Part CCSIR NET June 2025parallel-is-the-maximum-so-the-failure-probabilities-multiply-not-the-survivals

Parallel is the maximum so the failure probabilities multiply not the survivals

A system has two components $C_{1}$ and $C_{2}$ put in parallel. The components $C_{1}$ and $C_{2}$ have independent lifetimes $X_{1}$ and $X_{2}$ , respectively. The probability distribution of X_j is exponential with mean 1/j, j = 1, 2. Suppose that R(t) and h(t) are the reliability and the hazard rate functions of the system, respectively. Then, which of the following statements are true?

A.R(t) = $e^{- 2 t}$ + $e^{- t}$ − $e^{- 3 t}$ , t > 0✓
B.The expected lifetime of the given system is 1
C. $h (1) = (2 e + e^{2} - 3) / (e + e^{2} - 1)$ ✓
D. $h (3) = (4 e^{3} + e^{6} - 5) / (e^{3} + e^{6} - 1)$

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests execution slip.

See pricing

50 are analysed free — try those first.

The trap it tests

Execution slip

The idea was right. The computation was not.

Drill statements like this

Related counterexample: The maximum of independent exponentials is exponential

Parallel is the maximum so the failure probabilities multiply not the survivals

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