1 — The real phenomenon
Two identical units can share power, software, cooling, sensors, spares, contamination or maintenance error. A common cause can therefore defeat several channels simultaneously. Technology diversity can reduce some risks but adds interfaces, training and different spare inventories.
The guiding question is: When does apparent redundancy disappear exactly when it is needed? Reasoning starts with the physical or operational function before introducing the mathematical relationship. The goal is not to accumulate terminology, but to know which quantity changes, why it changes and what becomes hazardous when it leaves its domain. For “Redundancy and common causes: two machines do not always make two backups”, the first task here is therefore to identify the mechanism specific to this subject before searching for an equation or reference value.
2 — Vocabulary and problem boundary
In “Redundancy and common causes: two machines do not always make two backups”, distinguish the phenomenon, available measurement, any command, the margin and the success criterion. The calculation boundary states what is included and excluded; without that boundary, a percentage, mass or time may be mathematically correct but wrong as an engineering conclusion. For “Redundancy and common causes: two machines do not always make two backups”, the chosen boundary also states what would otherwise be double-counted or omitted from a mission budget.
- Primary observable
- failure rate, operating hours, margins, cycles, temperature, leaks, repair time and availability
- Characteristic failure
- common cause, slow drift, uncovered fatigue, consumed margin or a repair introducing a new defect
- Expected evidence
- duration tests, reasoned accelerated cycling, FMEA/FMECA, injected faults and configuration tracking
3 — Course-specific system view
This lesson does not reuse one generic picture for every subject. The system view follows cause → measured quantity → decision or physical response → limit for “Redundancy and common causes: two machines do not always make two backups”. The English text remains fully equivalent while large translated illustrations are intentionally deferred until their dedicated artwork is supplied. For “Redundancy and common causes: two machines do not always make two backups”, the system view must expose inputs, outputs, measured quantity and the consequence of drift without relying on a generic module diagram.
4 — Mathematical relationship and reading the symbols
Read aloud : simultaneous-loss probability depends on the intersection of events A and B; it cannot be found by simple multiplication when events are dependent.
Before substituting numbers, write the unit of every term, state whether the relationship is a physical law, approximation or project indicator, and check dimensional consistency. This is especially important here because “Redundancy and common causes: two machines do not always make two backups” combines quantities that do not all have the same evidence status. For “Redundancy and common causes: two machines do not always make two backups”, this relationship is chosen because of the phenomenon under study; a different dominant quantity would require a different equation or model.
5 — Worked calculations and interpretation
1. 1. Ideal independence
0.02 × 0.02 = 0.0004 = 0.04%
2. 2. Teaching common cause
if 0.5% of cases defeat both, that common cause dominates the previous example
3. 3. N+1 capacity
Three 10 kW units for 20 kW required → one single failure tolerated
6 — What the formula does not contain
The relationship “P_perte = P(A∩B)” does not by itself contain all of “Redundancy and common causes: two machines do not always make two backups”. It does not automatically tell us whether a sensor is valid, a structure is aging, a resource is accessible, a command arrives in time or a secondary failure removes margin. The example 0.02 × 0.02 = 0.0004 = 0.04% therefore remains a local calculation rather than a complete architecture.
To make the model useful, explicitly add the quantities that dominate this subject: failure rate, operating hours, margins, cycles, temperature, leaks, repair time and availability. We can then ask which variation truly changes the result, which is negligible and which forces an architectural change. For “Redundancy and common causes: two machines do not always make two backups”, this model limitation states exactly what a correct calculation still cannot establish about the real system.
7 — Instrumentation, observability and data quality
For “Redundancy and common causes: two machines do not always make two backups”, observability relies on failure rate, operating hours, margins, cycles, temperature, leaks, repair time and availability. Each datum has a unit, acquisition rate, uncertainty, timestamp and validity domain. A value arriving without context can be more dangerous than no measurement because it creates unjustified confidence.
Consistency is checked with at least one independent piece of information when the function is critical. A trend, physical balance or second measurement principle helps distinguish a real system change from a drifting sensor. For “Redundancy and common causes: two machines do not always make two backups”, the selected instrumentation must distinguish a real physical change from sensor drift or a bad state estimate.
8 — Phenomenon-specific failures and recovery
The reference failure is not a vague “broken component.” For “Redundancy and common causes: two machines do not always make two backups”, test in particular common cause, slow drift, uncovered fatigue, consumed margin or a repair introducing a new defect. Diagnosis asks which symptoms appear first, which are only consequences and which action preserves the most options.
The degraded mode must be defined before failure: minimum function, allowable duration, consumed stock, crew action, abort condition and return-to-nominal criterion. That sequence is topic-specific and cannot be replaced by one universal paragraph about redundancy. For “Redundancy and common causes: two machines do not always make two backups”, the degraded mode is defined around the minimum function specific to this subject, with an abort threshold and a return-to-nominal condition.
9 — NASA / reference case
NASA material is used as an evidence dossier: requirements, reliability, maintainability, testing and configuration. The lesson never turns a generic failure rate into a universal truth; it shows how evidence is bounded to defined hardware, environment and duration.
The case is used only within what it actually demonstrates. Flight measurement, human-system standard, component test and architecture study are different kinds of evidence; the text therefore states what is observed, calculated, simulated or still prospective. For “Redundancy and common causes: two machines do not always make two backups”, the cited NASA case is used as targeted evidence for this phenomenon and is never turned into one universal Mars architecture.
10 — Architecture trade
A good solution for “Redundancy and common causes: two machines do not always make two backups” does not maximize one metric. Compare nominal performance, mass, energy, simplicity, maintenance, crew time, common dependencies and recoverability. An option that improves if 0.5% of cases defeat both, that common cause dominates the previous example can still be rejected if it makes failure detection or repair much harder.
The trade is recorded together with its assumptions. If environment data, mass or mission cadence changes, we know which conclusions must be recomputed instead of silently preserving an obsolete choice. For “Redundancy and common causes: two machines do not always make two backups”, the trade is evaluated against the interfaces actually touched by this subject rather than a generic list of desirable qualities.
11 — Demonstration, testing and success criteria
The evidence strategy for “Redundancy and common causes: two machines do not always make two backups” combines duration tests, reasoned accelerated cycling, FMEA/FMECA, injected faults and configuration tracking. Every test records exact hardware, software, configuration, environment, tolerances and success criterion. A successful demonstration outside the mission domain does not replace qualification inside it.
Evidence grows by levels: analytical relationship, simulation, component, subsystem, integrated system, duration and failure. This hierarchy prevents one spectacular test from being presented as validation of the whole mission. For “Redundancy and common causes: two machines do not always make two backups”, demonstration must reproduce the constraints that make this phenomenon difficult; a spectacular test outside the mission domain is insufficient.
12 — Decision exercise
Situation: revisit “Redundancy and common causes: two machines do not always make two backups” with a 20% increase in the most penalizing quantity from the first worked example while one measurement or backup path is unavailable.
13 — What to retain without over-generalizing
- Redundancy and common causes: two machines do not always make two backups has its own observables and failure modes.
- The relationship P_perte = P(A∩B) remains attached to its units and boundary.
- NASA evidence is cited at the phenomenon level instead of reusing one reference bundle for an entire module.
14 — Topic-specific primary sources
These references directly document the phenomenon, technology or human constraint addressed in this lesson. They do not by themselves define an official Mars architecture. For “Redundancy and common causes: two machines do not always make two backups”, the bibliography is deliberately targeted to this page so that readers can trace each claim back to the relevant primary document.