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must be capable of achieving the goals that we set for it. These goals may include per-
formance, production, uptime, and dependability. Bottom line, we will rely on the robot
and it has to come through.
The Institute of Electrical and Electronics Engineers (IEEE) defines reliability as
“the ability of a system or component to perform its required functions under stated
conditions for a specified period of time” [IEEE 90]. Further definitions can be found
at http://athos.rutgers.edu/ rmartin/teaching/fall99/lectures/10/gfx004.html.
By observation, engineers have documented the failure rates of various component
types. Bellcore, now called Telcordia, has documented many of these failure rates and
published them at www.t-cubed.com/faq_bell.htm.

MATHEMATICS

Let’s call the failure rate of a component l, measured in failures per unit time. Loosely
speaking, if l is .001 per year, we could expect an average of one failure per year in a
population of 1,000 such components. We further define Mean Time to Failure (MTTF),
as the inverse of l. It represents the average amount of time a single component is likely
to last before it fails the first time.
MTTF 1>l

We adopt MTTF as a convenient way of measuring and doing calculations about reli-
ability. However, some limitations exist, as explained at www.reliasoft.com/newsletter/
2Q2000/mttf.htm.
Once we accept MTTF and l as viable metrics, they can be used in calculations in
the following ways:
Clearly, the reliability of a component can be defined from either MTTF or l,
since they are the computational inverse of one another.
If a system has multiple components, then l of the combined population is the
sum of the individual ls. lpop l1 l2 l3 ... ln. Effectively, the fail-
ure rates add up. If the components are all on a printed circuit board (PCB), for
instance, then the failure rate of the PCB is the sum of all the failure rates of the
individual components. Clearly, the PCB will be less reliable than any one com-
ponent, and since the least reliable components have the highest l values, they
may well determine the overall reliability of the PCB.
Note that a combined population of even the most reliable components may not be
reliable. The chance of having one failure in the population may be high if many
individual components exist, even if they all have a low failure rate. Said another
way, since lpop n l, if n is large, lpop may be large even if l is small.