Infrastructure Engineering · Lesson 14 of 24 · 25 minutes

Test capacity, paths and common dependencies

The existing lessons show how a surviving path or shared controller can govern electrical service. Now extend that intuition into a state matrix. Installed equipment, connected equipment and independently substitutable equipment are different sets. A spare counts only when it can reach the required load in the state being assessed.

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Learning objectives

Calculate available capacity after specified losses.
Distinguish a bank screen from a connectivity proof.
Explain how common dependence changes an ideal availability model.

Editorial derivation

Capacity belongs to an operating state

For each normal, maintenance, failure and restoration state, sum the ratings of the equipment that remains connected and usable after site derating and any imposed loading ceiling. A bus, breaker, cable or interlock can restrict the route even when the bank total is adequate. The simple N+1 count is ceil(required demand / usable unit rating) + 1; this is a capacity screen, not a complete classification.

Illustrative assumption

Count the usable units

The review exercise uses 9 MW required demand, 2 MW units, a 0.9 derating and a 0.9 loading limit. Each usable unit contributes 1.62 MW. Seven installed units leave six after one loss, giving 9.72 MW and a 0.72 MW arithmetic margin. Six installed units would leave only 8.1 MW. The scene must not show a spare behind an isolated bus as available to the load.

Editorial derivation

Interrogate independence

For the declared stationary two-state model, availability equals MTBF divided by MTBF plus MTTR. Two conditionally independent substitutable paths have unavailability qA × qB while the shared dependency is healthy. Including shared unavailability q0 gives total availability (1−q0)(1−qAqB). With the manuscript’s illustrative path and common-dependency values, expected unavailable time is about 52.56 minutes per 8,760-hour year. That is neither an outage-duration guarantee nor Tier certification.

Predict → run → explain

Read the declared boundary and units. Predict the selected result before calculating.
Run the starting case and inspect the ledger, assumptions and model limits.
Apply the challenge, run again, and explain the difference. Export only the last completed inputs and results.

Usable unit MW = unit MW × derating × loading; available MW = (installed − unavailable) × usable unit MW; elementary N+1 count = ceil(required MW / usable unit MW) + 1.

Declared starting inputs

{
  "requiredMW": 9,
  "unitMW": 2,
  "derating": 0.9,
  "loading": 0.9,
  "installed": 7,
  "unavailable": 1
}

Worked default — unrounded educational outputs
Quantity	Value	Unit
usableUnitMW	1.62	MW/unit
availableMW	9.72	MW
marginMW	0.7200000000000006	MW
minimumNPlusOne	7	units
status	screen-satisfied	screen state

Challenge

Does one spare still leave enough usable capacity?

{
  "installed": 6
}

Five usable units remain: 8.1 MW, a 0.9 MW shortfall. The minimum elementary N+1 count is seven.

Worked challenge
Quantity	Value	Unit
usableUnitMW	1.62	MW/unit
availableMW	8.100000000000001	MW
marginMW	-0.8999999999999986	MW
minimumNPlusOne	7	units
status	screen-failed	screen state

A/B paths with visible common cause — static equivalent

Expose physically separate A and B corridors.
Remove one unit and recalculate connected capacity.
Highlight a shared control/fuel/cooling dependency using a distinct dependency edge.
Compare state rows without converting them into a certification badge.

State-by-state capacity and dependency table; each failed route also carries a text label.

Choose normal, maintenance, one-failure and restoration states; inspect why a component is excluded.

Narrative steps are not physical seconds. Essential states and quantities remain available without animation.

Assessment and answer criteria

2.1 · Size an N+1 bank for 9 MW with 2 MW units and both factors equal to 0.9.

Read answer and marking criterion

Seven installed; six remaining provide 9.72 MW.

Criterion: Use both factors once and round up before adding the spare.

Source: DCIE-R1 Appendix A, PDF pp.59-61

2.2 · Explain the common-dependency availability expression.

Read answer and marking criterion

Condition service on the shared dependency being healthy, then multiply by the conditional parallel-path availability.

Criterion: State conditional independence rather than silently assuming all failures are independent.

Source: DCIE-R1 Appendix A, PDF pp.59-61

2.3 · Why are two utility cables in one duct not universally independent?

Read answer and marking criterion

The duct remains one shared failure domain for an excavation event.

Criterion: Tie independence to the initiating event and route evidence.

Source: DCIE-R1 Appendix A, PDF pp.59-61

Source and model boundaries

Data Centre Infrastructure Engineering, reference manuscript revision 1 (DCIE-R1), 11 October 2026, chapter 2, PDF pp.14–17. PDF page 1 includes the cover. manuscript-derived; not independent source verification.

No probability estimate from the original deterministic simulator is implied.
Use Uptime Tier and TIA Rated terminology separately; no certification is awarded.

Original educational adaptation. The private PDF and missing archive are not public downloads. Source statement, Editorial derivation, Illustrative assumption and Unresolved remain distinct.

Result schema: infrastructure-screen-1; content 2.0.0; model 1.0.0. Raw inputs, outputs, units, assumptions, source locators and canonical hashes. No supported in-browser Python verification protocol exists for this result family.