8. Assessing Product Reliability
8.4. Reliability Data Analysis

## How do you compare reliability between two or more populations?

Several methods for comparing reliability between populations are described

Comparing reliability among populations based on samples of failure data usually means asking whether the samples came from populations with the same reliability function (or CDF). Three techniques already described can be used to answer this question for censored reliability data. These are:

Comparing Sample Proportion Failures

Assume each sample is a random sample from possibly a different lot, vendor or production plant. All the samples are tested under the same conditions. Each has an observed proportion of failures on test. Call these sample proportions of failures $$p_1, \, p_2, \, p_3, \, \ldots, \, p_n$$. Could these all have come from equivalent populations?

This is a question covered in Chapter 7 for two populations, and for more than two populations, and the techniques described there apply equally well here.

Likelihood Ratio Test Comparisons

The Likelihood Ratio test was described earlier. In this application, the Likelihood ratio $$\lambda$$ has as a denominator the product of all the Likelihoods of all the samples assuming each population has its own unique set of parameters. The numerator is the product of the Likelihoods assuming the parameters are exactly the same for each population. The test looks at whether $$-2\mbox{ ln } \lambda$$ is unusually large, in which case it is unlikely the populations have the same parameters (or reliability functions).

This procedure is very effective if, and only if, it is built into the analysis software package being used and this software covers the models and situations of interest to the analyst.