
Example

Example: : The reliability of a computer is
defined as the probability of successful operation throughout
a particular mission. A study determines that the reliability
for a given mission as 0.9. Because the mission is very important
and computer failure is extremely serious, we provide five identical
computers for this mission. The computers operate independently
and the failure or success of one does not affect the probability
of failure or success of the others. Our job is to compute the
probability of mission success, or system reliability, under
the following three operating rules:
a. All five computers must work for mission success
b. At least three out of five must work for mission success
c. At least one computer must work for mission success 

The success or failure
of each computer is a Bernoulli random variable with 1 representing
success and 0 representing failure. The probability of success
is p, and we assume that the computers are independent
with respect to failure. The number of working computers, x,
is the random variable of interest, and the binomial distribution,
with parameters n = 5 and p = 0.9, is the
appropriate PDF.
The solution of the problem is computed above using functions
provided by the addin. These results show the value of redundancy
for
increasing reliability. In case a, none of the computers
is redundant since all are required for successful operation.
In case b, we say that two computers are redundant
since only three are required. In case c, all but
one are redundant. The reliability of the system
increases
as redundancy is increased 