Running out of water is clearly not desirable. Part of managing the resource, then, is
determining the acceptable level of "excess" capacity that enables the demand to be met
at an acceptably small failure likelihood. (a) Determine the daily reliability of the
town’s supply, i.e., the likelihood of providing a sufficient quantity of water on any
given day P[ M > 0 ], and (b) discuss the potential for growth in the number of users in
light of an apparent excess capacity for the water supply (see note below).
The manager wants you to use a safety margin approach:
M = S – D
where M is the margin on any random day, S represents the daily supply, and D
represents the daily demand. All three quantities are random variables, one being a
function of the other two. Margins greater than zero mean that the supply is greater than
the demand and there is enough water.
The manager understands that the number of people in town on any given day fluctuates
what with travelers, births, deaths, etc. For an initial estimate of the total demands, the
manager wants you to assume that the number of users is 100,000; they further want you
to continue to use per capita water usage values of a mean of 82 gpd and a 30% c.o.v.
Include a discussion of why the manager now suggests that you model the total demand
D as normally distributed regardless of the underlying model for per capita usage.
The hydrologists and water resource engineers estimate that the town’s system is capable
of providing water for culinary use on average 8.35 million gallons per day (MGD) with
a coefficient of variation of 0.005. Assume independence between the supply and
demand and that there are no seasonal fluctuations in the population measures.
For the last directive, consider:
 Based only on averages, how many additional users to the system could be added
for the current capacity and supply? If the capacity instead were 8.5 MGD, how
many theoretical additional users could there be?
 If the daily reliability is 99.98% now, why is it not 100% given what you just
calculated based on averages?
 What does a daily reliability of 99.98% imply about reliability on an annual
basis? 10 year basis? 20 year basis?
 Typically, we find that the variance is what drives these types of analyses. In
what ways is that true here? In what ways not?
 What about the system as is suggests that it already is at its threshold of
acceptable performance (reliability)?