111: Terminating Abstract Rewriting Systems

A terminating abstract rewriting system is one in which, given any starting element or term, there is no infinite sequence of rewritings which can be done on that starting element. That is, any sequence of rewritings on an element will eventually end in a ‘final’ rewritten form. Terminating ARSs are a subset of normal ARSs.

59: Bathtub Curve

In reliability engineering, a bathtub curve is a particular form (shape) which the hazard function of a system can take. Its namesake is the cross-section of the typical bathtub: relatively steep slopes on either side with a relatively flat section in between. This corresponds to:

1. a decreasing failure rate at the beginning of the expected life of the system (due to ‘infant mortality’ or ‘early failures’), followed by
2. a relatively constant failure rate in the middle of the expected life of the system, followed by
3. an increasing failure rate towards the end of the expected life of the system (due to ‘wear-out’ failures).