Repairable System Availability Calculator

Purpose and model boundary

This model evaluates an initially operational two-state repairable system with constant failure and repair rates. It reports transient, interval-average, and steady-state inherent availability plus maintainability and no-failure reliability. It does not model operational availability, maintenance logistics, queues, spares, or preventive maintenance.

Inputs and units

The user may enter mean times (MTBF, MTTR) or rates (λ, μ) in a consistent unit. Analysis horizon T and repair target time t_r are always active. In mean-time mode the workbook converts λ = 1/MTBF and μ = 1/MTTR; rate mode applies the reciprocals for displayed effective mean times.

Governing relationships

A_ss = μ / (λ + μ)

For an initially up system:

A(T) = A_ss + [λ/(λ+μ)] exp[-(λ+μ)T]

The interval-average availability is:

A_avg(T) = A_ss + [λ/(λ+μ)] × { [1-exp(-(λ+μ)T)] / [(λ+μ)T] }

The continuous limit at T = 0 is handled explicitly. Further outputs are:

expected downtime = T(1-A_avg)

maintainability(t_r) = 1 - exp(-μ t_r)

time to 90% repair = ln(10)/μ

no-failure reliability = exp(-λT)

Near zero, the maintainability and average-availability exponential terms use stable series expressions. The chart compares point, average, and steady-state availability over time.

Calculation sequence

1. Validate parameter mode, time unit, active positive mean times or rates, and nonnegative horizons.
2. Convert the active parameterization into effective λ, μ, MTBF, and MTTR.
3. Calculate steady-state, point, and interval-average availability.
4. Calculate downtime, maintainability, repair percentile, no-failure reliability, and convergence index z=(λ+μ)T.
5. Evaluate status using the exact convergence rule below.

Outputs and interpretation

Point availability is the probability the system is operational at the selected instant; interval-average availability is its average over the horizon; steady-state availability is the long-run limit. Reliability is the probability of no failure and does not recover after repair, while availability can. MTTR is treated as active corrective repair time, so these outputs are inherent rather than operational availability.

Validation and status logic

This is the exact Validation!B20 precedence. CHECK indicates that the transient point has not approached the steady-state limit by the workbook's review threshold; it does not invalidate the transient calculation.

Assumptions and limitations

• Failure and repair times are exponential with constant rates.
• Every repair restores the modeled aggregate system to the same up state.
• The system starts operational at time zero.
• Preventive maintenance, logistics and administrative delay, repair crews, queues, spares, imperfect repair, and multiple degraded states are excluded.
• The convergence threshold is an interpretation aid, not an industry acceptance limit.

Restrictions and non-computing states

Active mean times or rates must be positive and within the published limits. Analysis and target times must be nonnegative. Hidden-mode values do not participate. T = 0 and t_r = 0 are valid continuous-limit cases.

Errors and warnings

NOT VALID blocks interpretation. CHECK means the valid result is still materially transient relative to steady state. A connection or calculation-service failure is not an availability result.

The mode conversions, stable exponential expressions, named outputs, and z-based status precedence were verified directly against the delivered workbook, its published input rules, tests, and reviewer packet. The workbook identifies these technical sources:

• NASA — Inherent Availability and Reliability with Constant Failure and Repair Rates — Steady-state, point, and interval availability relationships.
• NIST/SEMATECH e-Handbook — HPP constant-rate model — Constant failure-rate repairable-system context.
• NIST/SEMATECH e-Handbook — Exponential distribution — No-failure reliability and exponential repair-time relationships.