Six Sigma and Beyond: Design for Six Sigma, Volume VI

Certainly we can use DOE in passive observation of the covariates in the tested components . We can also use DOE in directed experimentation as part of our reliability improvement. Covariates are usually called factors in the experimentation framework. Two main technical problems arise in the reliability area, however, when standard methods of experimental design are employed.

1. Failure time data are rarely normally distributed, so standard analysis tools that rely on symmetry, e.g., normal plots, do not work too well.

2. Censoring.

The first problem can be overcome by considering a transformation of the fail times to make them approximately normal ” the log transformation is usually a good choice. The exact form of the fail time distribution is not important because we are looking for effects that improve reliability, rather than exact predictions of the reliability itself.

The second problem of censoring is a little bit trickier but can be dealt with by iteration as follows :

1. Choose a basic model to fit to the data.

2. Fit the model to the data, treating the censor times as failure times.

3. Using this model, make a conditional prediction for the unobserved fail times for each censored observation. The prediction is conditional because the actual failure time must be consistent with the censoring mechanism.

4. Replace censor times with the fail time predictions from step 3.

5. Go back to step 2.

Eventually this process will converge, i.e., the predictions for the fail times of the censorings will stop changing from one iteration to the next . If necessary, the process can be tried with several model choices for step 1. In fact, the algorithm of the five steps leads to the same results as maximum likelihood estimation.