5 Conclusion

To summarize in few words, $\mathrm{M}_{r}$ is the key object, $\widehat{\mathrm{M}_{r}}$ is a computing trick and $\mathrm{M}_{a}$ is nothing. That fact is especially apparent when using the repairman's paradigm to illustrate the importance sampling method [1]. Nothing useful can be done by observing a reduced availability chain instead of the original one (for example, by reducing $M=5$ to $M=4$ as in FIG. 5). Conversely, conditioning properties that allow variance reduction are obtained when considering the repairing chains, as it appears from a comparison between FIG. 4 and FIG. 6.

FIG. 6: The M/D repairing chain, with one more machine.

The M/D repairman, provides a model easily tractable nowadays, with the growth in power of the formal computing tools and that model is especially useful to detect confusions between individual probabilities, obtained by an uniform sorting over a discrete chain, and the temporal probabilities, obtained by an uniform sorting over the continuous time.