Discussion
Suppose that in a K-unit parallel system each unit has life time distribution with distribution function F. Then reliability function of the system at time \(t\) is given by :
Answer: C
The reliability is \(1 - (F(t))^{K}\).
A parallel system works as long as at least one unit works, so it fails only when all K units have failed by time \(t\). With independent units each failing by \(t\) with probability \(F(t)\), that probability is \(F(t)^{K}\), and the reliability is its complement.
\((1 - F(t))^{K}\) is the reliability of a series system, which needs every unit to survive. \(F(t)^{K}\) is the failure probability of the parallel system, and \(1 - (1 - F(t))^{K}\) is the failure probability of the series system.
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