Question:
There are a number of identical components in a parallel system. When the system reliability is 0.97 and the reliability of each individual component is 0.68, the number of identical components in the system is (if actual value is a fraction, it may be rounded up to the next higher integer).
There are a number of identical components in a parallel system. When the system reliability is 0.97 and the reliability of each individual component is 0.68, the number of identical components in the system is (if actual value is a fraction, it may be rounded up to the next higher integer).
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In parallel systems, the reliability increases as more components are added. Use the formula to determine the number of components required for a given system reliability.
Updated On: Dec 26, 2025
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The Correct Option is B
Solution and Explanation
For a parallel system, the reliability \( R_{\text{sys}} \) is given by:
\[
R_{\text{sys}} = 1 - \prod_{i=1}^{n} (1 - R_i)
\]
where \( R_i \) is the reliability of each individual component, and \( n \) is the number of components in parallel.
Here, \( R_{\text{sys}} = 0.97 \) and \( R_i = 0.68 \). Substituting these values:
\[
0.97 = 1 - (1 - 0.68)^n
\]
\[
0.03 = (0.32)^n
\]
Taking the natural logarithm of both sides:
\[
\ln(0.03) = n \ln(0.32)
\]
\[
n = \frac{\ln(0.03)}{\ln(0.32)} \approx 3.44.
\]
Rounding up, we get \( n = 4 \). Thus, the number of components in the system is (B) 4.
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