A system consisting of n components or subsystems, of which only k need to be functioning for system success, is called a “k-out-of-n” configuration. For such a system, k is less than n. An example of such a system might be an air traffic control system with n displays of which k must operate to meet the system reliability requirement.
The binomial distribution is used for those situations in which there are only two outcomes, such as success or failure, and the probability remains the same for all trials. It is very useful in reliability and quality assurance work. The probability density function (pdf) of the binomial distribution is