Page 50 - Electrical Safety of Low Voltage Systems

Mathematical Principles of Electrical Safety 33

For a practical understanding of the previous definition of risk, let
us consider the following example:
A simultaneous failure of the supports of a bridge, during rush
hour, can cause significant damage to persons (i.e., loss of human
life; v(t) is high). In addition, the probability of commuters transiting
over the bridge is high (i.e., k(t) is high). On the other hand, how-
ever, the probability that the bridge collapses should be remote (i.e.,
[1−S(t)] is very low), thanks to the redundancy in the bridge’s sup-
ports. Ergo, the resulting risk is low, although not zero, and deemed
acceptable.
To quantify the residual risk r(t) for direct contact, we can still
apply Eq. (3.5). In this case, v(t) has the same value as in indirect con-
tact because its value depends on the maximum permissible voltage,
which is common for both cases; also k(t) has equal value, as live
parts, erroneously considered harmless, have the same probability to
be touched just as an ECP.
The major difference in the two expressions of the residual risk is
the value of the insecurity [1−S(t)]: in the case of direct contact, the
probability that the part is energized equals, of course, 100%, whereas
in indirect contact such probability is much lower because of the pro-
tective measures. As a result, in correspondence of the very same
maximum permissible voltage, the residual risk for direct contact is
greater than the residual risk for indirect contact.

3.4 The Acceptable Residual Risk
In reality, the risk against electric shock can be reduced, but not com-
pletely eliminated, if not at unsustainable expenses. For example, a
protective device can fail, but in general we do not, nor are we re-
quired to, install multiple identical devices in series as a redundant
4
protection because this practice would be cost-prohibitive. Thus, the
residual risk must be “acceptable” with regard to electric shocks as a
compromise between achievable safety and its cost. What is the ac-
ceptable risk then?
The residual risk is deemed acceptable after the application of
standard protective measures, if its probabilistic value calculated in
Eq. (3.5) falls below an arbitrary threshold as basically established by:

Up-to-date applicable technical standards and codes, indicat-

ing minimum safety requirements
Authorities Having Jurisdiction’s dictates, which may provide

technical and “legal” interpretation of the aforementioned
minimum safety requirements
Economic resources available to increase safety beyond the

minimum aforementioned requirements