Discussion
Consider a series system with 3 components. Suppose the component lifetimes are independent but with failure rates \(\lambda_{1}\), \(\lambda_{2}\) and \(\lambda_{3}\). Then the failure rate of the system lifetime :
Answer: D
The failure rate of the series system is \(\lambda_{1} + \lambda_{2} + \lambda_{3}\).
A series system works only while every component works, so its reliability is the product of the component reliabilities. With independent components,
\[ \begin{aligned} R(t) &= R_{1}(t)R_{2}(t)R_{3}(t) \\ h(t) &= -\frac{d}{dt}\ln R(t) = h_{1}(t) + h_{2}(t) + h_{3}(t) \end{aligned} \]
so failure rates add. For constant rates the system lifetime is exponential with rate \(\lambda_{1} + \lambda_{2} + \lambda_{3}\).
The product of the rates has the wrong units, the minimum would describe the most reliable component alone, and the information given is enough.
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