System Reliability Block Calculator

Purpose and model boundary

This model calculates independent-component mission reliability for a heterogeneous series grid, a heterogeneous parallel grid, or an identical-component K-out-of-N architecture. It evaluates mission reliabilities entered by the user; it does not convert failure rates or MTBF, model repair or standby logic, or account for dependence.

Inputs and units

Series and parallel modes use active grid rows containing a component label and mission reliability p_i between zero and one. K-out-of-N mode instead uses common component reliability p, integer total count N, and integer required successes K with 1 ≤ K ≤ N ≤ 100.

Governing relationships

For independent series components:

R_series = product(p_i)

For independent active parallel components:

R_parallel = 1 - product(1-p_i)

For identical independent K-out-of-N components:

R_K/N = sum from j=K to N of C(N,j) p^j (1-p)^(N-j)

failure probability = 1 - system reliability

The workbook also calculates failure tolerance N-K, the probability that exactly K components succeed, and redundancy benefit relative to requiring every modeled component. The chart applies the selected architecture to equal component-reliability values as a sensitivity benchmark; it does not reproduce a heterogeneous grid.

Calculation sequence

1. Validate the architecture and only its active grid or identical-component inputs.
2. In grid mode, require at least one complete row and validate all 12 rows as either complete or empty.
3. Calculate the selected series product, parallel complement product, or exact binomial tail.
4. Calculate supporting counts, failure tolerance, weakest active component, exact-K probability, and redundancy benefit where applicable.
5. Evaluate duplicate component labels only after the active grid is otherwise valid.

Outputs and interpretation

System reliability is a mission success probability under the selected logical architecture. Parallel and K-out-of-N improvements can be optimistic when failures share causes or loads. Component labels identify rows but do not bring any reliability data into the model.

Validation and status logic

This is the exact Validation!B20 precedence. A duplicate-name check never overrides an invalid grid. Invalid states return protected zero outputs and NOT AVAILABLE architecture text.

Assumptions and limitations

• Every component reliability refers to the same mission duration and environment.
• Component success/failure outcomes are statistically independent.
• K-out-of-N mode uses identical active components.
• Common-cause failure, dependency, load sharing, repair, standby switching, imperfect coverage, degraded success criteria, and sequence logic are outside scope.
• No failure-rate database or architecture optimization is included.

Restrictions and non-computing states

Grid reliability cells must lie from zero through one. Each active row must include both its label and reliability; unused capacity rows must be empty. K and N must be integers with 1 ≤ K ≤ N ≤ 100. Inputs for inactive architectures are ignored.

Errors and warnings

NOT VALID blocks interpretation. CHECK warns that duplicate labels may make the modeled architecture ambiguous even though the arithmetic remains available. A connection or calculation-service failure is not a system-reliability finding.

The grid activation rules, series/parallel products, binomial sum, named outputs, and status precedence were verified directly against the delivered workbook, its published input rules, tests, and reviewer packet. The workbook identifies these technical sources:

• NIST/SEMATECH e-Handbook — Series model — Independent series-system reliability.
• NIST/SEMATECH e-Handbook — Parallel model — Independent parallel-system reliability.
• NIST/SEMATECH e-Handbook — R-out-of-N model — Identical independent K-out-of-N reliability.