ITPEC FE Morning April 2019 Question 15

System Availability (Series-Parallel) — calculate availability for a series-parallel configuration.

Given 4 devices each with availability R, arranged as two parallel pairs in series:

• •Step 1: Each parallel pair: 1 - (1-R)²
• •Step 2: Two pairs in series: multiply them
• •Result: (1 - (1-R)²)²

Why not others:
- (b) (1 - (1-R²))² — uses R² (series availability) inside the parallel formula, mixing up the formulas
- (c) 1 - (1-R)⁴ — treats all 4 devices as one parallel group, ignoring the series connection
- (d) 1 - (1-R²)² — same error as (b), applies series formula where parallel is needed

Key rule:
- Parallel: 1 - (1-A)(1-B) (either works → higher availability)
- Series: A × B (both must work → lower availability)
- Solve inside-out: resolve parallel groups first, then combine in series.

AI-generated — may contain errors