8. Assessing Product Reliability
8.2. Assumptions/Prerequisites
8.2.3. How can you test reliability model assumptions?

8.2.3.2.

Goodness of fit tests

A Goodness of Fit test checks on whether your data are reasonable or highly unlikely, given an assumed distribution model

General tests for checking the hypothesis that your data are consistent with a particular model are discussed in Chapter 7. Details and examples of the Chi-Square Goodness of Fit test and the Kolmolgorov-Smirnov (K-S) test are given in Chapter 1. The Chi-Square test can be used with Type I or Type II censored data and readout data if there are enough failures and readout times. The K-S test generally requires complete samples, which limits its usefulness in reliability analysis. 

These tests control the probability of rejecting a valid model as follows: 

• the analyst chooses a confidence level designated by \(100(1-\alpha\)).
• a test statistic is calculated from the data and compared to likely values for this statistic, assuming the model is correct. 
• if the test statistic has a very unlikely value, or less than or equal to an \(\alpha\) probability of occurring, where \(\alpha\) is a small value like 0.1 or 0.05 or even 0.01, then the model is rejected.

So the risk of rejecting the right model is kept to \(\alpha\) or less, and the choice of \(\alpha\) usually takes into account the potential loss or difficulties incurred if the model is rejected.