Self-Assessment Quiz: Reliability, Testing, and Why Rockets Fail

Twenty questions to check your grasp of reliability math, redundancy, FMEA, the test campaign, and the lessons of real failures. Answer each before opening the key. Aim for 16 or more.

Question 1

Reliability is best defined as:

A) the average lifetime of a component B) the probability a system performs its function, under stated conditions, for a stated duration C) the number of redundant units in a system D) a synonym for "high quality"

Question 2

For independent components in series (all required to work), the system reliability is:

A) the sum of the individual reliabilities B) the reliability of the weakest component C) the product of the individual reliabilities D) the average of the individual reliabilities

Question 3

For $n$ identical independent units in active (parallel) redundancy, the system reliability is:

A) $R^n$ B) $1 - (1-R)^n$ C) $nR$ D) $R/n$

Question 4

A series system's reliability is always:

A) higher than its most reliable component B) equal to the average of its components C) lower than its least reliable component D) exactly 1 if every component exceeds 0.9

Question 5

A single point of failure is:

A) a component that fails only once B) any element whose failure alone causes loss of the mission C) a redundant backup unit D) the first failure detected in a test

Question 6

Two "redundant" flight computers running identical software are vulnerable to a:

A) wear-out failure B) common-cause failure C) infant-mortality failure D) random independent failure

Question 7

An FMEA is a __ analysis, while a fault tree is a ____ analysis:

A) top-down; bottom-up B) bottom-up; top-down C) statistical; deterministic D) hardware-only; software-only

Question 8

The difference between qualification and acceptance testing is:

A) qualification tests each flight unit; acceptance tests a spare B) qualification over-stresses a design to prove margin; acceptance screens each flight unit at flight levels C) they are two names for the same test D) acceptance is done in flight; qualification on the ground

Question 9

"Test like you fly" means:

A) fly the vehicle before testing it B) test only the parts that are cheapest to test C) reproduce the flight hardware, software, interfaces, sequence, and environment as closely as possible D) test each component in isolation, never as a system

Question 10

Root-cause analysis is distinguished from noting the proximate cause because it:

A) is faster and cheaper B) traces the failure to the underlying (often organizational) cause so the real defect is fixed C) only considers hardware, never process D) assigns blame to an individual

Question 11

In the exponential reliability model $R(t) = e^{-\lambda t}$, the MTBF equals:

A) $\lambda t$ B) $1/\lambda$ C) $e^{-\lambda}$ D) $\lambda^2$

Question 12

Given a fixed budget for one redundant unit, you gain the most system reliability by backing up:

A) the most reliable component B) the heaviest component C) the weakest (least reliable) component D) it makes no difference which

Question 13

The "bathtub curve" describes:

A) the shape of a rocket nozzle B) a failure rate that is high early (infant mortality), low in useful life, and rising at wear-out C) the cost of a mission over time D) the reliability gain from adding redundancy

Question 14

The root cause of the Ariane 5 Flight 501 loss (1996) was:

A) an engine explosion B) a reused-software assumption (small horizontal velocity) never re-validated for the new vehicle C) a lightning strike D) a fuel leak

Question 15

The Mars Climate Orbiter (1999) was lost because of:

A) a units mismatch at an unmanaged software interface (pound-force vs. newton-seconds) B) a heat-shield failure C) a solar-array deployment failure D) running out of propellant

Question 16

The Soviet N-1's repeated failures are most associated with which reliability lesson?

A) too much redundancy B) the integrated first stage (30 engines) was never static-fired as a unit before flight C) overly conservative testing D) using hydrogen instead of kerosene

Question 17 (True/False, justify)

"Ten thousand components in series, each 99.99% reliable, give a very reliable system." True or false? Justify with the approximate system reliability.

Question 18 (True/False, justify)

"Adding a redundant unit always improves reliability, regardless of how the two units are connected or powered." True or false? Explain in one sentence.

Question 19 (Short answer)

Three functions are in series with reliabilities $0.99$, $0.97$, and $0.98$. Compute the system reliability (show the product) and the probability of mission loss.

Question 20 (Short answer)

Explain in one or two sentences why "you cannot test reliability into a design at the end," and what testing actually does for reliability.

Answer Key

Q Ans Note
1 B Reliability is a probability tied to function, conditions, and duration.
2 C Series → reliabilities multiply, $R = \prod R_i$.
3 B Parallel fails only if all fail: $R = 1-(1-R)^n$.
4 C Multiplying by numbers $\le 1$ drags the product below the weakest link.
5 B A no-backup element whose failure alone loses the mission.
6 B Identical software fails identically on the same input — a common-cause failure.
7 B FMEA is bottom-up (parts → effects); fault trees are top-down (event → causes).
8 B Qual proves the design has margin (over-stress); acceptance screens each unit for workmanship.
9 C Reproduce flight config, sequence, and environment; gaps hide failures.
10 B Fix the root (technical and organizational), not just the symptom.
11 B MTBF $= 1/\lambda$ in the constant-hazard model.
12 C Redundancy pays most on the weakest link; doubling a strong link barely moves the product.
13 B High infant mortality, flat useful life, rising wear-out.
14 B A 64→16-bit overflow from reused Ariane-4 code, unneeded and un-revalidated on Ariane 5.
15 A A units interface error (lbf·s vs. N·s) accumulated over cruise; a systems/interface failure.
16 B Cost/schedule ruled out static-firing the assembled stage — "test like you fly" violated.
17 False $0.9999^{10{,}000} = e^{-1} \approx 0.37$ — it fails almost two flights in three.
18 False Only if the units are independent; a shared cause (software, power, environment) defeats it.
19 — $0.99 \times 0.97 \times 0.98 = 0.9411$; mission-loss probability $= 1 - 0.9411 = 0.0589 \approx 5.9\%$.
20 — Reliability is designed in (simplicity, margin, redundancy, derating); testing verifies it and reveals defects to fix, but cannot add reliability that the design lacks.

Topics to review by question

Questions Topic Section
1, 11, 13 Reliability as a probability; exponential model; bathtub curve §32.1
2, 3, 4, 12, 17, 19 Series and redundancy math §32.2
5, 6, 18 Single point of failure; common-cause §32.2
7 FMEA vs. fault tree §32.3
8, 9, 16 Qualification/acceptance; "test like you fly" §32.4
10, 14, 15 Root-cause analysis; case studies §32.5
20 You cannot test reliability in §32.4