the following figure, the are compared for equality at the 10% level.

The LR test statistic, , is calculated to be 0.481. Therefore, the s do not differ significantly at the 10% level. The individual likelihood values for each of the test stresses are shown next.