| Scenario | Critical Load (kW) | Unit Capacity (kW) | Utilization (%) | Architecture | MTBF (h) | MTTR (h) | Beta (β) | Target (%) |
|---|---|---|---|---|---|---|---|---|
| Edge site power train | 80 | 40 | 80 | N+1 | 75000 | 6 | 0.03 | 99.90 |
| Control system modules | 35 | 20 | 70 | N+2 | 120000 | 4 | 0.02 | 99.95 |
| High-availability plant | 200 | 60 | 85 | 2N+1 | 150000 | 3 | 0.01 | 99.99 |
- Effective unit capacity: Ceff = Crated × (Utilization% / 100)
- Active units required: N = ceil(CriticalLoad / Ceff)
- Total units planned: T = N + X (or per chosen architecture such as 2N)
- Unit availability: Aunit = MTBF / (MTBF + MTTR)
- System availability (k-out-of-n): Asys = Σk=N..T C(T,k) Aunitk(1-Aunit)T-k
- Common-cause adjustment (beta): U = (1-Asys) + β(1-Aunit), then A = 1 - U
- Expected downtime: Downtime = (1 - A) × 8760 hours/year
- Lifecycle cost (NPV): LCC = Capex + Σ O&M / (1+r)t
- Enter your critical load and unit capacity.
- Set design utilization to reflect derating and loading policy.
- Select an architecture (N+1, 2N, N+N, or Custom N+X).
- Provide MTBF, MTTR, and a reasonable beta value.
- Add cost assumptions to estimate capex and lifecycle cost.
- Press Calculate to view results above the form.
- Use Download CSV or Download PDF to share outputs.
Capacity Sizing and Utilization Policy
Start by converting rated module capacity to usable capacity through the utilization limit. At 80% utilization, a 50 kW unit contributes 40 kW of protected capacity. The calculator sets N = ceil(CriticalLoad / Ceff), ensuring the design can carry the load even before adding spares. Keep at least 10–20% headroom when step loads, harmonics, or ambient derating are expected.
Availability Modeling With k-out-of-n
Unit availability is modeled as MTBF/(MTBF+MTTR). For MTBF 100,000 h and MTTR 4 h, Aunit is about 99.996%. System availability rises as T increases because any N units can satisfy the load. The k‑out‑of‑n sum captures this behavior across N..T operating combinations. This approach assumes comparable unit performance under the selected utilization policy. Use this view to compare N+1 versus N+2 rather than relying on a single redundancy label.
Common-Cause Risk and Beta Selection
Independence is optimistic when units share rooms, firmware, cooling loops, or operators. The beta factor adds a small shared unavailability term: Uadj = Uind + βUunit. In practice, β often falls between 0.01 and 0.05 for well-isolated paths, and can exceed 0.10 when dependencies are strong. Use β as a sensitivity knob by running low, medium, and high cases to bound the plan. Reducing β through segregation, diverse suppliers, or procedural controls can outperform adding hardware.
Cost and Lifecycle Trade-Offs
Capital cost scales with total units, while O&M repeats annually. The lifecycle cost uses discounted cash flow so a 6% rate values near-term costs more than distant ones. When comparing architectures, look at cost per protected kW rather than total spend; it normalizes the design to the critical load. If the target is missed, the tool also estimates the minimal N+X spares (up to ten) to reach the availability threshold. Include major replacements in O&M if your asset strategy requires periodic inverter, fan, or battery refreshes.
Interpreting Results for Design Decisions
Translate availability into downtime to communicate risk. 99.9% implies roughly 8.76 hours per year, while 99.99% is about 0.88 hours. Pair downtime with capacity headroom and redundancy factor (T/N) to avoid overbuilding. A common practice is to validate promising designs with fault-tree analysis once the architecture is selected. Use scenario runs with realistic MTTR and beta values, then export CSV or PDF to document assumptions for reviews and procurement planning.
What does the value N represent in the results?
N is the minimum number of active units required to carry the critical load at the chosen utilization level. Redundancy adds extra units beyond N so the load can still be supported during failures or maintenance.
How do I choose a realistic utilization percentage?
Use the maximum continuous loading you are willing to allow per unit, after derating for temperature, altitude, harmonics, and aging. Many power and controls designs start at 70–85% to preserve transient margin.
What is the common-cause beta factor?
Beta approximates the share of unit unavailability that can affect multiple units at once due to shared dependencies. Start with 0.01–0.05 for well-separated paths, then test higher values to see sensitivity.
Why can a 2N design still miss my availability target?
If MTTR is long or beta is high, shared events and repairs dominate the outage risk. Improving repair logistics, spares, monitoring, or physical segregation can increase availability more effectively than adding capacity.
What does the suggested minimal N+X spares mean?
When the current plan is below target, the tool checks additional spares up to X=10 and reports the smallest X that meets the availability threshold. Treat it as a planning hint, not a final specification.
Can I use these results for final compliance documentation?
Use the outputs for early sizing and trade studies. For compliance, validate assumptions with vendor reliability data and apply fault-tree, Markov, or simulation models that match your operational procedures and failure modes.